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[(netw)12(orks—trained)-265(to)-289.1(predict)-289.1(stock)-289.1(mark)12(et)-277(data—can)-277(gen-)]TJ
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[(erate)-277(counterintuiti)24.1(v)12(e)-240.9(results,)-289.1(reminiscent)-265(of)-277(so-called)]TJ
/TT4 1 Tf
21.8321 0 TD
(vot-)Tj
-21.8321 -1.2045 TD
[(ing)-409.5(par)12(adoxes)]TJ
/TT2 1 Tf
6.2268 0 TD
[(in)-421.6(the)-409.5(social)-421.6(choice)-397.5(literature.)-807(Section)-397.5(8)]TJ
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[(summarizes)-228.9(and)-240.9(discusses)-252.9(future)-228.9(w)12(ork.)]TJ
/TT6 1 Tf
11.9552 0 0 11.9552 55.44 580.7401 Tm
[(2.)-250.9(Ensemble)-261(Lear)10(ning)]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 561.3 Tm
[(W)84.3(e)-433.6(present)-397.5(a)-421.6(v)12(ery)-397.5(brief)-409.5(o)12(v)12(ervie)24.1(w)-385.4(o)0(f)-409.5(ensemble)-409.5(learning;)]TJ
T*
[(see)-349.3(\(Dietterich,)-349.3(1997\))-325.2(for)-325.2(an)-349.3(e)12(xcellent)-325.2(surv)12(e)12(y)60.2(.)-566.1(Represen-)]TJ
0 -1.2045 TD
[(tati)24.1(v)12(e)-277(algorithms)-265(include)-277(bagging)-252.9(\(Breiman,)-277(1996\),)-265(boost-)]TJ
T*
[(ing)-313.2(\(e.g.,)-361.4(A)]TJ
7.9701 0 0 7.9701 102.7581 525.42 Tm
0.0151 Tc
(DA)Tj
9.9626 0 0 9.9626 114.8696 525.42 Tm
0 Tc
(B)Tj
7.9701 0 0 7.9701 121.9946 525.42 Tm
0.0602 Tc
(OOST)Tj
9.9626 0 0 9.9626 147.8472 525.42 Tm
0 Tc
[(\(Freund)-301.1(&)-325.2(Schapire,)-325.2(1999\)\),)-313.2(and)-313.2(a)]TJ
-9.2754 -1.1925 TD
[(method)-289.1(based)-313.2(on)-301.1(Error)24.1(-Correcting)-277(Output)-289.1(Codes)-313.2(\(ECOC\))]TJ
0 -1.2045 TD
[(\(Dietterich)-325.2(&)-325.2(Bakiri,)-361.3(1995\).)-542(Ensemble)-313.2(algorithms)-325.2(gener)24.1(-)]TJ
T*
[(ally)-289.1(proceed)-277(in)-289.1(tw)12(o)-301.1(phases:)-397.5(\(1\))-289.1(generate)-277(and)-277(train)-289.1(a)-301.1(set)-301.1(of)]TJ
0 -1.1925 TD
[(weak)-240.9(learners,)-228.9(and)-240.9(\(2\))-228.9(aggre)12(gate)-216.8(their)-240.9(classi)]TJ
/TT7 1 Tf
17.4599 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(cations.)Tj
-18.016 -1.8068 TD
(The)Tj
/TT7 1 Tf
1.8919 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(rst)-349.3(step)-349.3(is)-349.3(to)-337.3(construct)-325.2(component)-313.2(learners)-337.3(of)-337.3(suf)]TJ
/TT7 1 Tf
20.0583 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(-)Tj
-23.0625 -1.1925 TD
[(cient)-313.2(di)24.1(v)12(ersity)-301.1(\(Hansen)-301.1(&)-325.2(Salamon,)-313.2(1990\).)-493.8(One)-313.2(common)]TJ
0 -1.2045 TD
[(technique)-180.7(is)-216.8(to)-204.8(subsample)-204.8(the)-204.8(training)-180.7(e)12(xamples,)-204.8(either)-192.7(ran-)]TJ
0 -1.1925 TD
[(domly)-325.2(with)-337.3(replacement)-313.2(\(Breiman,)-349.3(1996\),)-337.3(by)-337.3(lea)24.1(ving)-325.2(out)]TJ
0 -1.2045 TD
[(random)-313.2(subsets)-325.2(\(as)-337.3(in)-337.3(cross-v)24.1(alidation\),)-313.2(or)-325.2(by)-325.2(an)-325.2(induced)]TJ
T*
[(distrib)24.1(ution)-204.8(meant)-204.8(to)-216.8(magnify)-192.7(the)-216.8(ef)24.1(fect)-216.8(of)-204.8(dif)]TJ
/TT7 1 Tf
17.9911 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cult)-216.8(training)]TJ
-18.5473 -1.1925 TD
[(e)12(xamples)-313.2(\(Freund)-313.2(&)-337.3(Schapire,)-337.3(1999\).)-542(Another)-313.2(technique)]TJ
0 -1.2045 TD
[(bases)-277(each)-277(learner’)60.2(s)-265(predictions)-252.9(on)-265(dif)24.1(ferent)-252.9(input)-265(features)]TJ
T*
[(\(T)48.2(umer)-277(&)-289.1(Ghosh,)-289.1(1996\).)-409.5(The)-289.1(method)-265(of)-289.1(Error)24.1(-Correcting)]TJ
0 -1.1925 TD
[(Output)-216.8(Codes)-228.9(\(ECOC\))-228.9(generates)-204.8(classi)]TJ
/TT7 1 Tf
15.4872 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ers)-240.9(by)-216.8(ha)24.1(ving)-216.8(each)]TJ
-16.0433 -1.2045 TD
[(learn)-313.2(whether)-313.2(an)-325.2(e)12(xample)-301.1(f)12(alls)-325.2(within)-325.2(a)-325.2(randomly)-289.1(chosen)]TJ
T*
[(subset)-204.8(of)-204.8(the)-204.8(classes.)-301.1(Another)-192.7(approach)-180.7(injects)-204.8(randomness)]TJ
0 -1.1925 TD
[(into)-325.2(the)-337.3(training)-313.2(algorithms)-313.2(themselv)12(es.)-554.1(These)-325.2(four)-313.2(tech-)]TJ
0 -1.2045 TD
[(niques)-385.4(apply)-373.4(to)-397.5(arbitrary)-361.4(classi)]TJ
/TT7 1 Tf
12.7921 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(er)-409.5(algorithms—there)-361.3(are)]TJ
-13.3482 -1.1925 TD
[(also)-216.8(man)12(y)-204.8(algorithm-speci)]TJ
/TT7 1 Tf
10.5179 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(c)-180.7(techniques.)-277(And,)-216.8(of)-204.8(course,)-216.8(it)]TJ
-11.0741 -1.2045 TD
[(is)-301.1(possible)-289.1(to)-289.1(create)-277(an)-289.1(ensemble)-277(by)-289.1(mixing)-277(and)-277(matching)]TJ
T*
[(dif)24.1(ferent)-228.9(techniques)-216.8(for)-240.9(dif)24.1(ferent)-216.8(classi)]TJ
/TT7 1 Tf
15.404 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(ers.)Tj
-15.9602 -1.7947 TD
[(After)-373.4(generating)-349.3(and)-373.4(training)-349.3(a)-385.4(set)-385.4(of)-373.4(weak)-373.4(learners,)-397.5(the)]TJ
0 -1.2045 TD
[(ensemble)-252.9(algorithm)-240.9(combines)-252.9(the)-265(indi)24.1(vidual)-240.9(learners’)-252.9(pre-)]TJ
0 -1.1925 TD
[(dictions)-313.2(into)-325.2(a)-325.2(composite)-313.2(prediction.)-505.9(The)-325.2(choice)-313.2(of)-313.2(com-)]TJ
0 -1.2045 TD
[(bination)-240.9(method)-228.9(is)-265(the)-252.9(focus)-240.9(of)-252.9(this)-252.9(paper)60.2(.)-325.2(Common)-228.9(meth-)]TJ
T*
[(ods)-325.2(can)-325.2(be)-325.2(cate)12(gorized)-301.1(loosely)-325.2(into)-313.2(tw)12(o)-337.3(cate)12(gories:)-457.7(those)]TJ
0 -1.1925 TD
[(that)-493.8(combine)]TJ
/TT4 1 Tf
5.9065 0 TD
(votes)Tj
/TT2 1 Tf
2.0547 0 TD
[(,)-542(and)-481.8(those)-481.8(that)-493.8(can)-481.8(combine)-469.8(con)]TJ
/TT7 1 Tf
14.5301 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(-)Tj
-23.0474 -1.2045 TD
[(dence)-240.9(scores.)-325.2(The)-252.9(former)-228.9(type)-240.9(includes)-240.9(plurality)-240.9(v)24.1(ote)]TJ
6.9738 0 0 6.9738 268.56 182.34 Tm
(1)Tj
9.9626 0 0 9.9626 275.04 178.74 Tm
(and)Tj
-22.0423 -1.1925 TD
[(weighted)-228.9(plurality;)-228.9(the)-240.9(latter)-240.9(includes)-240.9(stacking,)-228.9(serial)-240.9(com-)]TJ
0 -1.2045 TD
[(bination,)-289.1(weighted)-289.1(a)24.1(v)12(erage,)-301.1(and)-289.1(weighted)-289.1(geometric)-277(a)24.1(v)12(er)24.1(-)]TJ
T*
(age.)Tj
0 -1.7947 TD
[(Bagging)-361.3(and)-373.4(ECOC)-385.4(are)-373.4(e)12(xamples)-361.4(of)-373.4(algorithms)-361.3(that)-373.4(use)]TJ
ET
q
57.72 0 0 -0.48 55.428 119.088 cm
/Im1 Do
Q
BT
5.9776 0 0 5.9776 68.04 111.9 Tm
(1)Tj
8.9664 0 0 8.9664 71.52 108.06 Tm
[(This)-294.4(is)-294.4(the)-294.4(f)13.4(amiliar)-294.4(“one)-307.8(person,)-307.8(one)-307.8(v)13.4(ote”)-294.4(procedure)-307.8(where)]TJ
-1.7934 -1.1108 TD
[(the)-254.3(candidate)-281(recei)26.8(ving)-267.7(the)-267.7(most)-254.3(v)13.4(otes)-267.7(wins.)-321.2(W)80.3(e)-254.3(reserv)13.4(e)]TJ
/TT4 1 Tf
22.7658 0 TD
(majority)Tj
-22.7658 -1.1108 TD
(vote)Tj
/TT2 1 Tf
1.9198 0 TD
[(to)-254.3(refer)-254.3(to)-240.9(the)-254.3(special)-267.7(case)-254.3(of)-254.3(tw)13.4(o)-254.3(candidates.)]TJ
9.9626 0 0 9.9626 307.44 722.8201 Tm
[(plurality)-277(v)24.1(ote.)-445.7(The)-289.1(ensemble’)60.2(s)-277(chosen)-277(class)-313.2(is)-301.1(simply)-277(that)]TJ
0 -1.1925 TD
[(which)-361.4(is)-373.4(predicted)-349.3(most)-373.4(often)-349.3(by)-361.4(the)-373.4(indi)24.1(vidual)-337.3(learners.)]TJ
0 -1.2045 TD
[(W)84.3(eighted)-469.8(plurality)-457.7(is)-481.8(a)-469.8(generalization)-445.7(of)-469.8(plurality)-457.7(v)24.1(ote,)]TJ
T*
[(where)-337.3(each)-337.3(algorithm’)60.2(s)-337.3(v)24.1(ote)-337.3(is)-349.3(discounted)-325.2(\(or)-337.3(magni)]TJ
/TT7 1 Tf
21.548 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(ed\))Tj
-22.1041 -1.1925 TD
[(by)-252.9(a)-252.9(multiplicati)24.1(v)12(e)-240.9(weight;)-252.9(classes)-277(are)-252.9(then)-240.9(rank)12(ed)-240.9(accord-)]TJ
0 -1.2045 TD
[(ing)-252.9(to)-252.9(the)-252.9(sum)-252.9(of)-240.9(the)-252.9(weighted)-240.9(v)24.1(otes)-252.9(the)12(y)-252.9(recei)24.1(v)12(e)0(.)-313.2(W)84.3(eights)]TJ
T*
[(can)-228.9(be)-240.9(chosen)-228.9(to)-240.9(correspond)-204.8(with)-240.9(the)-228.9(observ)12(ed)-216.8(accurac)12(y)-216.8(o)0(f)]TJ
0 -1.1925 TD
[(the)-228.9(indi)24.1(vidual)-204.8(classi)]TJ
/TT7 1 Tf
7.9081 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ers,)-228.9(using)-216.8(Bayesian)-228.9(techniques,)-204.8(or)-228.9(us-)]TJ
-8.4642 -1.2045 TD
(ing)Tj
/TT4 1 Tf
1.5187 0 TD
[(gating)-228.9(networks)]TJ
/TT2 1 Tf
6.6363 0 TD
[(\(Jordan)-228.9(&)-240.9(Jacobs,)-240.9(1994\),)-216.8(among)-216.8(other)]TJ
-8.155 -1.1925 TD
[(methods.)-337.3(The)-277(A)]TJ
7.9701 0 0 7.9701 372.9743 615.3 Tm
0.0151 Tc
(DA)Tj
9.9626 0 0 9.9626 385.0858 615.3 Tm
0 Tc
(B)Tj
7.9701 0 0 7.9701 392.2108 615.3 Tm
0.0602 Tc
(OOST)Tj
9.9626 0 0 9.9626 417.4634 615.3 Tm
0 Tc
[(algorithm)-240.9(computes)-240.9(weights)-252.9(in)]TJ
-11.0436 -1.2045 TD
[(an)-240.9(attempt)-240.9(to)-240.9(minimize)-240.9(the)-240.9(error)-228.9(of)-240.9(the)]TJ
/TT7 1 Tf
15.632 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(nal)-240.9(classi)]TJ
/TT7 1 Tf
3.6843 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(cation.)Tj
/TT4 1 Tf
-20.4285 -1.8068 TD
[(Stac)24.1(king)]TJ
/TT2 1 Tf
3.6963 0 TD
[(turns)-289.1(the)-289.1(problem)-277(of)]TJ
/TT7 1 Tf
8.5315 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(nding)-277(a)-301.1(good)-277(combination)]TJ
-12.7839 -1.1925 TD
[(function)-433.6(into)-445.7(a)-445.7(learning)-433.6(problem)-433.6(itself)-445.7(\(Breiman,)-493.8(1996;)]TJ
0 -1.2045 TD
[(Lee)-325.2(&)-337.3(Srihari,)-337.3(1995;)-349.3(W)84.3(olpert,)-349.3(1992\):)-445.7(The)-325.2(constituent)-313.2(al-)]TJ
0 -1.1925 TD
[(gorithms’)-361.3(outputs)-385.4(are)-373.4(fed)-385.4(to)-385.4(a)-397.5(meta)-385.4(learner’)60.2(s)-373.4(inputs;)-457.7(the)]TJ
0 -1.2045 TD
[(meta)-349.3(learner’)60.2(s)-349.3(output)-337.3(is)-373.4(tak)12(en)-349.3(as)-361.3(the)-349.3(ensemble)-349.3(classi)]TJ
/TT7 1 Tf
21.6281 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(ca-)Tj
-22.1842 -1.2045 TD
(tion.)Tj
/TT4 1 Tf
2.3356 0 TD
[(Serial)-325.2(combination)]TJ
/TT2 1 Tf
8.0145 0 TD
[(uses)-325.2(one)-313.2(learner’)60.2(s)-313.2(top)]TJ
/T1 1 Tf
0.12 0 0 -0.12 501.7924 525.54 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 510.5524 525.54 Tm
(choices)Tj
-20.3874 -1.1925 TD
[(to)-313.2(reduce)-301.1(the)-313.2(space)-313.2(of)-313.2(candidate)-301.1(classes,)-349.3(passing)-301.1(the)-313.2(sim-)]TJ
0 -1.2045 TD
(pli)Tj
/TT7 1 Tf
1.0557 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ed)-277(problem)-252.9(onto)-265(the)-277(ne)12(xt)-265(learner)36.1(,)-277(etc.)-397.5(\(Madhv)24.1(anath)-240.9(&)]TJ
-1.6118 -1.2045 TD
[(Go)12(vindaraju,)-180.7(1995\).)]TJ
/TT4 1 Tf
8.2652 0 TD
[(W)96.4(eighted)-192.7(alg)12(ebr)12(aic)-192.7(\(or)-204.8(g)12(eometric\))-192.7(av-)]TJ
-8.2652 -1.1925 TD
-0.012 Tc
[(e)-12(rage)]TJ
/TT2 1 Tf
2.4696 0 TD
0 Tc
[(computes)-216.8(the)-240.9(aggre)12(gate)-204.8(con)]TJ
/TT7 1 Tf
11.0347 0 TD
(о)Tj
/TT2 1 Tf
0.5561 0 TD
[(dence)-204.8(in)-240.9(each)-228.9(class)-240.9(as)-240.9(a)]TJ
-14.0604 -1.2045 TD
[(weighted)-192.7(algebraic)-192.7(\(or)-204.8(geometric\))-180.7(a)24.1(v)12(erage)-192.7(of)-204.8(the)-204.8(indi)24.1(vidual)]TJ
0 -1.1925 TD
(con)Tj
/TT7 1 Tf
1.4438 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(dences)-301.1(in)-325.2(that)-313.2(class)-337.3(\(Jacobs,)-325.2(1995;)-349.3(T)84.3(a)0(x)-313.2(e)0(t)-325.2(al.,)-349.3(1997\).)]TJ
-2 -1.2045 TD
[(Some)-277(v)24.1(ariants)-265(of)-277(boosting)-265(emplo)12(y)-265(weighted)-265(a)24.1(v)12(erage)-265(com-)]TJ
T*
[(bination)-228.9(\(Druck)12(er)-216.8(et)-252.9(al.,)-240.9(1993\).)]TJ
/TT6 1 Tf
11.9552 0 0 11.9552 307.44 401.34 Tm
[(3.)-250.9(Notation)]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 307.44 382.02 Tm
(Let)Tj
/T2 1 Tf
0.12 0 0 -0.12 323.7154 382.02 Tm
()Tj
/T3 1 Tf
103.9998 0 TD
()Tj
/T4 1 Tf
96.0002 0 TD
()Tj
/T1 1 Tf
32 0 TD
(
)Tj
/T5 1 Tf
62.3716 12 TD
()Tj
/T1 1 Tf
38 -12 TD
14 Tc
(
)Tj
/T5 1 Tf
99 12 TD
0 Tc
(
)Tj
/T1 1 Tf
37 -12 TD
14 Tc
(
)Tj
/T6 1 Tf
246.9998 12 TD
0 Tc
()Tj
/T4 1 Tf
50 -12 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 422.4 382.02 Tm
[(denote)-289.1(a)-301.1(v)12(ector)-289.1(of)]TJ
/T1 1 Tf
0.12 0 0 -0.12 498.0886 382.02 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 507.9285 382.02 Tm
[(attrib)24.1(ute)]TJ
-20.124 -1.2045 TD
[(v)24.1(ariables)-228.9(with)-240.9(domain)]TJ
/T2 1 Tf
0.12 0 0 -0.12 397.5939 370.02 Tm
(
)Tj
/T3 1 Tf
95.9998 0 TD
()Tj
/T1 1 Tf
88.0002 0 TD
()Tj
/T5 1 Tf
72.7175 12 TD
()Tj
/T4 1 Tf
53.0002 -12 TD
16 Tc
[()2000.2()2000()-0.2()]TJ
/T1 1 Tf
275 0 TD
0 Tc
()Tj
/T6 1 Tf
69 12 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 482.04 370.02 Tm
[(.)-301.1(Denote)-228.9(a)-240.9(cor)24.1(-)]TJ
-17.5255 -1.1925 TD
[(responding)-252.9(v)12(ector)-265(of)-277(v)24.1(alues)-277(\(i.e.,)-289.1(instantiated)-277(v)24.1(ariables\))-265(as)]TJ
/T2 1 Tf
0.12 0 0 -0.12 307.44 346.14 Tm
()Tj
/T3 1 Tf
81 0 TD
()Tj
/T4 1 Tf
100 0 TD
()Tj
/T1 1 Tf
32 0 TD
()Tj
/T5 1 Tf
44 12 TD
()Tj
/T1 1 Tf
37 -12 TD
14 Tc
()Tj
/T5 1 Tf
81 12 TD
0 Tc
(
)Tj
/T1 1 Tf
37 -12 TD
14 Tc
()Tj
/T6 1 Tf
228.9998 12 TD
0 Tc
()Tj
/T4 1 Tf
49 -12 TD
(
)Tj
67 0 TD
()Tj
/T2 1 Tf
90.0002 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 417.84 346.14 Tm
[(.)-542(Each)-313.2(v)12(ector)]TJ
/T2 1 Tf
0.12 0 0 -0.12 476.6534 346.14 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 485.4133 346.14 Tm
[(is)-337.3(cate)12(gorized)]TJ
-17.8641 -1.2045 TD
[(into)-228.9(one)-228.9(of)]TJ
/T1 1 Tf
0.12 0 0 -0.12 352.462 334.14 Tm
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 365.662 334.14 Tm
(classes)Tj
/TT2 1 Tf
2.833 0 TD
(,)Tj
/T1 1 Tf
0.12 0 0 -0.12 398.7769 334.14 Tm
()Tj
/T5 1 Tf
61.8591 12 TD
()Tj
/T1 1 Tf
38 -12 TD
14 Tc
()Tj
/T5 1 Tf
95.9998 12 TD
0 Tc
(
)Tj
/T1 1 Tf
37 -12 TD
14 Tc
()Tj
/T6 1 Tf
244 12 TD
0 Tc
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 464.88 334.14 Tm
[(.)-301.1(There)-216.8(are)]TJ
/T1 1 Tf
0.12 0 0 -0.12 510.3204 334.14 Tm
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/TT2 1 Tf
9.9626 0 0 9.9626 183.4561 455.7 Tm
[(th)-385.4(column)-349.3(of)]TJ
/T2 1 Tf
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 246.7874 455.7 Tm
[(.)-710.7(I)0(n)-373.4(other)]TJ
-19.2065 -1.1925 TD
[(w)12(ords,)]TJ
/T2 1 Tf
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()Tj
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40.3108 12 TD
()Tj
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()Tj
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93.0001 0 TD
()Tj
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103 0 TD
()Tj
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()Tj
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27.9999 -12 TD
()Tj
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32 0 TD
()Tj
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46 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 142.56 443.82 Tm
[(is)-361.4(learner)]TJ
/T1 1 Tf
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(\012)Tj
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9.9626 0 0 9.9626 187.2952 443.82 Tm
[(’)60.2(s)-349.3(classi)]TJ
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[(cation,)-373.4(and)]TJ
/T2 1 Tf
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()Tj
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 431.82 Tm
[(is)-277(the)-277(v)12(ector)-252.9(of)-277(all)-277(con)]TJ
/TT7 1 Tf
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(о)Tj
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[(dence)-252.9(scores)-265(for)-265(class)]TJ
/T1 1 Tf
0.12 0 0 -0.12 240.4378 431.82 Tm
(\015)Tj
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9.9626 0 0 9.9626 245.1178 431.82 Tm
[(.)-397.5(Note)-265(that)]TJ
/T2 1 Tf
0.12 0 0 -0.12 55.44 419.82 Tm
()Tj
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39.0001 12 TD
()Tj
/T2 1 Tf
28 -12 TD
()Tj
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94.9999 12 TD
()Tj
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78 -12 TD
()Tj
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106 0 TD
()Tj
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51 12 TD
0.0001 Tc
()Tj
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0 Tc
[(.)-674.5(W)84.3(e)-385.4(denote)-349.3(the)-373.4(ensemble)-349.3(classi)]TJ
/TT7 1 Tf
13.5706 0 TD
(о)Tj
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[(cation)-373.4(by)]TJ
/T2 1 Tf
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()Tj
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53 12 TD
()Tj
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72 -12 TD
()Tj
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99 0 TD
()Tj
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32 0 TD
()Tj
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()Tj
/T1 1 Tf
70.9999 -12 TD
14 Tc
()Tj
/T5 1 Tf
87.9999 12 TD
0.0001 Tc
(
)Tj
/T1 1 Tf
70.0001 -12 TD
14 Tc
[()1000()]TJ
/T5 1 Tf
234.9999 12 TD
0 Tc
()Tj
/T6 1 Tf
33 0 TD
(
)Tj
/T4 1 Tf
74 -12 TD
(
)Tj
/T3 1 Tf
67 0 TD
()Tj
/T1 1 Tf
99.0001 0 TD
()Tj
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43 0 TD
()Tj
/T2 1 Tf
32 0 TD
()Tj
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52.9999 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 199.92 407.94 Tm
[(.)-530(W)84.3(e)-337.3(write)]TJ
/T2 1 Tf
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()Tj
/T1 1 Tf
86.0002 0 TD
()Tj
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99 0 TD
()Tj
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(to)Tj
-22.6994 -1.2045 TD
[(indicate)-301.1(that)-301.1(e)24.1(v)12(ery)-289.1(component)-277(of)]TJ
/T2 1 Tf
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()Tj
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9.9626 0 0 9.9626 200.1218 395.94 Tm
[(is)-313.2(strictly)-313.2(greater)-289.1(than)]TJ
-14.5224 -1.2045 TD
[(the)-240.9(corresponding)-204.8(component)-216.8(of)]TJ
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 194.571 383.94 Tm
(.)Tj
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11.9552 0 0 11.9552 55.44 355.38 Tm
[(4.)-250.9(Multiple)-250.9(Classes)]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 336.06 Tm
[(In)-252.9(this)-265(section,)-265(we)-252.9(propose)-240.9(a)-265(normati)24.1(v)12(e)-240.9(basis)-265(for)-240.9(ensemble)]TJ
T*
[(learning)-313.2(when)]TJ
/T1 1 Tf
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()Tj
/T4 1 Tf
126.0001 0 TD
(	)Tj
/T3 1 Tf
101.9999 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 148.4205 324.06 Tm
[(.)-566.1(Our)-325.2(treatment)-313.2(is)-349.3(similar)-337.3(in)-325.2(spirit)]TJ
-9.3329 -1.1925 TD
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0 -1.2045 TD
[(axiomatic)-228.9(foundations)-216.8(of)-240.9(collaborati)24.1(v)12(e)]TJ
/TT7 1 Tf
15.5845 0 TD
(о)Tj
/TT2 1 Tf
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(ltering.)Tj
/TT6 1 Tf
-16.1407 -2.5174 TD
[(4.1)-385.4(An)-252.9(Impossibility)-252.9(Theor)12(em)]TJ
/TT2 1 Tf
0 -1.879 TD
[(W)84.3(e)-289.1(present)]TJ
/TT7 1 Tf
4.7451 0 TD
(о)Tj
/TT2 1 Tf
0.5321 0 TD
[(v)12(e)-265(properties)-252.9(adopted)-252.9(from)-252.9(social)-277(choice)-265(the-)]TJ
-5.2772 -1.1925 TD
[(ory)60.2(,)-240.9(a)0(r)12(gue)-240.9(their)-252.9(merits)-252.9(in)-265(the)-252.9(conte)12(xt)-240.9(of)-252.9(ensemble)-240.9(learning,)]TJ
0 -1.2045 TD
[(and)-192.7(describe)-192.7(which)-204.8(e)12(xisting)-192.7(algorithms)-180.7(e)12(xhibit)-192.7(which)-192.7(prop-)]TJ
T*
[(erties.)-505.9(Each)-301.1(property)-289.1(places)-301.1(a)-313.2(constraint)-301.1(on)-301.1(the)-313.2(allo)24.1(w)12(able)]TJ
0 -1.1925 TD
[(form)-228.9(of)]TJ
/T1 1 Tf
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 92.9448 208.62 Tm
(.)Tj
/TT6 1 Tf
-3.7645 -1.8549 TD
[(Pr)12(operty)-216.8(1)-493.8(\(UNIV\))-252.9(Uni)12(v)12(ersal)-240.9(domain.)]TJ
/T2 1 Tf
0.12 0 0 -0.12 220.8865 190.14 Tm
()Tj
/T3 1 Tf
98 0 TD
23 Tc
()Tj
/T4 1 Tf
120.0001 0 TD
0 Tc
()Tj
/T6 1 Tf
64.2788 -30 TD
(
)Tj
/T3 1 Tf
74.0002 30 TD
()Tj
/T6 1 Tf
32 -49 TD
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 275.04 190.14 Tm
(.)Tj
/TT2 1 Tf
-22.0423 -1.6863 TD
[(UNIV)-373.4(requires)-361.3(that)]TJ
/T1 1 Tf
0.12 0 0 -0.12 138.5275 173.34 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 147.4075 173.34 Tm
[(be)-373.4(de)]TJ
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2.2611 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ned)-361.4(for)-373.4(an)12(y)-361.4(combination)-349.3(of)]TJ
-12.0485 -1.2045 TD
(classi)Tj
/TT7 1 Tf
2.2217 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cation)-277(v)12(ectors.)-409.5(Since)-277(an)-277(arbitrary)-265(classi)]TJ
/TT7 1 Tf
15.9042 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(er)-289.1(may)-277(re-)]TJ
-19.2382 -1.1925 TD
[(turn)-397.5(an)-409.5(arbitrary)-397.5(classi)]TJ
/TT7 1 Tf
9.4232 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cation,)-445.7(it)-421.6(seems)-421.6(only)-397.5(reasonable)]TJ
-9.9794 -1.2045 TD
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/T1 1 Tf
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 81.8991 137.46 Tm
[(should)-301.1(return)-301.1(some)-313.2(result)-325.2(in)-313.2(all)-325.2(circumstances.)-505.9(All)]TJ
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[(e)12(xisting)-180.7(ensemble)-180.7(combination)-168.6(methods,)-180.7(to)-192.7(our)-180.7(kno)24.1(wledge,)]TJ
0 -1.1925 TD
[(are)-240.9(de)]TJ
/TT7 1 Tf
2.4055 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ned)-228.9(for)-240.9(all)-252.9(possible)-240.9(classi)]TJ
/TT7 1 Tf
10.0725 0 TD
(о)Tj
/TT2 1 Tf
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[(er)-240.9(output)-228.9(patterns.)]TJ
/TT6 1 Tf
-13.5902 -1.6863 TD
[(Pr)12(operty)-216.8(2)-493.8(\(ND\))-289.1(Non-dictatorship.)]TJ
/TT4 1 Tf
15.3915 0 TD
[(Ther)36.1(e)-301.1(i)0(s)-301.1(n)0(o)-289.1(dictator)]TJ
/T1 1 Tf
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(\012)Tj
/TT4 1 Tf
9.9626 0 0 9.9626 61.44 84.78 Tm
[(suc)12(h)-240.9(that,)-240.9(for)-252.9(all)-252.9(classi)]TJ
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9.1148 0 TD
(о)Tj
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/T2 1 Tf
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()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 230.1204 84.78 Tm
[(and)-240.9(all)-252.9(classes)]TJ
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(\015)Tj
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(and)Tj
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()Tj
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(,)Tj
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()Tj
/T6 1 Tf
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()Tj
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82 -12.0005 TD
22 Tc
()Tj
/T6 1 Tf
138 12.0005 TD
0 Tc
()Tj
/T4 1 Tf
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(\012)Tj
/T1 1 Tf
106 0 TD
()Tj
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51 12.0005 TD
()Tj
/T6 1 Tf
33 0 TD
()Tj
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58.0002 -12.0005 TD
22 Tc
()Tj
/T5 1 Tf
138 12.0005 TD
0 Tc
()Tj
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33 0 TD
()Tj
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9.9626 0 0 9.9626 440.76 722.8201 Tm
(.)Tj
/TT2 1 Tf
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[(In)-349.3(w)12(ords,)]TJ
/T1 1 Tf
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 358.4217 706.14 Tm
[(is)-361.4(not)-361.4(permitted)-337.3(to)-349.3(completely)-337.3(ignore)-349.3(all)-361.3(b)24.1(u)0(t)]TJ
-5.1173 -1.1925 TD
[(one)-204.8(of)-204.8(the)-204.8(classi)]TJ
/TT7 1 Tf
6.3345 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ers,)-228.9(irrespecti)24.1(v)12(e)-192.7(of)]TJ
/T2 1 Tf
0.12 0 0 -0.12 450.8418 694.26 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 457.2018 694.26 Tm
[(.)-301.1(W)84.3(e)-216.8(consider)-204.8(the)-204.8(de-)]TJ
-15.0323 -1.2045 TD
[(sirability)-301.1(of)-289.1(this)-301.1(axiom)-289.1(to)-301.1(be)-301.1(self-e)24.1(vident,)-289.1(since)-301.1(the)-301.1(whole)]TJ
T*
[(point)-301.1(of)-301.1(ensemble)-289.1(learning)-289.1(is)-325.2(to)-301.1(impro)12(v)12(e)-289.1(upon)-289.1(the)-301.1(perfor)24.1(-)]TJ
0 -1.1925 TD
[(mance)-228.9(of)-240.9(the)-252.9(indi)24.1(vidual)-216.8(classi)]TJ
/TT7 1 Tf
11.8563 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(ers.)Tj
/TT6 1 Tf
-12.4125 -1.6742 TD
[(Pr)12(operty)-216.8(3)-493.8(\(WP\))-240.9(W)60.2(eak)-240.9(P)12(a)0(r)12(eto)-216.8(principle.)]TJ
/TT4 1 Tf
17.6375 0 TD
[(F)108.4(o)0(r)-252.9(all)-240.9(classes)]TJ
/T1 1 Tf
0.12 0 0 -0.12 307.44 629.7001 Tm
(\015)Tj
/TT4 1 Tf
9.9626 0 0 9.9626 314.64 629.7001 Tm
(and)Tj
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0.12 0 0 -0.12 331.864 629.7001 Tm
()Tj
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9.9626 0 0 9.9626 337.384 629.7001 Tm
(,)Tj
/T2 1 Tf
0.12 0 0 -0.12 342.2746 629.7001 Tm
-0.0002 Tc
()Tj
/T6 1 Tf
96.7114 12.0005 TD
0 Tc
()Tj
/T1 1 Tf
58.9998 -12.0005 TD
()Tj
/T2 1 Tf
87 0 TD
0.0002 Tc
()Tj
/T6 1 Tf
95 12.0005 TD
0 Tc
()Tj
/T4 1 Tf
65.0002 -12.0005 TD
(\012)Tj
/T1 1 Tf
106 0 TD
()Tj
/T5 1 Tf
51 12.0005 TD
()Tj
/T6 1 Tf
32.9998 0 TD
()Tj
/T1 1 Tf
58.0002 -12.0005 TD
23 Tc
()Tj
/T5 1 Tf
139 12.0005 TD
0 Tc
()Tj
/T6 1 Tf
32.9998 0 TD
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 445.8 629.7001 Tm
(.)Tj
/TT2 1 Tf
-13.8879 -1.6622 TD
[(WP)-457.7(captures)-433.6(the)-445.7(natural)-445.7(ideal)-445.7(that,)-493.8(if)]TJ
/TT4 1 Tf
16.3011 0 TD
(all)Tj
/TT2 1 Tf
1.5134 0 TD
(classi)Tj
/TT7 1 Tf
2.2217 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ers)-457.7(are)]TJ
-20.5923 -1.2045 TD
[(strictly)-325.2(more)-313.2(con)]TJ
/TT7 1 Tf
6.9143 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(dent)-313.2(about)-313.2(one)-313.2(class)-337.3(than)-313.2(another)36.1(,)-325.2(then)]TJ
-7.4704 -1.2045 TD
[(this)-325.2(relationship)-301.1(should)-301.1(be)-325.2(re)]TJ
/TT7 1 Tf
11.8064 0 TD
(п)Tj
/TT2 1 Tf
0.5562 0 TD
[(ected)-313.2(in)-313.2(the)-325.2(ensemble)-301.1(clas-)]TJ
-12.3625 -1.1925 TD
(si)Tj
/TT7 1 Tf
0.667 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cation.)-698.6(Essentially)-373.4(all)-385.4(v)24.1(oting)-361.4(schemes)-373.4(\(e.g.,)-397.5(plurality)60.2(,)]TJ
-1.2231 -1.2045 TD
[(pairwise)-228.9(majority)60.2(,)-216.8(Borda)-228.9(count\))-216.8(satisfy)-228.9(WP.)-313.2(W)84.3(eighted)-228.9(plu-)]TJ
0 -1.1925 TD
[(rality)-289.1(and)-277(weighted)-277(a)24.1(v)12(eraging)-277(methods)-277(obe)12(y)-265(W)0(P)-313.2(when)-277(all)]TJ
0 -1.2045 TD
[(weights)-349.3(are)-349.3(nonne)12(gati)24.1(v)12(e)-313.2(\(and)-337.3(at)-361.4(least)-361.4(one)-349.3(is)-361.3(positi)24.1(v)12(e\).)-614.3(If)]TJ
T*
[(a)-361.3(particular)-337.3(classi)]TJ
/TT7 1 Tf
7.1952 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(er’)60.2(s)-373.4(predictions)-337.3(are)-361.4(bad)-349.3(enough,)-361.3(some)]TJ
-7.7513 -1.1925 TD
[(combination)-301.1(functions)-301.1(\(e.g.,)-337.3(weighted)-313.2(a)24.1(v)12(erage)-313.2(with)-325.2(ne)12(ga-)]TJ
0 -1.2045 TD
[(ti)24.1(v)12(e)-301.1(weights,)-301.1(or)-289.1(stacking\))-289.1(may)-289.1(establish)-301.1(a)-301.1(n)0(e)12(gati)24.1(v)12(e)-277(depen-)]TJ
T*
[(dence)-349.3(between)-361.4(that)-361.4(classi)]TJ
/TT7 1 Tf
10.4563 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(er’)60.2(s)-385.4(opinion)-337.3(and)-361.4(the)-361.3(ensemble)]TJ
-11.0124 -1.1925 TD
[(result,)-216.8(and)-204.8(thus)-216.8(violate)-204.8(WP.)-301.1(Ho)24.1(we)24.1(v)12(e)0(r)36.1(,)-192.7(researchers)-192.7(typically)]TJ
0 -1.2045 TD
[(stri)24.1(v)12(e)-228.9(to)-228.9(generate)-216.8(ensembles)-228.9(of)-228.9(algorithms)-216.8(that)-228.9(are)-228.9(as)-240.9(accu-)]TJ
0 -1.1925 TD
[(rate)-240.9(as)-240.9(possible)-240.9(for)-228.9(a)-240.9(g)0(i)24.1(v)12(en)-228.9(amount)-216.8(of)-240.9(di)24.1(v)12(ersity)-228.9(\(Dietterich,)]TJ
0 -1.2045 TD
[(1997;)-228.9(Dietterich,)-228.9(in)-252.9(press\).)]TJ
/TT6 1 Tf
0 -1.6743 TD
[(Pr)12(operty)-216.8(4)-493.8(\(IIA\))-252.9(Independence)-252.9(of)-240.9(irr)12(ele)12(v)12(ant)]TJ
0 -1.2045 TD
[(alter)12(nati)12(v)12(es.)]TJ
/TT4 1 Tf
5.5015 0 TD
[(Consider)-240.9(two)-252.9(classi)]TJ
/TT8 1 Tf
7.8835 0 TD
(о)Tj
/TT4 1 Tf
0.5 0 TD
[(cation)-216.8(matrices)]TJ
/T2 1 Tf
0.12 0 0 -0.12 509.6626 417.06 Tm
()Tj
/T1 1 Tf
53 0 TD
()Tj
/T2 1 Tf
37 0 TD
()Tj
/T7 1 Tf
57.812 -31 TD
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 530.16 417.06 Tm
(.)Tj
-17.658 -1.5538 TD
(If)Tj
/T2 1 Tf
0.12 0 0 -0.12 380.2456 401.58 Tm
0.0002 Tc
()Tj
/T6 1 Tf
95.2869 12 TD
0 Tc
()Tj
/T3 1 Tf
58.0002 -12 TD
()Tj
/T2 1 Tf
88 0 TD
()Tj
/T7 1 Tf
52.9998 -34.0002 TD
()Tj
/T2 1 Tf
23.0002 34.0002 TD
()Tj
/T6 1 Tf
42 12 TD
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 432.6 401.58 Tm
(and)Tj
/T2 1 Tf
0.12 0 0 -0.12 452.344 401.58 Tm
()Tj
/T6 1 Tf
96.467 12 TD
()Tj
/T3 1 Tf
64 -12 TD
()Tj
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87.9998 0 TD
()Tj
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53.0002 -34.0002 TD
()Tj
/T2 1 Tf
23 34.0002 TD
()Tj
/T6 1 Tf
42 12 TD
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()Tj
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[(.I)385.4(f)]TJ
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0 Tc
()Tj
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()Tj
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()Tj
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()Tj
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()Tj
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()Tj
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()Tj
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()Tj
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/TT4 1 Tf
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[(for)-277(all)]TJ
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[(and)-252.9(for)-277(any)-252.9(\(single\))-265(positive)-265(constant)]TJ
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9.9626 0 0 9.9626 216.295 301.02 Tm
[(and)-252.9(any)-252.9(constants)]TJ
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[(,)-240.9(then)]TJ
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()Tj
/T5 1 Tf
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()Tj
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()Tj
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23.0001 Tc
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()Tj
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()Tj
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()Tj
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()Tj
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()Tj
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138.0001 12 TD
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32.9999 0 TD
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 192.12 289.02 Tm
[(for)-240.9(all)-252.9(classes)]TJ
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(\015)Tj
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9.9626 0 0 9.9626 257.1278 289.02 Tm
(and)Tj
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()Tj
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(.)Tj
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[(TI)-277(can)-289.1(be)-277(enforced)-265(by)-277(an)-277(additi)24.1(v)12(e)-265(normalization,)-265(or)-277(align-)]TJ
0 -1.2045 TD
[(ing)-361.3(all)-361.3(classi)]TJ
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(о)Tj
/TT2 1 Tf
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[(ers’)-373.4(scores)-361.3(with)-361.4(a)-361.3(common)-337.3(reference)-337.3(point)]TJ
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(\(e.g.,)Tj
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()Tj
/T6 1 Tf
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/T7 1 Tf
53 -29.9998 TD
()Tj
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46.0001 29.9998 TD
()Tj
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106 0 TD
()Tj
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38.9999 12 TD
()Tj
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28 -12 TD
()Tj
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72 0 TD
()Tj
/T3 1 Tf
83 0 TD
(	\012)Tj
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170 0 TD
()Tj
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39 12 TD
()Tj
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29 -12 TD
()Tj
/T3 1 Tf
53 0 TD
()Tj
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(\).)Tj
-12.1173 -1.8067 TD
[(This)-313.2(weak)12(ening)-289.1(is)-325.2(suf)]TJ
/TT7 1 Tf
8.8899 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cient)-313.2(to)-313.2(allo)24.1(w)-313.2(for)-301.1(a)-313.2(non-dictatorial)]TJ
-9.446 -1.1925 TD
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 149.4842 218.46 Tm
[(.)-542(Moreo)12(v)12(e)0(r)36.1(,)-301.1(the)-325.2(only)-313.2(such)]TJ
/T1 1 Tf
0.12 0 0 -0.12 259.2916 218.46 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 267.5716 218.46 Tm
(com-)Tj
-21.2927 -1.2045 TD
[(putes)-277(the)-277(ensemble)-265(con)]TJ
/TT7 1 Tf
9.3718 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(dence)-252.9(in)-277(each)-277(class)-289.1(as)-277(a)-289.1(weighted)]TJ
-9.9279 -1.1925 TD
[(a)24.1(v)12(erage)-469.8(of)-469.8(the)-481.8(component)-457.7(learners’)-469.8(con)]TJ
/TT7 1 Tf
16.8605 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(dences)-457.7(in)-481.8(that)]TJ
-17.4166 -1.2045 TD
(class.)Tj
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0 -2.1199 TD
[(Pr)12(oposition)-228.9(2)-493.8(\()0(W)60.2(eighted)-481.8(a)24.1(v)12(erage\))]TJ
/TT4 1 Tf
15.1191 0 TD
(If)Tj
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32 Tc
()Tj
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200 0 TD
0 Tc
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 246.2314 161.46 Tm
[(,)-566.1(then)-493.8(the)]TJ
-19.1507 -1.2045 TD
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()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 128.4035 149.46 Tm
[(satisfying)-614.3(UNIV)132.5(,)-602.2(W)0(P)132.5(,)-614.3(IIA,)-602.3(and)-602.3(TI)-614.3(is)]TJ
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[(suc)12(h)-566.1(that)]TJ
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0.0001 Tc
()Tj
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()Tj
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()Tj
138 0 TD
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()Tj
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[(,)-650.4(wher)36.1(e)]TJ
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14 Tc
()Tj
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96 12 TD
0 Tc
(
)Tj
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38 -12 TD
14 Tc
[()1000()0()]TJ
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243.0001 12 TD
0 Tc
()Tj
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63.9999 -12 TD
(
)Tj
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9.9626 0 0 9.9626 154.44 125.58 Tm
[(is)-313.2(a)-301.1(r)48.2(ow)-313.2(vector)-289.1(of)]TJ
/T1 1 Tf
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(	)Tj
/TT4 1 Tf
9.9626 0 0 9.9626 241.091 125.58 Tm
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()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 242.1184 113.58 Tm
[(is)-301.1(also)-277(con-)]TJ
-18.7378 -1.1925 TD
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()Tj
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23.0001 Tc
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32.9999 0 TD
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 229.32 101.7 Tm
(.)Tj
ET
q
57.72 0 0 -0.48 55.428 95.688 cm
/Im1 Do
Q
BT
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5.9776 0 0 5.9776 68.04 88.62 Tm
(3)Tj
8.9664 0 0 8.9664 71.52 84.78 Tm
(If)Tj
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(
)Tj
143 0 TD
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30.0001 0 TD
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36.2354 8.0002 TD
()Tj
/T9 1 Tf
27.0001 -8.0002 TD
(
)Tj
/T8 1 Tf
49 0 TD
21 Tc
[()20999.9()21000.1()]TJ
259.9999 0 TD
0 Tc
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30 0 TD
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36 8.0002 TD
()Tj
/T9 1 Tf
27.0001 -8.0002 TD
(
)Tj
/T8 1 Tf
48.9999 0 TD
()Tj
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8.9664 0 0 8.9664 168 84.78 Tm
[(then)-267.7(set)]TJ
/T9 1 Tf
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()Tj
/T10 1 Tf
35.3547 8.0002 TD
()Tj
/T9 1 Tf
27.0001 -8.0002 TD
(
)Tj
/T11 1 Tf
49 -31.9999 TD
()Tj
/TT2 1 Tf
8.9664 0 0 8.9664 216.24 84.78 Tm
(to)Tj
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()Tj
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(.)Tj
/TT6 1 Tf
9.9626 0 0 9.9626 307.44 722.8201 Tm
[(Pr)12(oof:)]TJ
/TT2 1 Tf
3.4916 0 TD
[(F)12(ollo)24.1(ws)-240.9(from)-228.9(Roberts’)60.2(s)-493.8(\(1980\))-216.8(Theorem)-228.9(2.)]TJ
ET
q
5.76 0 0 -5.76 519.228 728.5681 cm
/Im1 Do
Q
BT
9.9626 0 0 9.9626 307.44 700.26 Tm
[(Certainly)-505.9(there)-505.9(may)-505.9(e)12(xist)-517.9(classi)]TJ
/TT7 1 Tf
13.5753 0 TD
(о)Tj
/TT2 1 Tf
0.5561 0 TD
[(cation)-517.9(domains)-493.8(where)]TJ
-14.1315 -1.2045 TD
[(some)-349.3(of)-361.4(these)-361.3(properties)-337.3(do)-349.3(not)-349.3(seem)-361.4(appropriate)-325.2(or)-349.3(jus-)]TJ
0 -1.1925 TD
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/TT7 1 Tf
0.5557 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ed.)-301.1(Ho)24.1(we)24.1(v)12(e)0(r)36.1(,)-204.8(we)-240.9(belie)24.1(v)12(e)-228.9(that,)-228.9(because)-228.9(the)-240.9(properties)-216.8(are)]TJ
-1.1118 -1.2045 TD
[(v)12(ery)-289.1(natural,)-313.2(understanding)-277(the)-301.1(limitations)-301.1(that)-313.2(the)12(y)-301.1(place)]TJ
0 -1.1925 TD
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0 -1.2045 TD
[(ify)-240.9(what)-240.9(potential)-228.9(algorithms)-228.9(can)-240.9(and)-240.9(cannot)-228.9(do.)]TJ
/TT6 1 Tf
11.9552 0 0 11.9552 307.44 611.9401 Tm
[(5.)-250.9(Binary)-250.9(Classi)]TJ
/TT9 1 Tf
6.7529 0 TD
(о)Tj
/TT6 1 Tf
0.5562 0 TD
(cation)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 307.44 592.6201 Tm
[(No)24.1(w)-240.9(consider)-240.9(the)-252.9(subset)-240.9(of)-252.9(learning)-228.9(problems)-228.9(where)]TJ
/T1 1 Tf
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()Tj
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113 0 TD
()Tj
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-1875.6187 100 TD
(\015)Tj
/T1 1 Tf
23 0 TD
()Tj
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65 0 TD
(\015)Tj
/T3 1 Tf
51.9998 0 TD
29 Tc
()Tj
/TT2 1 Tf
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0 Tc
[(.)-409.5(I)0(n)-277(this)-289.1(case,)-301.1(the)-277(impossibility)-265(outlined)-277(in)-277(Propo-)]TJ
-3.3244 -1.2045 TD
[(sition)-277(1)-277(disappears;)-277(the)]TJ
/TT7 1 Tf
9.551 0 TD
(о)Tj
/TT2 1 Tf
0.5321 0 TD
[(v)12(e)-265(properties)-265(UNIV)132.5(,)-277(W)0(P)108.4(,)-277(IIA,)-265(SI,)]TJ
-10.0831 -1.1925 TD
[(and)-289.1(ND)-289.1(are)-301.1(in)-289.1(f)12(act)-301.1(perfectly)-277(compatible.)-421.6(F)12(o)0(r)-289.1(e)12(xample,)-289.1(all)]TJ
/TT7 1 Tf
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(о)Tj
/TT2 1 Tf
0.5321 0 TD
[(v)12(e)-240.9(are)-240.9(satis)]TJ
/TT7 1 Tf
4.4121 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ed)-252.9(by)-240.9(the)-240.9(standard)]TJ
/TT4 1 Tf
7.5168 0 TD
[(majority)-240.9(vote)]TJ
/TT2 1 Tf
5.2951 0 TD
(:)Tj
/T4 1 Tf
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()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
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50.9998 12 TD
()Tj
/T4 1 Tf
88 -12 TD
()Tj
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83 0 TD
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51.0002 12 TD
(
)Tj
/T4 1 Tf
71 -12 TD
21.9998 Tc
()Tj
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151.9998 -145 TD
0 Tc
()Tj
0 50 TD
()Tj
T*
()Tj
0 49 TD
()Tj
0 50 TD
()Tj
/T6 1 Tf
77.0002 -158 TD
()Tj
/T12 1 Tf
-31 24.9995 TD
(
)Tj
/T6 1 Tf
6 177.0005 TD
()Tj
/T5 1 Tf
22.9998 0 TD
()Tj
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105 -98 TD
()Tj
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42.0002 0 TD
()Tj
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50.9998 12 TD
()Tj
/T5 1 Tf
23.0002 0 TD
()Tj
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54.9998 -12 TD
()Tj
/T1 1 Tf
83.0002 0 TD
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/T4 1 Tf
38 -12 TD
()Tj
/T12 1 Tf
41.9998 -145 TD
()Tj
0 50 TD
()Tj
T*
()Tj
0 49 TD
()Tj
0 50 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 529.8 514.14 Tm
(\(2\))Tj
-22.3194 -2.9992 TD
(where)Tj
/T4 1 Tf
0.12 0 0 -0.12 363.72 462.78 Tm
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T4 1 Tf
46.9998 0 TD
()Tj
/T3 1 Tf
65.0002 0 TD
()Tj
/T12 1 Tf
88 -170 TD
()Tj
0 75 TD
()Tj
0 149 TD
()Tj
/T3 1 Tf
178.9998 -154 TD
()Tj
125 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 441.96 474.78 Tm
(if)Tj
/T1 1 Tf
0.12 0 0 -0.12 450.5656 474.78 Tm
22.9998 Tc
()Tj
/T3 1 Tf
157.9998 0 TD
0 Tc
()Tj
-460.7131 99 TD
()Tj
125 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 441.96 462.9 Tm
(if)Tj
/T1 1 Tf
0.12 0 0 -0.12 450.5656 462.9 Tm
()Tj
/T3 1 Tf
69.9998 0 TD
23 Tc
()Tj
/T4 1 Tf
-436.7131 100 TD
0 Tc
()Tj
/T3 1 Tf
65 0 TD
()Tj
124 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 441.96 450.9 Tm
(if)Tj
/T1 1 Tf
0.12 0 0 -0.12 450.5656 450.9 Tm
22.9998 Tc
()Tj
/T3 1 Tf
157.9998 0 TD
0 Tc
()Tj
/T1 1 Tf
107.2871 -99 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 307.44 433.98 Tm
[(Note)-252.9(that)-252.9(the)-240.9(properties)-240.9(are)-252.9(necessary)-240.9(b)24.1(u)0(t)-240.9(not)-252.9(suf)]TJ
/TT7 1 Tf
19.476 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cient)-240.9(for)]TJ
-20.0322 -1.2045 TD
[(characterizing)-204.8(majority)-228.9(v)24.1(ote.)-301.1(Proposition)-216.8(3)-228.9(belo)24.1(w)-228.9(pro)12(vides)]TJ
0 -1.1925 TD
[(one)-240.9(suf)]TJ
/TT7 1 Tf
2.8828 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cient)-228.9(characterization.)]TJ
/TT6 1 Tf
-3.439 -2.5295 TD
[(5.1)-385.4(Majority)-228.9(V)96.4(ote)]TJ
/TT2 1 Tf
0 -1.867 TD
[(The)-421.6(use)-433.6(of)-421.6(majority)-409.5(v)24.1(ote)-421.6(for)-421.6(ensemble)-421.6(learning)-409.5(is)-433.6(typi-)]TJ
0 -1.2045 TD
[(cally)-204.8(moti)24.1(v)24.1(ated)-192.7(by)-204.8(its)-216.8(simplicity)60.2(,)-216.8(its)-216.8(observ)12(ed)-180.7(ef)24.1(fecti)24.1(v)12(eness,)]TJ
T*
[(and)-289.1(its)-301.1(percei)24.1(v)12(e)0(d)-265(f)12(airness)-301.1(when)-277(the)-301.1(constituent)-277(algorithms)]TJ
0 -1.1925 TD
[(are)-301.1(essentially)-289.1(“created)-289.1(equal”)-289.1(\(Dietterich,)-301.1(1997\).)-433.6(F)12(o)0(r)-289.1(e)12(x-)]TJ
0 -1.2045 TD
[(ample,)-385.4(the)-373.4(component)-337.3(algorithms)-349.3(emplo)12(yed)-349.3(for)-361.4(bagging,)]TJ
0 -1.1925 TD
[(ECOC,)-325.2(and)-301.1(randomization)-277(are)-313.2(generally)]TJ
/TT4 1 Tf
16.5953 0 TD
[(a)-313.2(priori)]TJ
/TT2 1 Tf
3.4603 0 TD
(indistin-)Tj
-20.0556 -1.2045 TD
[(guishable,)-313.2(and)-301.1(\(2\))-313.2(is)-325.2(typically)-301.1(used)-301.1(to)-325.2(combine)-289.1(classi)]TJ
/TT7 1 Tf
21.6035 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
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(\),)Tj
-22.9096 -1.1925 TD
[(then,)-228.9(under)-204.8(POSR,)-252.9(an)12(y)-216.8(change)-216.8(by)-228.9(an)12(y)-216.8(algorithm)]TJ
/T1 1 Tf
0.12 0 0 -0.12 248.3764 365.34 Tm
(\012)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 254.1364 365.34 Tm
[(in)-228.9(a)-240.9(pos-)]TJ
-19.9441 -1.2045 TD
[(iti)24.1(v)12(e)-252.9(direction)-240.9(for)]TJ
/T1 1 Tf
0.12 0 0 -0.12 127.1328 353.34 Tm
()Tj
/T5 1 Tf
62.5598 12 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 141.72 353.34 Tm
(\(i.e.,)Tj
/T1 1 Tf
0.12 0 0 -0.12 162.2195 353.34 Tm
()Tj
/T6 1 Tf
52.1711 12 TD
()Tj
/T5 1 Tf
39 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 180.12 353.34 Tm
[(increases)-252.9(or)]TJ
/T1 1 Tf
0.12 0 0 -0.12 229.9676 353.34 Tm
()Tj
/T6 1 Tf
52.6036 12 TD
()Tj
/T5 1 Tf
39 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 247.92 353.34 Tm
(decreases\))Tj
-19.3202 -1.1925 TD
[(breaks)-289.1(this)-301.1(deadlock,)-289.1(yielding)]TJ
/T1 1 Tf
0.12 0 0 -0.12 178.576 341.46 Tm
()Tj
/T5 1 Tf
56.8669 12 TD
()Tj
/T1 1 Tf
102 -12 TD
31.0001 Tc
()Tj
/T5 1 Tf
147 12 TD
0 Tc
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 223.68 341.46 Tm
[(.)-481.8(Moreo)12(v)12(e)0(r)36.1(,)-265(an)12(y)]TJ
-16.8871 -1.2045 TD
[(change)-168.6(of)-192.7(one)-180.7(of)-180.7(the)-192.7(constituent)-168.6(v)24.1(otes)-192.7(that)-192.7(strictly)-192.7(f)12(a)24.1(v)24.1(ors)]TJ
/T1 1 Tf
0.12 0 0 -0.12 276.5763 329.46 Tm
()Tj
/T5 1 Tf
69.1973 12 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 317.46 Tm
[(cannot)-301.1(swing)-301.1(the)-313.2(ensemble)-301.1(v)24.1(ote)-313.2(in)-313.2(the)-301.1(opposite)-301.1(direction,)]TJ
0 -1.1925 TD
(from)Tj
/T1 1 Tf
0.12 0 0 -0.12 78.2858 305.58 Tm
()Tj
/T5 1 Tf
60.6179 12 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 93.84 305.58 Tm
[(to)-361.4(undecided)-349.3(or)-361.4(to)]TJ
/T1 1 Tf
0.12 0 0 -0.12 172.8577 305.58 Tm
()Tj
/T5 1 Tf
63.5192 12 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 185.04 305.58 Tm
[(.)-674.5(Combined)-349.3(with)-361.4(NTRL,)]TJ
-13.0086 -1.2045 TD
[(POSR)-385.4(is)-397.5(a)-373.4(stronger)-361.4(v)12(ersion)-361.4(of)-373.4(WP)108.4(,)-385.4(b)24.1(ut)-373.4(is)-397.5(still)-385.4(quite)-373.4(rea-)]TJ
T*
[(sonable.)-517.9(Note)-325.2(that,)-337.3(because)-313.2(there)-313.2(are)-325.2(only)-301.1(tw)12(o)-325.2(classes,)-349.3(if)]TJ
0 -1.1925 TD
[(an)12(y)-216.8(learner’)60.2(s)-228.9(v)24.1(otes)-228.9(are)-228.9(observ)12(ed)-204.8(to)-228.9(be)-228.9(ne)12(gati)24.1(v)12(ely)-192.7(correlated)]TJ
0 -1.2045 TD
[(with)-192.7(the)-180.7(correct)-180.7(classi)]TJ
/TT7 1 Tf
8.5506 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cation)-180.7(\(and,)-180.7(for)-180.7(e)12(xample,)-180.7(a)-192.7(weighted)]TJ
-9.1068 -1.1925 TD
[(a)24.1(v)12(erage)-313.2(method)-313.2(assigns)-325.2(a)-337.3(n)0(e)12(gati)24.1(v)12(e)-301.1(weight\),)-337.3(then)-313.2(its)-337.3(v)24.1(otes)]TJ
0 -1.2045 TD
[(can)-313.2(simply)-313.2(be)-301.1(re)24.1(v)12(ersed,)-313.2(rendering)-289.1(POSR)-325.2(\(and)-301.1(a)-325.2(nonne)12(ga-)]TJ
T*
[(ti)24.1(v)12(e)-240.9(weight\))-228.9(appropriate)-216.8(again.)]TJ
/TT6 1 Tf
0 -2.2765 TD
[(Pr)12(oposition)-228.9(3)-493.8(\(Majority)-240.9(v)12(ote\))]TJ
/TT4 1 Tf
12.9117 0 TD
[(An)-265(a)12(g)12(g)0(r)36.1(e)36.1(gation)-228.9(function)]TJ
/T1 1 Tf
0.12 0 0 -0.12 282.8565 199.14 Tm
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 55.44 187.26 Tm
[(is)-325.2(the)-301.1(majority)-313.2(vote)-301.1(\(2\))-301.1(if)-325.2(and)-289.1(only)-301.1(if)-325.2(it)-313.2(satis)]TJ
/TT8 1 Tf
17.9271 0 TD
(о)Tj
/TT4 1 Tf
0.5 0 TD
[(es)-313.2(UNIV)132.5(,)-313.2(SI,)]TJ
-18.4271 -1.2045 TD
[(NTRL,)-252.9(SYM,)-240.9(and)-240.9(POSR.)]TJ
/TT6 1 Tf
0 -2.2765 TD
[(Pr)12(oof:)]TJ
/TT2 1 Tf
3.4916 0 TD
[(Choose)-216.8(scaling)-228.9(parameters)-216.8(as)-240.9(in)-228.9(Equation)-216.8(1:)]TJ
/T1 1 Tf
0.12 0 0 -0.12 268.2372 152.58 Tm
()Tj
/T6 1 Tf
61.6897 12 TD
()Tj
/T3 1 Tf
50 -12 TD
()Tj
-1885.0001 100 TD
()Tj
/T4 1 Tf
32 0 TD
(\015)Tj
/T1 1 Tf
23.0001 0 TD
()Tj
/T6 1 Tf
50.9999 12 TD
()Tj
/T5 1 Tf
23.0001 0 TD
()Tj
/T4 1 Tf
61.9999 -12 TD
()Tj
/T1 1 Tf
89.0001 0 TD
()Tj
/T6 1 Tf
50.9999 12 TD
()Tj
/T5 1 Tf
23.0001 0 TD
(
)Tj
/T4 1 Tf
38 -12 TD
(\015)Tj
/T3 1 Tf
22.9999 0 TD
()Tj
/T7 1 Tf
32 -30 TD
(
)Tj
/T5 1 Tf
52 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 123.24 140.58 Tm
[(\(or)-337.3(if)]TJ
/T1 1 Tf
0.12 0 0 -0.12 147.6622 140.58 Tm
()Tj
/T6 1 Tf
52.4819 12 TD
()Tj
/T5 1 Tf
23.0001 0 TD
()Tj
/T3 1 Tf
75 -12 TD
()Tj
/T1 1 Tf
102.9999 0 TD
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 191.4 140.58 Tm
[(,)-373.4(set)]TJ
/T1 1 Tf
0.12 0 0 -0.12 212.1575 140.58 Tm
()Tj
/T6 1 Tf
53.0204 12 TD
()Tj
/T3 1 Tf
65.0001 -12 TD
()Tj
102.9999 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 243.72 140.58 Tm
[(\))-325.2(and)]TJ
/T1 1 Tf
0.12 0 0 -0.12 268.0222 140.58 Tm
()Tj
/T6 1 Tf
48.4822 12 TD
()Tj
/T3 1 Tf
65 -12 TD
()Tj
/T4 1 Tf
-1885.0001 99.0001 TD
()Tj
/T1 1 Tf
65 0 TD
()Tj
/T6 1 Tf
53 12 TD
()Tj
/T3 1 Tf
41 -12 TD
0.0001 Tc
[(	\012)-999.9()]TJ
/T1 1 Tf
171.0001 0 TD
0 Tc
()Tj
/T6 1 Tf
50.9999 12 TD
()Tj
/T5 1 Tf
23.0001 0 TD
()Tj
/T1 1 Tf
36.9999 -12 TD
14.0001 Tc
()Tj
/T6 1 Tf
88.0001 12 TD
0 Tc
()Tj
/T5 1 Tf
22.9999 0 TD
(
)Tj
/T3 1 Tf
38 -12 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 130.08 128.7 Tm
[(.)-313.2(Let)]TJ
/T2 1 Tf
0.12 0 0 -0.12 151.3661 128.7 Tm
()Tj
/T6 1 Tf
39.6161 12 TD
()Tj
/T2 1 Tf
28 -12 TD
()Tj
/T7 1 Tf
53 -30.0001 TD
()Tj
/T3 1 Tf
47 30.0001 TD
()Tj
/T1 1 Tf
87 0 TD
()Tj
/T6 1 Tf
53 12 TD
()Tj
/T2 1 Tf
27.9999 -12 TD
()Tj
/T6 1 Tf
39.0001 12 TD
()Tj
/T2 1 Tf
28 -12 TD
()Tj
/T3 1 Tf
71 0 TD
()Tj
/T1 1 Tf
83.0001 0 TD
()Tj
/T6 1 Tf
46.9999 12 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 229.68 128.7 Tm
[(for)-228.9(all)]TJ
/T1 1 Tf
0.12 0 0 -0.12 256.0544 128.7 Tm
(\012)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 259.5344 128.7 Tm
[(.)-301.1(Then)]TJ
/T4 1 Tf
0.12 0 0 -0.12 87.36 95.22 Tm
()Tj
/T1 1 Tf
32.0001 0 TD
()Tj
/T7 1 Tf
56 -35.0001 TD
()Tj
/T6 1 Tf
-5.0001 55 TD
()Tj
/T5 1 Tf
23 0 TD
()Tj
/T1 1 Tf
38.0001 -19.9999 TD
13.9999 Tc
()Tj
/T7 1 Tf
92.9999 -35.0001 TD
0 Tc
()Tj
/T6 1 Tf
-4.9999 55 TD
()Tj
/T5 1 Tf
22.9999 0 TD
(
)Tj
/T4 1 Tf
37.0001 -19.9999 TD
(
)Tj
/T3 1 Tf
55.9999 0 TD
()Tj
/T12 1 Tf
87 -171.0001 TD
()Tj
0 75 TD
()Tj
0 150 TD
()Tj
/T4 1 Tf
116 -155.0001 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0001 0 TD
()Tj
/T3 1 Tf
36.9999 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/T3 1 Tf
114 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 198.24 107.34 Tm
(if)Tj
/T1 1 Tf
0.12 0 0 -0.12 206.8456 107.34 Tm
()Tj
/T6 1 Tf
51.2867 12 TD
()Tj
/T5 1 Tf
23 0 TD
()Tj
/T1 1 Tf
60 -12 TD
23 Tc
()Tj
/T6 1 Tf
139 12 TD
0 Tc
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/T4 1 Tf
-741 88 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0001 0 TD
()Tj
/T3 1 Tf
36.9999 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/T3 1 Tf
114 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 198.24 95.34 Tm
(if)Tj
/T1 1 Tf
0.12 0 0 -0.12 206.8456 95.34 Tm
()Tj
/T6 1 Tf
51.2867 12 TD
()Tj
/T5 1 Tf
23 0 TD
()Tj
/T3 1 Tf
60 -12 TD
()Tj
/T1 1 Tf
88 0 TD
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/T4 1 Tf
-741 87 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0001 0 TD
()Tj
/T3 1 Tf
36.9999 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/T3 1 Tf
114 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 198.24 83.46 Tm
(if)Tj
/T1 1 Tf
0.12 0 0 -0.12 206.8456 83.46 Tm
()Tj
/T6 1 Tf
51.2867 12.0001 TD
()Tj
/T5 1 Tf
23 0 TD
()Tj
/T1 1 Tf
60 -12.0001 TD
23 Tc
()Tj
/T6 1 Tf
139 12.0001 TD
0 Tc
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/T1 1 Tf
102.9999 -109.9999 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 307.44 722.8201 Tm
[(That)-240.9(is,)-252.9(with)-252.9(only)-228.9(tw)12(o)-252.9(classes,)-252.9(and)-240.9(tw)12(o)-252.9(d)0(e)12(grees)-228.9(of)-240.9(freedom)]TJ
0 -1.1925 TD
[(in)-385.4(choosing)-373.4(the)-385.4(scaling)-385.4(constants,)-421.6(SI)-397.5(ef)24.1(fecti)24.1(v)12(ely)-361.4(restricts)]TJ
0 -1.2045 TD
[(the)-204.8(domain)]TJ
/T2 1 Tf
0.12 0 0 -0.12 353.3342 698.9401 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 364.4942 698.9401 Tm
(of)Tj
/T1 1 Tf
0.12 0 0 -0.12 374.7132 698.9401 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 382.0332 698.9401 Tm
[(to)-204.8(v)24.1(otes.)-289.1(May)-192.7(\(1952\))-180.7(pro)12(v)12(e)0(s)-180.7(that)-204.8(NTRL,)]TJ
-7.4873 -1.2045 TD
[(SYM,)-192.7(and)-180.7(POSR)-192.7(are)-192.7(necessary)-168.6(and)-180.7(suf)]TJ
/TT7 1 Tf
15.2203 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cient)-180.7(conditions)-168.6(for)]TJ
-15.7764 -1.1925 TD
[(majority)-228.9(v)24.1(ote)-240.9(when)-228.9(inputs)-228.9(are)-240.9(v)24.1(otes.)-301.1(W)84.3(e)-252.9(refer)-240.9(the)-240.9(reader)-216.8(to)]TJ
0 -1.2045 TD
[(May’)60.2(s)-240.9(article)-252.9(for)-228.9(the)-240.9(remainder)-228.9(of)-240.9(the)-240.9(proof.)]TJ
ET
q
5.76 0 0 -5.76 486.468 668.808 cm
/Im1 Do
Q
BT
9.9626 0 0 9.9626 307.44 640.7401 Tm
[(Notice)-385.4(that,)-421.6(when)-385.4(the)-385.4(component)-361.3(algorithms)-361.4(return)-373.4(only)]TJ
0 -1.1925 TD
[(v)24.1(otes,)-216.8(and)-204.8(no)-204.8(other)-204.8(information)-180.7(is)-216.8(a)24.1(v)24.1(ailable,)-216.8(SI)-216.8(is)-216.8(a)-216.8(v)24.1(acuous)]TJ
0 -1.2045 TD
[(requirement;)-289.1(in)-289.1(this)-301.1(setting,)-301.1(Proposition)-277(3)-289.1(becomes)-277(a)-301.1(v)12(ery)]TJ
T*
[(compelling)-168.6(normati)24.1(v)12(e)-156.6(ar)12(gument)-168.6(for)-180.7(the)-192.7(use)-192.7(of)-180.7(majority)-180.7(v)24.1(ote)]TJ
0 -1.1925 TD
[(for)-240.9(classi)]TJ
/TT7 1 Tf
3.6286 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(er)-240.9(combination.)]TJ
/TT6 1 Tf
-4.1847 -2.5295 TD
[(5.2)-385.4(W)60.2(eighted)-240.9(Majority)-228.9(V)96.4(ote)]TJ
/TT2 1 Tf
0 -1.867 TD
[(When)-192.7(the)-204.8(component)-168.6(algorithms)-180.7(do)-192.7(return)-180.7(meaningful)-168.6(con-)]TJ
/TT7 1 Tf
0 -1.2045 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(dence)-240.9(scores,)-240.9(SI)-252.9(may)-240.9(seem)-252.9(o)12(v)12(erly)-216.8(se)24.1(v)12(ere,)-240.9(as)-252.9(it)-252.9(essentially)]TJ
-0.5562 -1.1925 TD
[(strips)-192.7(a)12(w)12(a)0(y)-180.7(magnitude)-168.6(information.)-252.9(Con)]TJ
/TT7 1 Tf
15.9071 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(dence)-168.6(scores)-192.7(may)]TJ
-16.4633 -1.2045 TD
(re)Tj
/TT7 1 Tf
0.7769 0 TD
(п)Tj
/TT2 1 Tf
0.5562 0 TD
[(ect)-192.7(man)12(y)-192.7(sources)-192.7(of)-192.7(information—for)-156.6(e)12(xample,)-180.7(the)-192.7(acti-)]TJ
-1.333 -1.2045 TD
[(v)24.1(ation)-228.9(le)24.1(v)12(els)-240.9(of)-228.9(a)-240.9(neural)-228.9(netw)12(ork’)60.2(s)-228.9(output)-216.8(nodes,)-228.9(the)-240.9(poste-)]TJ
0 -1.1925 TD
[(rior)-240.9(probabilities)-228.9(of)-240.9(a)-252.9(Bayesian)-252.9(netw)12(ork’)60.2(s)-228.9(output)-240.9(v)24.1(ariables,)]TJ
0 -1.2045 TD
[(or)-445.7(an)-445.7(algorithm’)60.2(s)-433.6(observ)12(ed)-421.6(performance)-409.5(on)-445.7(the)-445.7(training)]TJ
T*
[(data)-313.2(\(as)-325.2(is)-337.3(used)-313.2(in)-325.2(Boosting\).)-517.9(Re)12(gardless)-313.2(of)-313.2(its)-337.3(origin)-301.1(we)]TJ
0 -1.1925 TD
(interpret)Tj
/T1 1 Tf
0.12 0 0 -0.12 344.4255 453.54 Tm
()Tj
/T6 1 Tf
52.7874 12 TD
()Tj
/T5 1 Tf
22.9998 0 TD
()Tj
/T1 1 Tf
75 -12 TD
()Tj
102.0002 0 TD
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 391.56 453.54 Tm
[(as)-349.3(a)-337.3(prediction)-313.2(in)-337.3(f)12(a)24.1(v)24.1(o)0(r)-337.3(o)0(f)-325.2(class)-349.3(one,)]TJ
/T1 1 Tf
0.12 0 0 -0.12 307.44 441.54 Tm
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/T1 1 Tf
77.9998 -12 TD
()Tj
106 0 TD
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23.0002 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 355.44 441.54 Tm
[(as)-361.3(a)-373.4(prediction)-337.3(in)-361.3(f)12(a)24.1(v)24.1(o)0(r)-349.3(o)0(f)-349.3(class)-373.4(tw)12(o,)-385.4(and)-361.3(the)]TJ
-4.818 -1.2045 TD
[(magnitude)-180.7(of)-192.7(the)-192.7(dif)24.1(ference)-180.7(in)-192.7(con)]TJ
/TT7 1 Tf
13.4652 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(dence)-180.7(scores)]TJ
/T4 1 Tf
0.12 0 0 -0.12 499.0951 429.54 Tm
(\015)Tj
/T1 1 Tf
22.9995 0 TD
()Tj
/T6 1 Tf
60.8745 12 TD
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/T4 1 Tf
42 -12 TD
()Tj
/T1 1 Tf
69.9995 0 TD
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23 0 TD
()Tj
/T4 1 Tf
37.0005 -12 TD
(\015)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 307.44 417.66 Tm
[(as)-252.9(the)]TJ
/TT4 1 Tf
2.5485 0 TD
(weight)Tj
/TT2 1 Tf
2.9315 0 TD
[(of)-240.9(algorithm)]TJ
/T1 1 Tf
0.12 0 0 -0.12 413.6311 417.66 Tm
(\012)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 417.1111 417.66 Tm
[(’)60.2(s)-252.9(con)36.1(viction.)]TJ
-11.0082 -1.8068 TD
[(Then)-228.9(we)-252.9(de)]TJ
/TT7 1 Tf
4.6464 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ne)-240.9(the)]TJ
/TT4 1 Tf
2.6473 0 TD
[(weighted)-228.9(majority)-240.9(vote)]TJ
/TT2 1 Tf
9.3873 0 TD
(as)Tj
/T4 1 Tf
0.12 0 0 -0.12 320.28 369.66 Tm
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)Tj
/T1 1 Tf
32 0 TD
14.0001 Tc
()Tj
/T4 1 Tf
134.0002 0 TD
0 Tc
(
)Tj
/T3 1 Tf
32 0 TD
23 Tc
()Tj
/T1 1 Tf
-1665.0001 124 TD
0 Tc
()Tj
/T3 1 Tf
43 0 TD
()Tj
/T4 1 Tf
32 0 TD
0.0001 Tc
()Tj
/T3 1 Tf
64.0001 0 TD
0 Tc
()Tj
/T1 1 Tf
41.9999 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42.0001 0 TD
(
)Tj
/T1 1 Tf
32 0 TD
()Tj
/T4 1 Tf
37 0 TD
()Tj
/T1 1 Tf
31.9999 0 TD
()Tj
/T5 1 Tf
51 12.0005 TD
()Tj
/T3 1 Tf
89 -12.0005 TD
()Tj
/T1 1 Tf
83 0 TD
()Tj
/T5 1 Tf
51 12.0005 TD
(
)Tj
/T4 1 Tf
88 -12.0005 TD
()Tj
/T1 1 Tf
83.0001 0 TD
()Tj
/T5 1 Tf
50.9999 12.0005 TD
0.0001 Tc
(
)Tj
/T4 1 Tf
89.0001 -12.0005 TD
0 Tc
()Tj
/T1 1 Tf
82.9999 0 TD
()Tj
/T5 1 Tf
51 12.0005 TD
(

)Tj
/T1 1 Tf
69.9999 -12.0005 TD
()Tj
/T3 1 Tf
37.0001 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/T1 1 Tf
32 0 TD
()Tj
/T4 1 Tf
-247 125 TD
()Tj
/T3 1 Tf
32.0001 0 TD
()Tj
/T1 1 Tf
41.9999 0 TD
13.9999 Tc
()Tj
/T5 1 Tf
88 12.0005 TD
0.0001 Tc
(
)Tj
/T4 1 Tf
88 -12.0005 TD
0 Tc
()Tj
/T1 1 Tf
83 0 TD
()Tj
/T5 1 Tf
51 12.0005 TD
()Tj
/T4 1 Tf
71.0001 -12.0005 TD
(
)Tj
/T1 1 Tf
32 0 TD
14 Tc
()Tj
/T4 1 Tf
134 0 TD
0 Tc
(
)Tj
/T3 1 Tf
31.9998 0 TD
23.0002 Tc
()Tj
/T4 1 Tf
-1666.9999 124 TD
14 Tc
()Tj
/T3 1 Tf
150 0 TD
0 Tc
()Tj
/T1 1 Tf
-150 185 TD
()Tj
/T12 1 Tf
56 -141.9995 TD
-0.0001 Tc
()Tj
/T4 1 Tf
133.0001 141.9995 TD
0 Tc
()Tj
/T3 1 Tf
31.9999 0 TD
()Tj
/T1 1 Tf
42.0001 0 TD
()Tj
/T3 1 Tf
36.9999 0 TD
()Tj
/T4 1 Tf
42.0001 0 TD
(
)Tj
/T1 1 Tf
31.9999 0 TD
()Tj
/T4 1 Tf
37 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37.0001 0 TD
()Tj
/T4 1 Tf
41.9999 0 TD
(
)Tj
/T1 1 Tf
32 0 TD
()Tj
/T4 1 Tf
37 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37.0001 0 TD
()Tj
/T4 1 Tf
41.9999 0 TD
(
)Tj
/T1 1 Tf
32 0 TD
14 Tc
[()2000()]TJ
/T12 1 Tf
183 -141.9995 TD
0 Tc
()Tj
/T6 1 Tf
97 39 TD
()Tj
/T12 1 Tf
-30 24 TD
(
)Tj
/T6 1 Tf
6 177 TD
()Tj
/T5 1 Tf
23 0 TD
()Tj
/T1 1 Tf
104 -98.0005 TD
()Tj
/T6 1 Tf
51.0001 12.0005 TD
()Tj
/T5 1 Tf
22.9999 0 TD
()Tj
/T4 1 Tf
57 -12.0005 TD
()Tj
/T1 1 Tf
83.0001 0 TD
()Tj
/T6 1 Tf
51 12.0005 TD
()Tj
/T5 1 Tf
22.9998 0 TD
(
)Tj
/T1 1 Tf
37.0002 -12.0005 TD
()Tj
/T3 1 Tf
36.9998 0 TD
()Tj
/T12 1 Tf
42 -141.9995 TD
0.0002 Tc
()Tj
133 0 TD
0 Tc
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 514.02 Tm
[(Thus)-325.2(if)]TJ
/T12 1 Tf
0.12 0 0 -0.12 88.08 521.46 Tm
(	)Tj
/T6 1 Tf
87.9999 87 TD
()Tj
/T1 1 Tf
42.0001 -25 TD
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23.0001 0 TD
()Tj
/T4 1 Tf
60.9999 -12 TD
()Tj
/T1 1 Tf
88 0 TD
()Tj
/T6 1 Tf
51 12 TD
()Tj
/T5 1 Tf
23 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 147.24 514.02 Tm
[(is)-337.3(greater)-313.2(than)-325.2(\(less)-337.3(than,)-337.3(equal)-325.2(to\))]TJ
-9.2144 -1.2045 TD
[(zero,)-361.4(then)]TJ
/T1 1 Tf
0.12 0 0 -0.12 99.3059 502.02 Tm
()Tj
/T5 1 Tf
53.451 12 TD
()Tj
/T4 1 Tf
95.0001 -12 TD
()Tj
/T1 1 Tf
88.9999 0 TD
()Tj
/T5 1 Tf
51.0001 12 TD
-0.0001 Tc
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 145.92 502.02 Tm
0 Tc
[(is)-361.4(greater)-337.3(than)-337.3(\(less)-361.3(than,)-361.3(equal)-349.3(to\))]TJ
-9.0819 -1.1925 TD
[(zero,)-228.9(precisely)-240.9(the)-240.9(weighted)-228.9(majority)-228.9(v)24.1(ote)-240.9(\(3\).)]TJ
ET
q
5.76 0 0 -5.76 242.628 495.8881 cm
/Im1 Do
Q
BT
/TT6 1 Tf
11.9552 0 0 11.9552 55.44 461.58 Tm
[(6.)-250.9(Independence)-281(Pr)20.1(eser)10(v)10(ation)]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 442.14 Tm
[(Consider)-301.1(the)-313.2(learners’)-301.1(predictions)-289.1(when)-301.1(ask)12(ed)-313.2(to)-313.2(e)24.1(v)24.1(aluate)]TJ
0 -1.2045 TD
[(an)-397.5(e)12(xample)]TJ
/T2 1 Tf
0.12 0 0 -0.12 106.1487 430.14 Tm
()Tj
/T7 1 Tf
48.4271 -31.0002 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 120.6 430.14 Tm
[(with)-397.5(some)-397.5(missing)-385.4(v)24.1(alues.)-758.8(W)36.1(ithout)-385.4(loss)]TJ
-6.5404 -1.1925 TD
[(of)-252.9(generality)60.2(,)-228.9(let)]TJ
/T1 1 Tf
0.12 0 0 -0.12 122.8585 418.26 Tm
(
)Tj
/T5 1 Tf
65.1791 12 TD
()Tj
/T1 1 Tf
37 -12 TD
14 Tc
(
)Tj
/T5 1 Tf
99.0001 12 TD
0 Tc
(
)Tj
/T1 1 Tf
37.9999 -12 TD
14 Tc
[()1000(
)]TJ
/T6 1 Tf
246 12 TD
0 Tc
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 191.28 418.26 Tm
[(be)-252.9(the)-265(attrib)24.1(ute)-240.9(v)24.1(ariables)]TJ
-13.6349 -1.2045 TD
[(with)-397.5(missing)-397.5(v)24.1(alues,)-421.6(and)-385.4(let)]TJ
/T1 1 Tf
0.12 0 0 -0.12 176.2382 406.26 Tm
(
)Tj
/T6 1 Tf
65.3484 12 TD
()Tj
/T5 1 Tf
59.0001 0 TD
-0.0001 Tc
()Tj
/T1 1 Tf
88 -12 TD
14 Tc
(
)Tj
/T6 1 Tf
246.9999 12 TD
0 Tc
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 241.32 406.26 Tm
[(be)-397.5(the)-385.4(v)24.1(ari-)]TJ
-18.6577 -1.1925 TD
[(ables)-421.6(with)-421.6(kno)24.1(wn)-397.5(v)24.1(alues.)-831.1(Let)]TJ
/T2 1 Tf
0.12 0 0 -0.12 186.3195 394.38 Tm
()Tj
/T7 1 Tf
50.3374 -30 TD
()Tj
/T6 1 Tf
0 58.0002 TD
()Tj
/T13 1 Tf
59.0002 -17 TD
(
)Tj
/T3 1 Tf
101.9999 -11.0002 TD
()Tj
/T4 1 Tf
114 0 TD
()Tj
/T1 1 Tf
32 0 TD
()Tj
/T7 1 Tf
44 -30 TD
()Tj
/T6 1 Tf
0 51.0002 TD
()Tj
/T5 1 Tf
59 0 TD
-0.0002 Tc
()Tj
/T1 1 Tf
88.9999 -21.0002 TD
14.0001 Tc
[()1000.1()0.1()]TJ
/T7 1 Tf
228.0002 -30 TD
0 Tc
()Tj
/T6 1 Tf
0 53.0002 TD
()Tj
/T4 1 Tf
50 -23.0002 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 382.38 Tm
[(denote)-361.4(the)-373.4(v)12(ector)-361.4(of)-373.4(kno)24.1(wn)-361.3(v)24.1(alues.)-686.6(If)-373.4(we)-373.4(de)]TJ
/TT7 1 Tf
18.7255 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(ne)-373.4(a)-385.4(prior)]TJ
-19.2816 -1.2045 TD
[(joint)-301.1(probability)-277(distrib)24.1(ution)]TJ
/T3 1 Tf
0.12 0 0 -0.12 171.8854 370.38 Tm
()Tj
89 0 TD
()Tj
/T2 1 Tf
31.9999 0 TD
()Tj
/T3 1 Tf
46.0002 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 198.8854 370.38 Tm
[(o)12(v)12(e)0(r)-289.1(all)-313.2(possible)-301.1(com-)]TJ
-14.3983 -1.1925 TD
[(binations)-397.5(of)-397.5(attrib)24.1(ute)-397.5(v)24.1(alues,)-445.7(then)-397.5(we)-409.5(can)-409.5(compute)-385.4(each)]TJ
0 -1.2045 TD
[(learner’)60.2(s)-265(induced)-240.9(posterior)-252.9(distrib)24.1(ution)-252.9(o)12(v)12(e)0(r)-252.9(classi)]TJ
/TT7 1 Tf
19.984 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(cations)Tj
-20.5401 -1.2045 TD
[(gi)24.1(v)12(e)0(n)-228.9(the)-240.9(kno)24.1(wn)-228.9(v)24.1(alues)]TJ
/T2 1 Tf
0.12 0 0 -0.12 150.8363 334.5 Tm
()Tj
/T7 1 Tf
51.0305 -31 TD
()Tj
/T6 1 Tf
0 58.0002 TD
()Tj
/T13 1 Tf
59 -17 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 170.16 334.5 Tm
(:)Tj
/T3 1 Tf
0.12 0 0 -0.12 87.6 310.26 Tm
()Tj
/T6 1 Tf
89.0001 12 TD
()Tj
/T3 1 Tf
26.9999 -12 TD
()Tj
/T2 1 Tf
31.9999 0 TD
()Tj
/T6 1 Tf
39.0001 12 TD
()Tj
/T2 1 Tf
28.9999 -12 TD
()Tj
/T4 1 Tf
53 0 TD
(\015)Tj
/T2 1 Tf
23.0001 0 TD
()Tj
/T7 1 Tf
45.9999 -35 TD
()Tj
/T6 1 Tf
0 57.9998 TD
()Tj
/T13 1 Tf
59 -17 TD
(
)Tj
/T3 1 Tf
51.0001 -5.9998 TD
22.9999 Tc
()Tj
/T12 1 Tf
390 -79 TD
0 Tc
(
)Tj
/T15 1 Tf
-206.0001 207.9998 TD
()Tj
/T7 1 Tf
40 0 TD
0.0001 Tc
()Tj
/T6 1 Tf
79.0001 0 TD
0 Tc
()Tj
/T13 1 Tf
53.9999 8.0002 TD
()Tj
/T7 1 Tf
33.0001 -8.0002 TD
()Tj
110.9999 0 TD
()Tj
/T6 1 Tf
52.0001 0 TD
()Tj
/T14 1 Tf
53.9999 8.0002 TD
(
)Tj
/T7 1 Tf
55 -8.0002 TD
()Tj
/T5 1 Tf
34.0001 0 TD
()Tj
/T6 1 Tf
-482.0001 99.0002 TD
(	)Tj
/T14 1 Tf
32 7.9998 TD
()Tj
/T3 1 Tf
27 -1.9998 TD
()Tj
/T15 1 Tf
32 -6 TD
()Tj
/T6 1 Tf
40 0 TD
(\012)Tj
/T15 1 Tf
20.0001 0 TD
(
)Tj
/T16 1 Tf
37 -25 TD
()Tj
/T14 1 Tf
0 54 TD
(
)Tj
/T13 1 Tf
51 -12 TD
(
)Tj
/T3 1 Tf
50 -11 TD
()Tj
/T5 1 Tf
31.9999 -6 TD
()Tj
/T15 1 Tf
51 0 TD
()Tj
/T14 1 Tf
31 7.9998 TD
()Tj
/T15 1 Tf
26 -7.9998 TD
()Tj
/T3 1 Tf
-83 -228 TD
()Tj
89 0 TD
()Tj
/T2 1 Tf
32 0 TD
(\012)Tj
/T4 1 Tf
49.9999 0 TD
(\015)Tj
/T2 1 Tf
23.0001 0 TD
()Tj
/T7 1 Tf
46 -35 TD
()Tj
/T6 1 Tf
0 57.9998 TD
()Tj
/T13 1 Tf
59.0001 -17 TD
(
)Tj
/T3 1 Tf
51.9998 -5.9998 TD
()Tj
/T1 1 Tf
32 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 260.94 Tm
[(Similarly)60.2(,)-265(w)0(e)-277(can)-277(compute)-252.9(the)-277(ensemble’)60.2(s)-265(posterior)-265(distri-)]TJ
0 -1.1925 TD
[(b)24.1(ution)-228.9(o)12(v)12(e)0(r)-228.9(classi)]TJ
/TT7 1 Tf
6.9637 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
(cations:)Tj
/T3 1 Tf
0.12 0 0 -0.12 75.12 227.58 Tm
-0.0001 Tc
()Tj
/T5 1 Tf
88.9999 12.0001 TD
0 Tc
()Tj
/T3 1 Tf
37 -12.0001 TD
()Tj
/T2 1 Tf
32 0 TD
()Tj
/T5 1 Tf
53 12.0001 TD
()Tj
/T4 1 Tf
37.9999 -12.0001 TD
(\015)Tj
/T2 1 Tf
23.0001 0 TD
()Tj
/T7 1 Tf
46 -34 TD
()Tj
/T6 1 Tf
0 57 TD
()Tj
/T13 1 Tf
58.9999 -16 TD
(
)Tj
/T3 1 Tf
51.0001 -7 TD
23 Tc
()Tj
/T12 1 Tf
623.9999 -79 TD
0 Tc
(
)Tj
/T15 1 Tf
-205.9999 208 TD
()Tj
/T7 1 Tf
40.0001 0 TD
-0.0001 Tc
()Tj
/T6 1 Tf
78.9999 0 TD
0 Tc
()Tj
/T13 1 Tf
54 8.0001 TD
()Tj
/T7 1 Tf
32 -8.0001 TD
()Tj
111 0 TD
()Tj
/T6 1 Tf
52 0 TD
()Tj
/T14 1 Tf
54 8.0001 TD
(
)Tj
/T7 1 Tf
56 -8.0001 TD
()Tj
/T5 1 Tf
33.9999 0 TD
()Tj
/T6 1 Tf
-745.9999 100 TD
()Tj
/T3 1 Tf
34.0001 6 TD
()Tj
/T6 1 Tf
32.9999 -6 TD
(	)Tj
/T13 1 Tf
32 8.0001 TD
()Tj
/T3 1 Tf
33 -2.0001 TD
()Tj
/T15 1 Tf
32 -6 TD
()Tj
/T6 1 Tf
40 0 TD
(\012)Tj
/T15 1 Tf
20.0001 0 TD
(
)Tj
/T16 1 Tf
37 -25 TD
()Tj
/T14 1 Tf
0 53 TD
(
)Tj
/T13 1 Tf
51 -12 TD
(
)Tj
/T3 1 Tf
50 -10 TD
()Tj
/T6 1 Tf
31.9999 -6 TD
(\012)Tj
79.0001 0 TD
(\012	)Tj
/T14 1 Tf
51.9999 8.0001 TD
()Tj
/T3 1 Tf
54 -2.0001 TD
()Tj
/T15 1 Tf
32.0001 -6 TD
()Tj
/T6 1 Tf
39.9999 0 TD
(\012)Tj
/T15 1 Tf
19.9999 0 TD
(
)Tj
/T16 1 Tf
37.0001 -25 TD
()Tj
/T14 1 Tf
0 53 TD
(
)Tj
/T13 1 Tf
51 -12 TD
(
)Tj
/T3 1 Tf
50 -10 TD
()Tj
/T5 1 Tf
64.0001 -6 TD
()Tj
/T15 1 Tf
51 0 TD
()Tj
/T13 1 Tf
42 8.0001 TD
()Tj
/T3 1 Tf
-362.0001 -237.0001 TD
0.0001 Tc
()Tj
89 0 TD
0 Tc
()Tj
/T2 1 Tf
32 0 TD
(\012)Tj
/T4 1 Tf
50 0 TD
(\015)Tj
/T2 1 Tf
23 0 TD
()Tj
/T7 1 Tf
46.0001 -34 TD
()Tj
/T6 1 Tf
0 57 TD
()Tj
/T13 1 Tf
58.9998 -16 TD
(
)Tj
/T3 1 Tf
52.0002 -7 TD
()Tj
/T1 1 Tf
32 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 55.44 178.26 Tm
[(No)24.1(w)-277(w)0(e)-277(can)-277(ascertain)-265(whether)-265(some)-277(attrib)24.1(utes)-277(are)-277(statisti-)]TJ
0 -1.1925 TD
[(cally)-277(independent)-240.9(of)-265(the)-277(classi)]TJ
/TT7 1 Tf
12.1669 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cation.)-385.4(Again)-265(without)-265(loss)]TJ
-12.723 -1.2045 TD
[(of)-252.9(generality)60.2(,)-228.9(select)-265(attrib)24.1(ute)]TJ
/T1 1 Tf
0.12 0 0 -0.12 170.9352 154.38 Tm
(
)Tj
/T6 1 Tf
66.5402 12 TD
()Tj
/T5 1 Tf
59.0001 0 TD
-0.0001 Tc
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 199.2 154.38 Tm
0 Tc
[(for)-252.9(this)-252.9(purpose.)-313.2(What)]TJ
-14.4299 -1.2045 TD
(if)Tj
/TT4 1 Tf
0.8156 0 TD
[(e)12(very)]TJ
/TT2 1 Tf
2.3693 0 TD
[(constituent)-192.7(algorithm)-180.7(agrees)-204.8(that)]TJ
/T1 1 Tf
0.12 0 0 -0.12 217.8055 142.38 Tm
(
)Tj
/T6 1 Tf
67.9542 12 TD
()Tj
/T5 1 Tf
59 0 TD
0.0001 Tc
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 245.76 142.38 Tm
0 Tc
[(is)-228.9(indepen-)]TJ
-19.1034 -1.1925 TD
[(dent)-180.7(of)-180.7(the)-192.7(classi)]TJ
/TT7 1 Tf
6.5521 0 TD
(о)Tj
/TT2 1 Tf
0.5562 0 TD
[(cation,)-192.7(gi)24.1(v)12(e)0(n)-168.6(the)-180.7(remaining)-168.6(kno)24.1(wn)-168.6(v)24.1(alues)]TJ
/T1 1 Tf
0.12 0 0 -0.12 55.44 118.5 Tm
()Tj
/T7 1 Tf
44 -29.9998 TD
()Tj
/T6 1 Tf
0 50.9999 TD
()Tj
/T5 1 Tf
59 0 TD
0.0001 Tc
(
)Tj
/T1 1 Tf
88 -21.0002 TD
14 Tc
()Tj
/T7 1 Tf
229.0001 -29.9998 TD
0 Tc
()Tj
/T6 1 Tf
0 52.9999 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 111.72 118.5 Tm
[(?)-505.9(I)0(t)-313.2(seems)-325.2(natural)-301.1(and)-301.1(desirable)-301.1(that)-313.2(such)-301.1(a)]TJ
-5.6491 -1.2045 TD
[(unanimous)-252.9(judgment)-265(of)-277(“irrele)24.1(v)24.1(ance”)-252.9(should)-265(be)-289.1(preserv)12(ed)]TJ
0 -1.1925 TD
[(in)-325.2(the)-337.3(ensemble)-313.2(distrib)24.1(ution.)-542(The)-325.2(follo)24.1(wing)-313.2(property)-301.1(for)24.1(-)]TJ
0 -1.2045 TD
[(mally)-240.9(captures)-228.9(this)-252.9(ideal:)]TJ
8.9664 0 1.4974 8.9664 332.16 716.7001 Tm
[(T)80.3(able)-254.3(1.)]TJ
8.9664 0 0 8.9664 363.9756 716.7001 Tm
[(Example)-254.3(where)-254.3(plurality)-254.3(v)13.4(ote)-254.3(violates)-254.3(IPP)107.1(.)]TJ
/T1 1 Tf
0.12 0 0 -0.12 317.88 698.22 Tm
(
)Tj
/T5 1 Tf
62 12 TD
()Tj
/T1 1 Tf
137 -12 TD
(
)Tj
/T5 1 Tf
62 12 TD
(
)Tj
/T1 1 Tf
208 -12 TD
(
)Tj
/T5 1 Tf
62 12 TD
()Tj
ET
q
0.48 0 0 -12 400.428 706.608 cm
/Im1 Do
Q
BT
/T2 1 Tf
0.12 0 0 -0.12 409.92 698.22 Tm
()Tj
/T5 1 Tf
39 12 TD
()Tj
/T2 1 Tf
38 -12 TD
()Tj
206.9998 0 TD
()Tj
/T5 1 Tf
39 12 TD
(
)Tj
/T2 1 Tf
38 -12 TD
()Tj
207.0002 0 TD
()Tj
/T5 1 Tf
39 12 TD
()Tj
/T2 1 Tf
38 -12 TD
()Tj
ET
q
0.48 0 0 -12 502.788 706.608 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 514.56 698.22 Tm
()Tj
/T5 1 Tf
53 12 TD
()Tj
ET
q
225.24 0 0 -0.48 311.868 694.728 cm
/Im1 Do
Q
q
225.24 0 0 -0.48 311.868 692.688 cm
/Im1 Do
Q
BT
/TT2 1 Tf
9.9626 0 0 9.9626 321.36 683.8201 Tm
1.8911 Tc
[(00)-855.2(0)]TJ
ET
q
0.48 0 0 -12 400.428 692.328 cm
/Im1 Do
Q
BT
/T4 1 Tf
0.12 0 0 -0.12 406.504 683.8201 Tm
0 Tc
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
(
)Tj
131 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
130.9998 0 TD
()Tj
/T3 1 Tf
32.0002 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
0.48 0 0 -12 502.788 692.328 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 508.744 683.8201 Tm
()Tj
/T3 1 Tf
32.0005 0 TD
()Tj
/T1 1 Tf
41.9995 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 321.36 671.9401 Tm
1.8911 Tc
[(01)-855.2(0)]TJ
ET
q
0.48 0 0 -12 400.428 680.328 cm
/Im1 Do
Q
BT
/T4 1 Tf
0.12 0 0 -0.12 406.504 671.9401 Tm
0 Tc
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
(
)Tj
131 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
130.9998 0 TD
()Tj
/T3 1 Tf
32.0002 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
0.48 0 0 -12 502.788 680.328 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 508.744 671.9401 Tm
()Tj
/T3 1 Tf
32.0005 0 TD
()Tj
/T1 1 Tf
41.9995 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 321.36 659.9401 Tm
1.8911 Tc
[(10)-855.2(0)]TJ
ET
q
0.48 0 0 -12 400.428 668.328 cm
/Im1 Do
Q
BT
/T4 1 Tf
0.12 0 0 -0.12 406.504 659.9401 Tm
0 Tc
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
(
)Tj
131 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
130.9998 0 TD
()Tj
/T3 1 Tf
32.0002 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
0.48 0 0 -12 502.788 668.328 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 508.744 659.9401 Tm
()Tj
/T3 1 Tf
32.0005 0 TD
()Tj
/T1 1 Tf
41.9995 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 321.36 648.0601 Tm
1.8911 Tc
[(11)-855.2(0)]TJ
ET
q
0.48 0 0 -12 400.428 656.448 cm
/Im1 Do
Q
BT
/T4 1 Tf
0.12 0 0 -0.12 406.504 648.0601 Tm
0 Tc
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
(
)Tj
131 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
130.9998 0 TD
()Tj
/T3 1 Tf
32.0002 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
0.48 0 0 -12 502.788 656.448 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 508.744 648.0601 Tm
()Tj
/T3 1 Tf
32.0005 0 TD
()Tj
/T1 1 Tf
41.9995 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
225.24 0 0 -0.48 311.868 644.448 cm
/Im1 Do
Q
BT
/T3 1 Tf
0.12 0 0 -0.12 317.88 635.7001 Tm
()Tj
/T6 1 Tf
88.9998 12.0005 TD
()Tj
/T3 1 Tf
27 -12.0005 TD
()Tj
/T4 1 Tf
32.0002 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42.0002 0 TD
-0.0002 Tc
(
\015)Tj
/T1 1 Tf
55 0 TD
0 Tc
(
)Tj
/T5 1 Tf
62 12.0005 TD
()Tj
/T3 1 Tf
60.9998 -12.0005 TD
22 Tc
[()22000()]TJ
ET
q
0.48 0 0 -12 400.428 644.088 cm
/Im1 Do
Q
BT
/TT2 1 Tf
9.9626 0 0 9.9626 408.96 635.7001 Tm
0 Tc
[(0.75)-1903.1(0.5)-2156.1(0.5)]TJ
ET
q
0.48 0 0 -12 502.788 644.088 cm
/Im1 Do
Q
BT
9.9626 0 0 9.9626 513.2212 635.7001 Tm
(0.5)Tj
/T1 1 Tf
0.12 0 0 -0.12 317.88 611.7001 Tm
(
)Tj
/T5 1 Tf
62 12.0005 TD
()Tj
/T1 1 Tf
137 -12.0005 TD
(
)Tj
/T5 1 Tf
62 12.0005 TD
(
)Tj
/T1 1 Tf
208 -12.0005 TD
(
)Tj
/T5 1 Tf
62 12.0005 TD
()Tj
ET
q
0.48 0 0 -12 400.428 620.088 cm
/Im1 Do
Q
BT
/T2 1 Tf
0.12 0 0 -0.12 409.92 611.7001 Tm
()Tj
/T5 1 Tf
39 12.0005 TD
()Tj
/T2 1 Tf
38 -12.0005 TD
()Tj
206.9998 0 TD
()Tj
/T5 1 Tf
39 12.0005 TD
(
)Tj
/T2 1 Tf
38 -12.0005 TD
()Tj
207.0002 0 TD
()Tj
/T5 1 Tf
39 12.0005 TD
()Tj
/T2 1 Tf
38 -12.0005 TD
()Tj
ET
q
0.48 0 0 -12 502.788 620.088 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 514.56 611.7001 Tm
()Tj
/T5 1 Tf
53 12.0005 TD
()Tj
ET
q
225.24 0 0 -0.48 311.868 608.208 cm
/Im1 Do
Q
q
225.24 0 0 -0.48 311.868 606.288 cm
/Im1 Do
Q
BT
/TT2 1 Tf
9.9626 0 0 9.9626 321.36 597.42 Tm
1.8911 Tc
[(00)-855.2(1)]TJ
ET
q
0.48 0 0 -12 400.428 605.808 cm
/Im1 Do
Q
BT
/T4 1 Tf
0.12 0 0 -0.12 406.504 597.42 Tm
0 Tc
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
(
)Tj
131 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
130.9998 0 TD
()Tj
/T3 1 Tf
32.0002 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
0.48 0 0 -12 502.788 605.808 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 508.744 597.42 Tm
()Tj
/T3 1 Tf
32.0005 0 TD
()Tj
/T1 1 Tf
41.9995 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 321.36 585.42 Tm
1.8911 Tc
[(01)-855.2(1)]TJ
ET
q
0.48 0 0 -12 400.428 593.808 cm
/Im1 Do
Q
BT
/T4 1 Tf
0.12 0 0 -0.12 406.504 585.42 Tm
0 Tc
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
(
)Tj
131 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
130.9998 0 TD
()Tj
/T3 1 Tf
32.0002 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
0.48 0 0 -12 502.788 593.808 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 508.744 585.42 Tm
()Tj
/T3 1 Tf
32.0005 0 TD
()Tj
/T1 1 Tf
41.9995 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 321.36 573.54 Tm
1.8911 Tc
[(10)-855.2(1)]TJ
ET
q
0.48 0 0 -12 400.428 581.928 cm
/Im1 Do
Q
BT
/T4 1 Tf
0.12 0 0 -0.12 406.504 573.54 Tm
0 Tc
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
(
)Tj
131 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
130.9998 0 TD
()Tj
/T3 1 Tf
32.0002 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
0.48 0 0 -12 502.788 581.928 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 508.744 573.54 Tm
()Tj
/T3 1 Tf
32.0005 0 TD
()Tj
/T1 1 Tf
41.9995 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 321.36 561.54 Tm
1.8911 Tc
[(11)-855.2(1)]TJ
ET
q
0.48 0 0 -12 400.428 569.928 cm
/Im1 Do
Q
BT
/T4 1 Tf
0.12 0 0 -0.12 406.504 561.54 Tm
0 Tc
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
(
)Tj
131 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
130.9998 0 TD
()Tj
/T3 1 Tf
32.0002 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
0.48 0 0 -12 502.788 569.928 cm
/Im1 Do
Q
BT
0.12 0 0 -0.12 508.744 561.54 Tm
()Tj
/T3 1 Tf
32.0005 0 TD
()Tj
/T1 1 Tf
41.9995 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42 0 TD
(
)Tj
ET
q
225.24 0 0 -0.48 311.868 558.048 cm
/Im1 Do
Q
BT
/T3 1 Tf
0.12 0 0 -0.12 317.88 549.1801 Tm
()Tj
/T6 1 Tf
88.9998 12 TD
()Tj
/T3 1 Tf
27 -12 TD
()Tj
/T4 1 Tf
32.0002 0 TD
()Tj
/T3 1 Tf
32 0 TD
()Tj
/T1 1 Tf
41.9998 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
42.0002 0 TD
-0.0002 Tc
(
\015)Tj
/T1 1 Tf
55 0 TD
0 Tc
(
)Tj
/T5 1 Tf
62 12 TD
()Tj
/T3 1 Tf
60.9998 -12 TD
22 Tc
[()22000()]TJ
ET
q
0.48 0 0 -12 400.428 557.5681 cm
/Im1 Do
Q
BT
/TT2 1 Tf
9.9626 0 0 9.9626 408.96 549.1801 Tm
0 Tc
[(0.75)-1903.1(0.5)-2156.1(0.5)]TJ
ET
q
0.48 0 0 -12 502.788 557.5681 cm
/Im1 Do
Q
BT
9.9626 0 0 9.9626 510.8212 549.1801 Tm
(0.75)Tj
/TT6 1 Tf
-20.4144 -3.734 TD
[(Pr)12(operty)-216.8(11)-493.8(\(IPP\))-180.7(Independence)-252.9(pr)12(eser)12(v)12(ation)-228.9(pr)12(operty)24.1(.)]TJ
/TT4 1 Tf
1.1202 -1.7827 TD
(If)Tj
/T3 1 Tf
0.12 0 0 -0.12 334.6456 494.22 Tm
0.0002 Tc
()Tj
/T6 1 Tf
89.2869 12 TD
0 Tc
()Tj
/T3 1 Tf
27.0002 -12 TD
()Tj
/T2 1 Tf
32 0 TD
()Tj
/T6 1 Tf
38.9998 12 TD
()Tj
/T2 1 Tf
29.0002 -12 TD
()Tj
/T4 1 Tf
52.9998 0 TD
(\015)Tj
/T2 1 Tf
23.0002 0 TD
()Tj
/T7 1 Tf
45.9998 -30 TD
()Tj
/T6 1 Tf
0 56.9998 TD
()Tj
/T13 1 Tf
59.0002 -15.9998 TD
(
)Tj
/T3 1 Tf
51 -11 TD
23 Tc
[()23000()]TJ
/T6 1 Tf
231.9998 12 TD
0 Tc
()Tj
/T3 1 Tf
28.0002 -12 TD
()Tj
/T2 1 Tf
32 0 TD
()Tj
/T6 1 Tf
39 12 TD
()Tj
/T2 1 Tf
28 -12 TD
()Tj
/T4 1 Tf
53 0 TD
(\015)Tj
/T1 1 Tf
23 0 TD
()Tj
/T7 1 Tf
43.9998 -30 TD
()Tj
/T6 1 Tf
0 51 TD
()Tj
/T5 1 Tf
59 0 TD
(
)Tj
/T1 1 Tf
88 -21 TD
14 Tc
()Tj
/T7 1 Tf
229.0002 -30 TD
0 Tc
()Tj
/T6 1 Tf
0 53 TD
()Tj
/T3 1 Tf
49 -23 TD
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 510.84 494.22 Tm
[(for)-240.9(all)]TJ
/T1 1 Tf
0.12 0 0 -0.12 537.9035 494.22 Tm
(\012)Tj
/TT4 1 Tf
9.9626 0 0 9.9626 307.56 479.22 Tm
(then)Tj
/T3 1 Tf
0.12 0 0 -0.12 335.5125 479.22 Tm
()Tj
/T5 1 Tf
90.0627 12 TD
()Tj
/T3 1 Tf
38 -12 TD
()Tj
/T2 1 Tf
32 0 TD
()Tj
/T5 1 Tf
53 12 TD
()Tj
/T4 1 Tf
37 -12 TD
(\015)Tj
/T2 1 Tf
22.9998 0 TD
()Tj
/T7 1 Tf
46 -31 TD
()Tj
/T6 1 Tf
0 57.9998 TD
()Tj
/T13 1 Tf
59.0002 -16.9998 TD
(
)Tj
/T3 1 Tf
51.9998 -10 TD
23 Tc
[()23000()]TJ
/T5 1 Tf
232.0002 12 TD
0 Tc
()Tj
/T3 1 Tf
36.9998 -12 TD
()Tj
/T2 1 Tf
32 0 TD
()Tj
/T5 1 Tf
53.0002 12 TD
()Tj
/T4 1 Tf
37 -12 TD
(\015)Tj
/T1 1 Tf
22.9998 0 TD
()Tj
/T7 1 Tf
44.0002 -31 TD
()Tj
/T6 1 Tf
0 50.9998 TD
()Tj
/T5 1 Tf
59 0 TD
-0.0002 Tc
(
)Tj
/T1 1 Tf
87.9998 -19.9998 TD
14 Tc
()Tj
/T7 1 Tf
229.0002 -31 TD
0 Tc
()Tj
/T6 1 Tf
0 53 TD
()Tj
/T3 1 Tf
50 -22 TD
()Tj
/T1 1 Tf
32 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 307.44 461.46 Tm
[(T)84.3(able)-421.6(1)-433.6(presents)-421.6(a)-433.6(constructi)24.1(v)12(e)-397.5(proof)-409.5(that)-421.6(plurality)-421.6(v)24.1(ote)]TJ
0 -1.1925 TD
[(f)12(ails)-445.7(to)-433.6(satisfy)-433.6(IPP.)-891.3(Three)-421.6(attrib)24.1(utes)-433.6(each)-421.6(ha)24.1(v)12(e)-433.6(domain)]TJ
/T1 1 Tf
0.12 0 0 -0.12 307.44 437.58 Tm
()Tj
/T6 1 Tf
69 12 TD
()Tj
/T3 1 Tf
61 -12 TD
()Tj
/T4 1 Tf
97.9998 0 TD
()Tj
/T3 1 Tf
42 0 TD
()Tj
/T1 1 Tf
42.0002 0 TD
()Tj
/T3 1 Tf
37 0 TD
()Tj
/T4 1 Tf
41.9998 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 359.4 437.58 Tm
[(,)-313.2(and)-301.1(the)-313.2(prior)-301.1(distrib)24.1(ution)-301.1(o)12(v)12(e)0(r)-289.1(attrib)24.1(ute)-313.2(v)24.1(al-)]TJ
-5.2155 -1.2045 TD
(ues)Tj
/T3 1 Tf
0.12 0 0 -0.12 324.0803 425.58 Tm
()Tj
89 0 TD
()Tj
/T2 1 Tf
32 0 TD
()Tj
/T3 1 Tf
45.9998 0 TD
()Tj
71.0002 0 TD
()Tj
102 0 TD
()Tj
/T1 1 Tf
42 0 TD
()Tj
/T3 1 Tf
41.9998 0 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 383.2403 425.58 Tm
[(is)-349.3(uniform.)-566.1(V)108.4(ariables)]TJ
/T1 1 Tf
0.12 0 0 -0.12 473.9247 425.58 Tm
(
)Tj
/T5 1 Tf
65.6277 12 TD
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 489.84 425.58 Tm
(and)Tj
/T1 1 Tf
0.12 0 0 -0.12 507.4645 425.58 Tm
(
)Tj
/T5 1 Tf
63.1289 12 TD
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[(.)-337.3(S)0(o)-265(should)]TJ
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[(DO)30.1(WN)]TJ
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[(order)-265(predicted)-265(by)-277(the)-277(three-w)12(ay)-265(plurality)-265(v)24.1(ote.)-409.5(This)-277(is)-301.1(an)]TJ
T*
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8.8986 0 TD
[(,)-313.2(named)]TJ
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[(dence)-414.9(scores)-401.5(and)-414.9(corresponding)-428.3(v)13.4(ote)-401.5(patterns)-414.9(for)]TJ
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51 11.9995 TD
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)Tj
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[(ti)24.1(v)24.1(ation)-252.9(v)24.1(alues)-252.9(\(con)]TJ
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[(dence)-228.9(scores\))-252.9(of)-252.9(three)-252.9(netw)12(orks)-252.9(\(with)]TJ
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[(class)-313.2(highest.)-469.8(What)-301.1(about)-289.1(pairwise)-301.1(majority)-289.1(v)24.1(ote?)-469.8(In)-301.1(this)]TJ
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[(DO)30.1(WN)]TJ
9.9626 0 0 9.9626 500.0922 527.22 Tm
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[(by)-192.7(2:1.)-277(So)]TJ
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7.9701 0 0 7.9701 514.3833 515.34 Tm
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[(DO)30.1(WN)]TJ
9.9626 0 0 9.9626 307.44 503.34 Tm
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9.9626 0 0 9.9626 355.6936 503.34 Tm
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[(v)24.1(ote)-180.7(\(which)-180.7(actually)-180.7(satis)]TJ
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(
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ID џџџџў?џџџ№ў?џџџ€ќџџўјџџјџ№№џџрџј`џџРџќ@џџџџџўџџўџџџџџќџџџџџјџџџџџ№џџџџџр?џџџџџРџџџСџџ€џџџУџџџџџџУџџ
џџџџУџў
џџџџУџќџџџџЧџќџџџџЧџјџџџџЧџ№џџџџЧџ№џџџџЯџрџџџџЯџрџџџџџџрџџџџџџР?џџџџџџР?џџџџџџР?џџџџџџ€?џџџџџџ€џџџџџџ€џџџџџџ€џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџќџџџџџџќџџџџџџјџџџџџџљџџџџџџљџџ€џџџџёџџ€џџџџѓџџ€џџџџуџџ€џџџџЧџџРџџџЧџџРџџџџџрџџџџџр?џџў?џџ№џџќџџ№џџјџџјџџёџџџќџџУџџџўџџ‡џџџџџўџџџџР№?џџџџ№џџџџџќџџџџџџ€?џџџџ
EI
Q
endstream
endobj
70 0 obj
<<
/Length 595
>>
stream
67 0 3 0 72 57 d1
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69 0 0 57 3.1 -0.1 cm
BI
/W 69
/H 57
/BPC 1
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ID џќџџрџјџџРџјџџРџџјџџўџџџј
џџџƒџџџљ
џџџ‡џџџёџџџџџџё€џџџџџџѓ€џџŸџџџѓ€џџŸџџџуРџџџџџуР?џџ?џџџчр?џџ?џџџчрџџ?џџџЧрџў?џџџЧ№џўџџџЯ№џўџџџЯјџўџџџјџќџџџќџќџџџџŸќџќџџџџŸќџќџџџџўџјџџџџў
џљџџџџ?џ
џљџџџџ?џџљџџџў?џ€џёџџџў?џ€ѓџџџўџ€ѓџџџўџРѓџџџќџР?уџџџќџр?чџџџќџџрчџџџќџџ№чџџџјџџ№Чџџџјџџ№ЯџџџљџџјЯџџџљџџјЯџџџёџџќџџџёџџќŸџџџѓџџќŸџџџѓџџў
Ÿџџџуџџў
џџџуџџџ
?џџџчџџџ?џџџчџџџ€?џџџЧџџџ€?џџџЧџџџ€џџџЯџџџРџџџЯџџџРџџџџџџрџџџџџџрџџџџџџџ№џџџјџџџ№џџџџџ№џџџџџљџџџџџљџџџ
EI
Q
endstream
endobj
71 0 obj
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/Length 254
>>
stream
29 0 2 -1 23 56 d1
q
21 0 0 57 2.1 -1.1 cm
BI
/W 21
/H 57
/BPC 1
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ID џџџќџќџјџјџјџјџў?џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџќ
џј№џё№у№ч№Ч№Я№рŸрŸРРџ?Рџ?€џџџџџџ
џџџўџўџўџќџќџќџјчјчјЧ№Я№?Я№?№Ÿ№№?№~?№|јxџќ
џџџ
EI
Q
endstream
endobj
72 0 obj
<<
/Length 510
>>
stream
51 0 4 -2 53 59 d1
q
49 0 0 61 4.1 -2.1 cm
BI
/W 49
/H 61
/BPC 1
/IM true
ID џџџрќџџџќџџџќ
јџџџ№рpџџџРџј џџџџў
џџџџџ
џџўџџ
џџќџџџџќџџƒџџј?џџУџџ№џџУџџ№џџУџџрџџЧџџрџџџЧџџрџџџЧџџрџџџЧџџРџџџЯџџРџџџЯџџРџџЯџџРџџџџџР?џџџџџРџџџџџрџџџџџр
џџџџџрџџџџ№
џџџџј?џџџќџџџўџџџџџџџџр
џџџџќџџџџџРџџџџџќџџџџџџџџџџ€џџџџџРџџџџџрџџџџџрџџџџџрџѓџџџрџѓџџџ№џѓџџџ№џуџџџрџуџџџрџџуџџџрџџуџџџрџџУџџџСџџУџџџСџџУџџџƒџџСџџџџџџџџџџ€џџўџџ€џќџџ€?џ№?џџџрџџ
џ
џџџРџџџ№џџџ?ўџџџџ
EI
Q
endstream
endobj
73 0 obj
<<
/Length 541
>>
stream
41 0 4 -17 45 59 d1
q
41 0 0 76 4.1 -17.1 cm
BI
/W 41
/H 76
/BPC 1
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ID џџџџџџџџќ
џџџџ№xџџџџр№џџџСРџџџС€џџџƒ€џџџƒ€џџџ€џџџ€џџџџуџџџўџџџџўџџџџўџџџџўџџџџќџџџџќџџџџќџџџџќџџџџќџџџџјџџџџјџџџџјџџџјџџјџџјџџџ№џџџџ№?џџџџ№?џџџџ№?џџџџ№?џџџџр?џџџџрџџџџрџџџџрџџџџрџџџџРџџџџРџџџџџРџџџџџРџџџџџРџџџџџ€џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ
џџџџџџџџџџџџџџџџџџџџџџџџўџџџџўџџџџўџџџџўџџџџўџџџџќџџџџќџџџџќџџџџќџџџџќџџџџјџџџџјџџџџј?џџџсј?џџџРј?џџџ€pџџџ€pџџџpџџџџсџџџџ
сџџџџƒУџџџџ‡‡џџџџрџџџџј?џџџџ
EI
Q
endstream
endobj
74 0 obj
<<
/Length 452
>>
stream
34 0 -1 -17 32 56 d1
q
33 0 0 73 -0.9 -17.1 cm
BI
/W 33
/H 73
/BPC 1
/IM true
ID џџџ№џџџџРџџџРџџџ€џџџ€џџџ€џџџ€џџџџуџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ№џџџРџџџџџў?џџќџџќџџџјџџџёџџџѓџџџуџџџчўџџЧўџџЯўџџЯўџџџќџџџќџџџќџџџќџџџјџџџјџџџјџџџјџџџ№џџџ№џџџ№?џџџ№?џџџр?џџџр?џџџрџџџрџџџРџџџРџџџРџџџџРџџџџ€џџџџ€џџџџџџџџџџџџ
џџџџ
џџџџџџџџџџџўџџсўџџРўџџ€|џџ€|џџxџџ№?џџ
№џџƒрџџџџџџРџџџ№?џџџ
EI
Q
endstream
endobj
75 0 obj
<<
/Length 417
>>
stream
42 0 5 -21 36 62 d1
q
31 0 0 83 5.1 -21.1 cm
BI
/W 31
/H 83
/BPC 1
/IM true
ID џџџѓџџџсџџџСџџџСџџџУџџџƒџџџƒџџџ‡џџџџџџџџџџџўџџўџџўџџќџџќџџќ?џџј?џџј?џџјџџ№џџ№џџ№џџџрџџџрџџџсџџџСџџџСџџџУџџџƒџџџƒџџџ‡џџџџџџџџџџџўџџўџџўџџќџџќџџј?џџј?џџјџџ№џџ№џџ№џџџрџџџрџџџсџџџСџџџСџџџУџџџƒџџџƒџџџ‡џџџџџџџџџџџўџџўџџўџџќџџќџџќ?џџј?џџј?џџјџџ№џџ№џџ№џџџрџџџрџџџсџџџСџџџСџџџУџџџƒџџџƒџџџ‡џџџџџџџџџџџџŸџџџ
EI
Q
endstream
endobj
76 0 obj
<<
/Length 355
>>
stream
40 0 1 -17 39 37 d1
q
38 0 0 54 1.1 -17.1 cm
BI
/W 38
/H 54
/BPC 1
/IM true
ID џџјџџџрџџџƒуЧџўёџќјџјќџ№?ќџрўџРџўџ€џўџџќџ
џќџ
џќўџќўџјќџјќџјќџјќџ№јџ№јџ№?јџ№?јџр?јџр?јџрјџрјџРјџРјџРџќџ€џќџџўўџўќ
џџјџџƒс
џџр
џџјџџџџџџџўџџџўџџџўџџџўџџџќџсџќџРџќџ€јџ€јџ№?џџрџ
џРџџƒџџџУўџџрџџќџџџ
EI
Q
endstream
endobj
77 0 obj
<<
/Length 433
>>
stream
65 0 7 -4 57 46 d1
q
50 0 0 50 7.1 -4.1 cm
BI
/W 50
/H 50
/BPC 1
/IM true
ID Ÿџџџџџџџџџџџџџџџџџџ€?џџџџџрџџџџџјџџџџџўџџџџџџ€?џџџџџрџџџџџјџџџџџўџџџџџџ€?џџџџџрџџџџџјџџџџџўџџџџџџ€?џџџџџрџџџџџјџџџџџўџџџџџџ€?џџџџџрџџџџџјџџџџџўџџџџџџ€џџџџџр?џџџџџр?џџџџџ€џџџџўџџџџџјџџџџџрџџџџџ€?џџџџўџџџџџјџџџџџрџџџџџ€?џџџџўџџџџџјџџџџџрџџџџџ€?џџџџўџџџџџјџџџџџрџџџџџ€?џџџџўџџџџџјџџџџџРџџџџџ€?џџџџџџџџџџџџџџџџџџџџџџџ
EI
Q
endstream
endobj
78 0 obj
<<
/Length 311
>>
stream
53 0 3 -1 49 37 d1
q
46 0 0 38 3.1 -1.1 cm
BI
/W 46
/H 38
/BPC 1
/IM true
ID џџР?џџџџџџџјƒџџџ№рџџџРџрѓџџ№ѓџџј?уўџјчќџјчјџќЧ№џќЯ№?џќЯр?џќРџќŸРџќ€џќ?€џџќ?€џџќ€џџќџџќџ
џџќџ
џџќ
џ
џџќџ
џџќџџџќџџџќџџџќџџџќџџџќџџџјџџџ№џСџџтчРџџ†чрџџЧ№ј?ЯјРџƒўџР?џР?џ№
EI
Q
endstream
endobj
79 0 obj
<<
/Length 535
>>
stream
47 0 2 -16 47 59 d1
q
45 0 0 75 2.1 -16.1 cm
BI
/W 45
/H 75
/BPC 1
/IM true
ID џџџјџџџџр
џџџџ‡№џџџј?џџў?ќџџќўџџјџўџџёџўџџуџџџџЧџџџџЯџџџџџўџџŸџўџџџўџџ?џўџў?џќџўџќџўџќџќџјџќџџј?џќџџ№џјџџрџџљџџСџџљќ
ƒџџёјџџѓёќџџѓ№џџѓќ‡џџуџџƒџџчџџСџџчџџСџџчџџрџџЧџџрџџЯџџрџџЯџџрџџЯџџрџџџрџŸџџрџŸџџрџŸџџрџџџРџ?џџРџџ?џџРџџ?џџРџў?џџ€џў?џџџўџџџўџџ
џќџџџќ?џўџќ?џўџќ?џќџј?џјџљџ№?џљŸџрџљџСџџёЧџџџѓсќџџѓј?џџѓў
џџџуџџџџџчџџџџџчџџџџџчџџџџџЧџџџџџЯџџџџџЯџџџџџЯџџџџџџџџџџŸџџџџџŸџџџџџŸџџџџџџџџџџ?џџџџџ?џџџџџ
EI
Q
endstream
endobj
80 0 obj
<<
/Length 349
>>
stream
59 0 2 -1 56 37 d1
q
54 0 0 38 2.1 -1.1 cm
BI
/W 54
/H 38
/BPC 1
/IM true
ID џџџџџќ
џџўј№џўќё№ќќу№ќќч№ќќЧ№јўЯ№јџрјџƒŸрјџƒŸр№џУР№џЧ?Рџ№?џЧ?€џ№?џЧџџр?џЧџџр?џЯџ
џрџЯџџрџЯџџРџўџРџŸўџРџџŸўџРџџŸўџРџџќџ€џџ?ќџџџ?ќџџў?ќџџўќџџќќџџќџќџџјџќџ
џљџќџ
џёџўў
џуџўў@џЧџџќ`џџ№№?џџрќ?џџќџ€џџ
EI
Q
endstream
endobj
81 0 obj
<<
/Length 311
>>
stream
47 0 2 -1 43 37 d1
q
41 0 0 38 2.1 -1.1 cm
BI
/W 41
/H 38
/BPC 1
/IM true
ID џјўџџрјџџ‡Сё№џџрурџў?рЧРќ№€ќџ№јџ№ёџ№?џѓџ№?џѓџр?УџуџрџџчџрџџчџрџџџџРџџџџРџџџџРџџџџџРџџџџџ€џџџџџ€џџџџџџџџџџџџџџџ
џџџџџ
џџџџџџѓџџџџѓџџўџуџсўџчџРўџчџ€~џЧџ€|џџ|џŸџјџџ
ёƒў?џƒуƒќџ‡ЧС№џџр№џџј?ќџџ
EI
Q
endstream
endobj
82 0 obj
<<
/Length 433
>>
stream
65 0 7 -4 57 46 d1
q
50 0 0 50 7.1 -4.1 cm
BI
/W 50
/H 50
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ID џќџџџрџџџ€?џџјџўўџќ?џџјџƒџјџџСџ№џџсџёџџрџсџџ№џсџџ№џсџџ№џрџџ№џрџџ№џрџ№џрџрџрџсџ№џСџ№џУџ№
џ‡џјџј>џќ?џўџџџ
џџџРџџџр?џџрџџ€џџџќ€
џјрџ№џ№рџќСџў?Уџџ€?ƒџџР?‡џџ№џџјџџјџџќџџќџџўџџўџџўџџў?‡џџў?‡џџќ?ƒџџќСџџјџрџџ№џ№џсџјџƒџќќџџџџРџџјџџ
EI
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endstream
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/Length 373
>>
stream
42 0 4 -2 37 56 d1
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33 0 0 58 4.1 -2.1 cm
BI
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/H 58
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ID љџџѓџјџУџјќџјџјџјџјџјџџјџџљ€џџљџџџџљџџџџљџџџџљџџџџљџџџџљџџџџљџџџџљџџџџљџџџџљџџџџљџџџџљјџџљР
џџљ‡№џјјџјќџјџўџљџўџљџџџџџџ
џџџџ
џџџџџџџџ€џџџџ€џџџџ€џџџ€џџџ€џџџ€Сџџ€€џџ€џ€џ€џ€џ€џџ€џ
џџџџџџŸџџ
џџџ
џЯџўџЧџўџуџќџсџјџ№№џјРџўџџџ€џџџрџџ
EI
Q
endstream
endobj
125 0 obj
<<
/Length 256
>>
stream
23 0 2 0 20 58 d1
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18 0 0 58 2.1 -0.1 cm
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ID ќџџџџ№џќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџќџјџ???
EI
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endstream
endobj
126 0 obj
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/Length 378
>>
stream
42 0 5 -2 40 57 d1
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35 0 0 59 5.1 -2.1 cm
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ID ЯџџџџЧџџџџСџџџџРРРР?€?€€џџџљџŸџџёџŸџџуџŸџџчџџџЧџ?џџџ?џџџ?џџ?џџџў?џџџќџџџќџџџџјџџџџёџџџџѓџџџџуџџџџЧџџџџЧџџџџџџџџџџџџџџџўџџџўџџџќџџџќџџџќ?џџџј?џџџј?џџџ№?џџџ№?џџџ№?џџџрџџџрџџџрџџџРџџџРџџџРџџџРџџџРџџџ€џџџ€џџџ€џџџ€џџџ€џџџ€џџџ€џџџ€џџџ€џџџРџџџџсџџџ
EI
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endstream
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>>
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>>
stream
32 0 8 -20 27 62 d1
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19 0 0 82 8.1 -20.1 cm
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ID џџ?џўџќџќџќ?џј?џј?џјџ№џ№џрџџрџџсџџСџџСџџƒџџƒџџ‡џџџџџўџўџўџќџќџќ?џј?џј?џ№џ№џ№џџрџџрџџСџџСџџУџџƒџџƒџџ‡џџџџџџџџџџ‡џџƒџџƒџџУџџСџџСџџрџџрџџ№џџ№џ№џј?џј?џќ?џќџќџўџўџўџџџџџџ‡џџƒџџƒџџСџџСџџсџџрџџрџџ№џ№џјџј?џј?џќ?џќџќџўџџ?
EI
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endstream
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/Length 331
>>
stream
32 0 4 -20 23 62 d1
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ID Ÿџџџџџџџџ‡џџƒџџƒџџУџџСџџСџџрџџрџџ№џџ№џ№џј?џј?џќ?џќџќџўџўџџџџџџџџ‡џџƒџџƒџџСџџСџџсџџрџџрџџ№џ№џјџј?џј?џќ?џќџќџќџќџќ?џј?џј?џјџ№џ№џрџџрџџсџџСџџСџџƒџџƒџџ‡џџџџџџџўџўџќџќџќ?џј?џј?џ№џ№џ№џџрџџрџџСџџСџџУџџƒџџƒџџ‡џџџџџџџџŸџџ
EI
Q
endstream
endobj
132 0 obj
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/Length 283
>>
stream
65 0 12 1 52 41 d1
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40 0 0 40 12.1 0.9 cm
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ID Ÿџџџљџџџ№џџџрџџџРРџџџрџџ№?џўјџќќџјўџ№?џџрџџРџџРџџџрџџ№>џџјџџќџџў?џџџџџџ€џџџџ€џџџџџџў?џџќџџјџџ№>џџрџџРџџџџРџџџрўџ№?ќџјјџќ№?џўрџџРџџџџџџРџџџрџџџ№Ÿџџџљ
EI
Q
endstream
endobj
133 0 obj
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/Length 97
>>
stream
23 0 7 17 16 26 d1
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9 0 0 9 7.1 16.9 cm
BI
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ID уџ€џ€џуџ
EI
Q
endstream
endobj
134 0 obj
<<
/Length 333
>>
stream
55 0 7 -4 47 46 d1
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40 0 0 50 7.1 -4.1 cm
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ID џџр
џџџќџ№
џрџџџ€џџџ
џџџўџџџќџџџјџџџ№?џџџ№џџџрџџџџрџџџџСџџџџСџџџџƒџџџџƒџџџџ‡џџџџџџџџџџџџџџџџџџџџ

џџџџџџџџџџџџџџџџ‡џџџџƒџџџџƒџџџџСџџџџСџџџџрџџџџрџџџџ№џџџ№?џџџјџџџќџџџўџџџџ
џџџџ€џџџрџџџ№
џќџџџџр

EI
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endstream
endobj
135 0 obj
<<
/Length 517
>>
stream
60 0 4 -2 59 60 d1
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55 0 0 62 4.1 -2.1 cm
BI
/W 55
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/BPC 1
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ID џџџџ№џўџџџј
џќџё№№џуј?РxџЧќƒјџЧќќџўў
џў?ў
џџџџџџџџџџџ€џџџ€?џџџР?Чџ€џџРУџ€џџрсџ€џџр№џ€џџ№№€џџјј?€џџјќ?€џџќў€џџќџ€џў
џ€џў
џ€џўџ€џјџ€џрџ€џџџ€џџ€џџ€џџџ€€џŸ€РџŸ€РџŸŸ€РџŸ€Рџ€РџЮ?€РџР€Рџ№џ€џРџџџ€џРџџџ€џРџџџ€џРџџџ€џРџџџ€џРџџџ€џРџџџ€џРџџџ€џРџџџ€џРџŸџџРџƒџџРџƒџџРџџƒџРџGџџРџчџџРУуџџР?ƒѓўџр?ёўџрјќџ№?ќx?џјџўџџў
џџƒџџџƒџ
EI
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endstream
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136 0 obj
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>>
stream
83 0 5 -1 77 43 d1
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72 0 0 44 5.1 -1.1 cm
BI
/W 72
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ID џџџџџџсџџџџџџџџсџџџџџџџџсџџџџџџџџсџџџџџџџџрџџџџџџџџ№џџџџџџџџ№џџџџџџџџ№џџџџџџџјџџџџџџџј?џџџџџџџќџџџџџџџќџџџџџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџРџџџџџџџџрџџџџџџџ№?џџџџџџџј€€џџџџџџџјџџџџџџџ№?џџџџџџџрџџџџџџџРџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџўџџџџџџџќџџџџџџџќџџџџџџџј?џџџџџџџјџџџџџџџ№џџџџџџџ№џџџџџџџџ№џџџџџџџџрџџџџџџџџсџџџџџџџџсџџџџџџџџсџџџџџџџџсџџ
EI
Q
endstream
endobj
137 0 obj
<<
/Length 109
>>
stream
65 0 7 19 57 23 d1
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50 0 0 4 7.1 18.9 cm
BI
/W 50
/H 4
/BPC 1
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ID €??€
EI
Q
endstream
endobj
138 0 obj
<<
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>>
stream
65 0 7 -15 57 53 d1
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50 0 0 68 7.1 -15.1 cm
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ID џџ№џџ?џќ?џ№џрџџџџџ€џџџџџ
џџџџџўџџџџџќџџџџџјџџџџџ№?џџџџџ№џџџџџрџџџџџџрџџџџџџСџџџџџџСџџџџџџƒџџџџџџƒџџџџџџ‡џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ‡џџџџџџƒџџџџџџƒџџџџџџСџџџџџџСџџџџџџрџџџџџџрџџџџџџ№џџџџџ№?џџџџџјџџџџџќџџџџџўџџџџџџ
џџџџџџ€џџџџџрџџџџџ№џќ?џџ?џџ№џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџрР?Р?р
EI
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endstream
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139 0 obj
<<
/Length 561
>>
stream
65 0 7 -15 57 53 d1
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50 0 0 68 7.1 -15.1 cm
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ID Ÿџџџџџџџџџџџџ
џџџџџџ€џџџџџРџџџџџ№џџџџџќ
џџџџџџџџџџџРџџџџџ№џџџџџќ
џџџџџџџџџџџРџџџџџ№џџџџџќ
џџџџџџџџџџџРџџџџџ№џџџџџќ
џџџџџџџџџџџРџџџџџ№џџџџџќ
џџџџџџџџџџџР?џџџџџр?џџџџџ€џџџџўџџџџџјџџџџџрџџџџџ€?џџџџўџџџџџјџџџџџрџџџџџ€?џџџџўџџџџџјџџџџџрџџџџџ€?џџџџўџџџџџјџџџџџрџџџџџ€?џџџџўџџџџџјџџџџџрџџџџџ€?џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ€??€
EI
Q
endstream
endobj
140 0 obj
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/Length 515
>>
stream
83 0 5 -3 77 45 d1
q
72 0 0 48 5.1 -3.1 cm
BI
/W 72
/H 48
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ID џџџџџУџџџџџџџџУџџџџџџџџСџџџџџџџџсџџџџџџџџрџџџџџџџџ№џџџџџџџџ№џџџџџџџј?џџџџџџџќ?џџџџџџџќџџџџџџџўџџџџџџџџџџџџџџџџƒџџ€
џџџџџ€?џџџџџџџќџџџџџџџўџџџџџџџџ
џџџџџџџџРџџџџџџџрџџџџџџџјџџџџџџџўџџџџџџџўџџџџџџџјџџџџџџџрџџџџџџџРџџџџџџџ
џџџџџџџўџџџџџџџќџ€?џџџџ€
џџџџџџџџƒџџџџџџџџџџџџџџџўџџџџџџџќџџџџџџџќ?џџџџџџџј?џџџџџџџ№џџџџџџџ№џџџџџџџџрџџџџџџџџсџџџџџџџџСџџџџџџџџУџџџџџџџџУџџџ
EI
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endstream
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/Length 563
>>
stream
83 0 3 -3 79 45 d1
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76 0 0 48 3.1 -3.1 cm
BI
/W 76
/H 48
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ID Чƒ


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џџџџџџџџџџџџ€џџџџџџџџџџџџРџџџџџџџџџџџРџџџџџџџџџџџр?џџџџџџџџџџџ№џџџџџџџџџџџјџџџџџџџџџџџјџџџџџџџџџџџќџџџџџџџџџџџўџџџџџџџџџџџџ
џџџџџџџџџџџџ
џџџџџџџџџџџџ€џџџџџџџџџџџџРџџџџџџџџџџџр?џџџџџџџџџџџр?џџџџџџџџџџџ№џџџџџџџџџџџјџџџџџџџџџџџќџџџџџџџџџџџќџџџџџџџџџџџўџџџџџџџџџџџџ
џџџџџџџџџџџџ€
џџџџџџџџџџџџ€џџџџџџџџџџџџРџџџџџџџџџџџр?џџџџџџџџџџџ№?џџџџџџџџџџџ№џџџџџџџџџџџјџџџџџџџџџџџќџџџџџџџџџџџќџџџџџџџџџџџўџџџџџџџџџџџџџџџџџџџџџџџџ€џџџџџџџџџџџџ€џџџџџџџџџџџџРџџџџџџџџџџџџрџџџџџџџџџџџџр?џџџџџџџџџџџџРџџџџџџџџџџџџ€џџџџџџџџџџџџџ
џџџџџџџџџџџџџ
џџџџџџџџџџџџўџџџџџџџџџџџџќџџџџџџџџџџџџјџџџџџџџџџџџџ№џџџџџџџџџџџџр?џџџџџџџџџџџџрџџџџџџџџџџџџРџџџџџџџџџџџџ€џџџџџџџџџџџџџ
џџџџџџџџџџџџўџџџџџџџџџџџџќџџџџџџџџџџџџјџџџџџџџџџџџџјџџџџџџџџџџџџ№џџџџџџџџџџџџр?џџџџџџџџџџџџРџџџџџџџџџџџџ€џџџџџџџџџџџџџ
џџџџџџџџџџџџџ
џџџџџџџџџџџџўџџџџџџџџџџџџќџџџџџџџџџџџџјџџџџџџџџџчџџ№џџџџџџџџџЯџџр?џџџџџџџџџЯџџрџџџџџџџџџџџРџџџџџџџџџŸџџ€џџџџџџџџџџџџ
џџџџџџџџџўџўџџџџџџџџџќ?џќџџџџџџџџџј?џјџџџџџџџџџ№џјџџџџџџџџџрџ№џџџџџџџџџ€џр?џџџџџџџџџџџРџџџџџџџџќџџ€џџџџџџџџџ№џџ
џџџџџџџџџ€
џџ
џџџџџџџџќ
џўџџџџџџџџ€
џќџџџџџџџ€џјџ№џрџрџРџ€џџџ
EI
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џџј
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џџјџџ№џџрџџ€џџџџџџџџџџџџџџџ€џџрџџ№џџјџџќ
џџўџџџџџ€?џџРџџРџџрџџ№џџ№џџј
џџќ
џџќџџўџџўџўџџ?џџ?џџ€?џџ€џџ€џџ€џџРџџРџџРџџРџџРџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџрџџр
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ID ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџ?џџџџ€џџ€џџ€џџ€џџ€џџРџџРџџРџџрџџрџџ№џџ№џџј
џџј
џџќџџќџўџџ?џџ€џџ€џџРџџрџџ№
џџјџџќџў?џџ€џџРџџ№џџјџџў
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ID џџџџўџџџџќџџџџј?џџџџ№џџџџрџџџџрџџџџџСџџџџџƒџџџџџџџџџўџџџџўџџџџќџџџџјџџџџ№?џџџџ№џџџџрџџџџРџџџџџСџџџџџџџџџџџџџџџџџџџўџџџџќџџџџќџџџџјџџџџјџџџџ№џџџџ№?џџџџр?џџџџрџџџџРџџџџРџџџџџ€џџџџџџџџџџ
џџџџџџџџџўџџџџўџџџџўџџџџќџџџџќџџџџјџџџџјџџџџјџџџџ№џџџџ№џџџџр?џџџџр?џџџџр?џџџџРџџџџРџџџџРџџџџ€џџџџ€џџџџџ€џџџџџџџџџџ
џџџџџ
џџџџџ
џџџџў
џџџџўџџџџўџџџџўџџџџќџџџџќџџџџќџџџџќџџџџјџџџџјџџџџјџџџџјџџџџјџџџџ№џџџџ№џџџџ№џџџџ№џџџџ№џџџџ№џџџџрџџџџрџџџџрџџџџрџџџџр?џџџџр?џџџџР?џџџџР?џџџџР?џџџџР?џџџџР?џџџџР?џџџџР?џџџџРџџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ€џџџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџ€џџџџРџџџџР?џџџџР?џџџџР?џџџџР?џџџџР?џџџџР?џџџџР?џџџџр?џџџџр?џџџџрџџџџрџџџџрџџџџрџџџџ№џџџџ№џџџџ№џџџџ№џџџџ№џџџџ№џџџџјџџџџјџџџџјџџџџјџџџџјџџџџќџџџџќџџџџќџџџџќџџџџўџџџџўџџџџўџџџџў
џџџџџ
џџџџџ
џџџџџ
џџџџџџџџџџ€џџџџџ€џџџџџ€џџџџРџџџџРџџџџРџџџџр?џџџџр?џџџџр?џџџџ№џџџџ№џџџџјџџџџјџџџџјџџџџќџџџџќџџџџўџџџџўџџџџўџџџџџџџџџџ
џџџџџџџџџџ€џџџџџРџџџџџРџџџџрџџџџр?џџџџ№?џџџџ№џџџџјџџџџјџџџџќџџџџќџџџџўџџџџџџџџџџџџџџџџџџџџСџџџџџРџџџџџрџџџџ№џџџџ№?џџџџјџџџџќџџџџўџџџџўџџџџџџџџџџƒџџџџџСџџџџџрџџџџџрџџџџ№џџџџј?џџџџќџџџџў
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џџџџџ
џџџџџ€џџџџџ€џџџџџ€џџџџџРџџџџРџџџџРџџџџР?џџџџр?џџџџр?џџџџрџџџџ№џџџџ№џџџџ№џџџџ№џџџџјџџџџјџџџџјџџџџјџџџџјџџџџќџџџџќџџџџќџџџџќџџџџќџџџџўџџџџўџџџџў
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џџџџџ
џџџџџ
џџџџў
џџџџў
џџџџў
џџџџўџџџџўџџџџќџџџџќџџџџќџџџџќџџџџќџџџџјџџџџјџџџџјџџџџјџџџџјџџџџ№џџџџ№џџџџ№џџџџ№џџџџрџџџџр?џџџџр?џџџџР?џџџџРџџџџРџџџџРџџџџ€џџџџџ€џџџџџ€џџџџџ
џџџџџ
џџџџџџџџџўџџџџўџџџџўџџџџќџџџџќџџџџјџџџџјџџџџјџџџџ№џџџџ№?џџџџр?џџџџрџџџџРџџџџРџџџџџ€џџџџџџџџџџ
џџџџџџџџџўџџџџўџџџџќџџџџќџџџџјџџџџјџџџџ№?џџџџ№џџџџрџџџџРџџџџџСџџџџџџџџџџџџџџџџџџџўџџџџќџџџџќџџџџј?џџџџ№џџџџрџџџџџРџџџџџСџџџџџƒџџџџџџџџџџџџџџџ
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џџџџџџј?ўџџџџџџќ?ўџџџџџџўџџџџџџџџ€?џџџџџџŸџР?џџџџџџџРџџџџџџЯџрџџџџџџЯџ№џџџџџџчџ№џџџџџџџџјџџџџџџџџќ
џџџџџџџџўџџџџџџџџўџџџџџџџџџџџџџџџџџ€?џџџџџџџџРџџџџџџџџРџџџџџџџџрџџџџџџџџ№џџџџџџџџјџџџџџџџџјџџџџџџџџќ
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џР
џ€
џџџ
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џљџџџљџџƒџљџџƒџёџџУџџчџџчџ
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