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The Arrow Impossibility Theorem



斯学首通摇好寐衣 Kenneth J. Arrow Lecture Series 獯录匍好寐衣 2 す Sen ⊙ Maskin 愎搜洽橥唷砧虑喙阻艇⊙悍纳悍 Impossibility ⑼ Arrow 斯学首突眯⊥捍榍 2 酪 酪め谩嗷绻嗯∴渺 愎疏枪⑼ Sen 喙组退宜叛× 2 幻朽寸 ぷ 嗍雇驹寿ü旆纳悍拐 ⊙旱验Б橥恃о〉 5-6 ㈤通摇纺僧蘸 愎疏枪⑼ Maskin ㄐ举炊支纺僧蘸枫购迷悍⑼А颐嗯淄〉验 佃头橐锣拧嗒兔炻学琳 commentary ㄒ Ken Arrow 酪に叛о荤购筏且镣枰够眯⊥亨拭粤ㄒ∴拧嗒兔

纺僧蘸发艇 Arrow 寡楣嗷绻∫盲楣竞疽靡寸汀⑼ Condorcet (鹊敲蒙氛 18)  瑙 Ken 嗤А纭盆仪愎悍辉捶橐滤寡淄 The Origins of the Impossibility Theorem 氰 低贯∴使头纳悍拐楣验 淞栲ぢ得兴寡《支疽靡寸汀⑼ Condorcet 烈¤凸 嗑澡Ж辛颐匍氰曳纳悍囱枰嗷绻∶痴费枨浠⑼Ь颐掖缤~爨鸵氛伺学

疽靡寸汀⑼ Marquis de Condorcet 举炊支∶痴氛 堕亦靡琳喃绲⑼哟押で伊甸艇∫芒艇坟·广埂咆枇 嗝彝舀ㄐ淞枋伊颐躲喃绲寡楣拭橐哟押で伊甸艇∫芒艇∨罔龄撮$浯 ⑼隆笛峭妈咬狄恋亚吐枰Б艇 Sen 愎嗯∴渺剐涡 ∨罔亮 3 す 崤辛盏亚嗯淄 3 笛扦淄 x, y, z (獯 x, y, z ぷ褪澡Х砧ㄐ顿∴抛汀 鸵ㄠ荤雇袖谩玟撮 嗒韫 鸵艘, 识夜氛 嗣淄崃椤眯费瑙 social states) 堕窑贯谩嗯淄 x > y > z (肆衣で伊氰 す崦∴抛汀 x 嗷绻脱勾押 1 嗯淄 y 嗷绻脱勾押 2 崤朽抛汀 z 嗷绻脱勾押 3) す氛枋艇嗯淄 y > z > x 崤肖狗砧室拎抛汀 z > x > y 嗝舀芯呵枰 琳 2 愎 3 氛栲绥骨枰 x 凑∏枰 y ⒊朽凑虑⊙ 琳 2 愎 3 氛栲绥骨枰 y 凑∏枰 z 瑙獯路谚卿欢橐裂沽帐梁训 transitive 嗝摇绋型橐о说丶徘枰 嗑靡肖故枨广谁栲绥骨枰 x 凑∏枰 y 崤朽久倚す疏枪闼嗨绻氰 y 凑∏枰 z 嗑靡些泄验 x 凑∏枰 z 岬桡工且拎荤龚迷 2 愎 3 嗨绻氰 z 凑∏枰 x 寡韫ぷ 愎笛峭妈咬拐 ∫勉 simple majority rule 酚闼榧排丫胳⒁词梁训 transitive 酚闼猷靡淞枋伊颐躲嗒绲⑼允奠⑼Х验伊す烈拭橐允奠⑼А咆枇岷 democratic 浯 (岬琛缏学拭橐允奠岷 dictatorial 浯 嗒韫 嗝揖俅氰窑贯谩琳 3 嗍章 嗣淄旁实臁咆枇淞栲荤箍学§韫⑼允奠⑼Г狗砧 2 崤 3 嗝摇绋袖撮旁实膦艇∨罔沥淄 x > y > z)

纺僧蘸发艇 Arrow $づ橐 ⊙构砧崴判っ押 岬栲荤埂贸辗谚卿弧氰 Arrow ∮叛Ж惺瞄咬垦А飒谚沟亚斯骤Й骤Я这脆凉ぷ袜耽艇庞囱氦且恋橥А颐⑼п佃判す愎∨罔 崤辛锗霉ぷ团哟押で伊甸艇∫芒艇∨罔 Arrow 嗝章】学§韫囱А盆仪氰 social welfare function 崤蟹纳悍 Impossibility ⑼п〃泻汀氰铱学§韫寡楣淞枇胀沦瑷迷Ю衣愕 axioms 此怪瑙 酚闼猷靡室烈枚举翠撮驼⊥妈咬斯骤枰 axioms 垂臻拭橐оё柰逛⒎砧⒀瘁麻А压嗤 试瑙氛韫枰使悒ぷ 嗔阻袜靡驹ㄒ贸 axiom 氛判笛 (狄拎拧嗒兔膦艇 Sen 费椐肆戳 4 笛, 岬桡灌拧嗒兔膦艇 Maskin 瑙嗤伊揖俅吨с购迷悍⑼А颐嗯淄〉验 琳 5 笛) ㄐ嗨绻氰裔佃判笛青荤 axiom 氛栲荤狗砧甸艇∫冕判淞韫枰ㄐ⒀瘁麻Й骤А压崤小压 (酪滤叛 Maskin 窃ㄒ贸烨枰裂沽选ㄐ⒀瘁麻А压愎∶痴氛枇这汀沂嗷绻浠浯楣橥裸狗咬化院训, Maskin 拐栲荤谷陨蚂⑼ Arrow 剐涡)

举吹伊嗯∴渺⑼ Sen 恃ňü旆验 4 ㈤亭淄 U (unrestricted domain) 视嗣押獯嗔狗砧嗷绻浠浯榉亍笛 垦А飒谚构臻甸艇琳嗝龚 举赐铡吐枰枰 淞枨枰岬枧肖龚朽抛汀卵тА绲伊氛栲荤逛讳撮 (笛峭妈咬∫绵抛汀氛栲荤逛讳凌浯 嗒韫 琳す氛栲抛汀 c > x > y 嗔阻 c 淞柰沦桡灌耽艇嗯淄〉亚) 嗝舀械橥т撮旁实膦艇∨罔, I (independence of irrelevant alternatives) 愎∫猫汛庞囱孩艇恃Г潦铀醚氦勹 {x,y} 愦 ㄐ⒅楣吐勹⊙骸颐ㄑ磁哟押⑼п佃判す视嗣押 x 崤 y 喾枰寡楣

(ㄒ∴拧嗒兔膦艇 Maskin ㄐ举辞枰恃ňü膦橥拐椤莹汛 spoiler 嗔阻途俅吨с购迷悍∫绵抛汀笛椐 帷隆笛峭妈咬∫绵抛汀笛椐幻懈夜腋院凑⑼嗔迷∫徽 2000 眯饲枰Ш鬲⊙骸兔 瑙烈笛词怨楠械摇压氛杩磐迷撮 悚锚剐$浯猷荤够眯敢挂冈捍 瑙‘氛桡愎∫霉押寂馑堑⑼寻拐椁淄 plurality rule (す肖淄す氛桎撮ば峁光饲点雇压囱 1 寿卮, 寂叛靖歙摇∫勉 plurality rule ⊙ majority rule 鸵ㄡ怠佃咬⊙逛撮剐涡 崤卸支低构臻 嗝揖土艇屯′撮淞杪摇判氰 majority rule ㄐ琳谎摇押恃ňü U 愎∶痴疽靡寸汀⑼ Condorcet) 守捶橐潞鬲小兔熹淮榍陇嗅构归吐∏枰 600 嗍章 氛拐 谎耀押凸裂雇沦璧莽氛枇 Nader 嗷绻假槭裂っす氛枋伊愎颗兔源橐 吨п灵守捶橐箩砰 Nader ㄐ浯猷收搂馑堑淞瓒支 2% 岬栳 玎荤故煌锣磐渺 嗑靡肖 2% 拐榱这汀沂ㄐ馑堑闼椤兔炝摇∏枰贺橐 Nader 淞枧 寡韫肆衣で伊氰 庞囱孩艇恃Г潦铀醚氦勹 {贺,⊥渺} ⒅楣吐勹⊙ Nader 瑙嗷绻 irrelevant alternative 愎岌璺砧氰业亚⑼п∴艇卵тА玟凌琳馔∫湿剐吐勹崤榍, 幻朽寸耿艇 Maskin ぷ plurality rule 淞杓枰故穴鲸轨 I)

P (Pareto principle) 堕曳亍す吐摇浯 x 烈 氰 y 崤榍 x 嗷绻试瑙氛枋学ち甸艇∫昧摇∏枰 y, 守捶橐 D (nondictatorship) ㄐ甸艇淞枇栅狗砧堕亦⒁甸艇∫ x 烈 氰 y 崤榍 恃Г哩械橥А颐 x 烈 氰 y 獯落凌崧崾氰窑雇阻龚械橥А颐吐枰т

纺僧蘸发艇 Arrow 和∏枰 堕伊帐澡Х砧顿∴抛汀 (social states) 氛栳怠佃咬⊙雇妈咬归吐 3 笛轻判幻歇摇勉故学ち琳ㄓ骨龚印汛崤榍 ㄐ淞枇 social welfare function 酪裸甸唰阻凸洧 U, I, D, 崤 P 愎嗯∴渺 Sen 悛 spread of decisiveness ⊙ contraction of decisive sets 愎∫镁允侉轨氰 堕亦靡拭橐 social ranking 浯槔衣愕 U, I, 崤 P 崤榍嗝舀兴窑狗砧嗷绻嗉寸ā颐啜袜柿 靡屡朽驼麓∫镁允侉轨雇〃摇愎疏枪⑼о拧嗒兔炻学丸夜浯楱摇酪 2 ⑼寡淄愎悍で伊 The Information Basis of Social Choice

斯学首屯枰逛撮嗑旁 使亍 淞杪摇ü唷怨浠

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Create Date : 09 秆骨窑 2557
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