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【W.A】社会的選択のさまざまな不可能性について.pptx
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【W.A】社会的選択のさまざまな不可能性について.pptx
1.
社会的選択のさまざまな 不可能性について ~制度設計論に向けて~ 希望の天使、アヴェシン
2.
社会的選択とは-良いルールを作ろう- • 決められたルールの中で人はどのように動くのか(非協力ゲーム 理論) ⇨あまり今日は深く話さない •
世の中はどうあるべきか(協力ゲーム理論)⇨今回の内容 →あるべき姿を実現できるか、できるなら、どのような仕組みを 以ってしてか(メカニズムデザイン論) ⇨今回例を紹介 欲深な 人間ども 世のあるべき姿 ルール
3.
社会的選択に求められること -良いルールを作ろう- 社会的選択(政策を値域とする写像)に求められること • (パレート)効率性 • 耐戦略性 •
独裁的でない 欲深な 人間ども 世のあるべき姿 ルール
4.
全社会議の時に出した例1 –設定- • 気温は今24℃
(9月下旬ごろ) • 2人部屋にいて、冷房装置も2つ。各々冷房のスイッチを持って いる。 • 起動した冷房1つごとに気温は2℃下がる • 一方の人は22℃、他方は24℃が好み。 22℃ 24℃ Aさん Bさん
5.
耐戦略性の説明のための発展–設定- • 5人の温度の好みは22℃、23℃または24℃ • それぞれ自分の好みに近づけたい •
5人部屋にいて、単純多数決投票でエアコンの設定温度を決め る(同数トップならそれらの平均、端数切り上げ) f: {22,23,24}5→{22,23,24}
6.
耐戦略性の説明のための発展–戦略操作- 投票の参加者 好みの温度 A1 24℃ A2
24℃ A3 23℃ A4 23℃ A5 22℃ 投票の参加者 好みの温度 A1 24℃ A2 24℃ A3 23℃ A4 23℃ A5 23℃ 24℃ 23℃ A5にとって より好まし い
7.
パレート効率性の説明 –最適反応戦略1- →そんなルールは世の中に定着しない こうでない現実の実例がなかなか見つかりません パレート効率性(口語的): 社会的選択関数が、全員にとっ てより好ましい値を取らないこと。 先ほどの例でいえば、f(23,23,23,24,24)
= 22 とするとこれに反する。
8.
効率性の観点から危ない例–ボストン方式a- ボストン方式: 次のステップを1から|A|まで行う ステップ1 :
Aの各元に関して、Sの中で、志望順で最大となるものがそれであるも のを成績順に「内定」とする。このステップで内定させた生徒が定員に達したな ら、それ以上を内定させない。 ステップn : ステップ1を行うが、Sは「Sの元かついずれのAにも内定してないも の」、「志望順で最大となるもの」は「志望順で大きい方からn-1つを除き最大と なるもの」、「このステップで」は「これ以前のステップで」と読み替える。 教育機関の集合Aと生徒Sに関して、 Aの元に自然数の定員とS上の全順序(生徒の入学試験の成績順)を 対応させ、Sの元にはA上の全順序(志望順)を対応させる。
9.
効率性の観点から危ない例–ボストン方式b- S1:A1>A2>A3 成績順 S1 S2 S3 A1 A2 A3 S2:A1>A2>A3 S3:A2>A1>A3
10.
効率性の観点から危ない例–ボストン方式b- S1:A1>A2>A3 成績順 S1 S2 S3 A1 A2 A3 S2:A1>A2>A3 S3:A2>A1>A3
11.
効率性の観点から危ない例–ボストン方式b- S1:A1>A2>A3 成績順 S1 S2 S3 A1 A2 A3 S2:A1>A2>A3 S3:A1>A1>A3 うちはS2 の方がいいし彼もうちの方が いいらしいのに😡
12.
ギバート・サタスウェイト定理 • パレート効率性と耐戦略性を満たす社会のルールは独裁性しか 存在しない →ギバート・サタスウェイト定理 常に俺の最も好きなようにすれば耐戦略性を満た す! 俺は誰に投票しても 帰結が変わらん!
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