BETWEEN ARROW AND GIBBARD-SATTERTHWAITE A REPRESENTATION THEORETIC APPROACH

D Falik, Ehud Friedgut

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

A central theme in social choice theory is that of impossibility theorems, such as Arrow's theorem [Arr63] and the Gibbard-Satterthwaite theorem [Gib73, Sat75], which state that under certain natural constraints, social choice mechanisms are impossible to construct. In recent years, beginning in Kalai [Kal01], much work has been done in finding robust versions of these theorems, showing "approximate" impossibility remains even when most, but not all, of the constraints are satisfied. We study a spectrum of settings between the case where society chooses a single outcome (a-laGibbard-Satterthwaite) and the choice of a complete order (as in Arrow's theorem). We use algebraic techniques, specifically representation theory of the symmetric group, and also prove robust versions of the theorems that we state. Our relaxations of the constraints involve relaxing of a version of "independence of irrelevant alternatives", rather than relaxing the demand of a transitive outcome, as is done in most other robustness results.
اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)247-297
عدد الصفحات51
دوريةIsrael Journal of Mathematics
مستوى الصوت201
رقم الإصدار1
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - يناير 2014

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