Israel Journal of Mathematics

, Volume 201, Issue 1, pp 247–297 | Cite as

Between arrow and Gibbard-Satterthwaite; A representation theoretic approach

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Abstract

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 (à-la-Gibbard-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.

Keywords

Boolean Function Cayley Graph Constraint Satisfaction Problem Social Welfare Function Social Choice Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Hebrew University of Jerusalem 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  2. 2.Faculty of Mathematics and Computer ScienceWeizmann Institute of ScienceRehovotIsrael

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