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A central theme in social choice theory is that of impossibility theorems,such as Arrow's theorem and the Gibbard-Satterthwaite theorem, which state thatunder certain natural constraints, social choice mechanisms are impossible toconstruct. In recent years, beginning in Kalai`01, much work has been done infinding \textit{robust} versions of these theorems, showing "approximate"impossibility remains even when most, but not all, of the constraints aresatisfied. We study a spectrum of settings between the case where societychooses a single outcome (\'a-la-Gibbard-Satterthwaite) and the choice of acomplete order (as in Arrow's theorem). We use algebraic techniques,specifically representation theory of the symmetric group, and also proverobust versions of the theorems that we state. Our relaxations of theconstraints involve relaxing of a version of "independence of irrelevantalternatives", rather than relaxing the demand of a transitive outcome, as isdone in most other robustness results.

Between Arrow and Gibbard-Satterthwaite; A representation theoretic approach