Almost all social choice rules are highly manipulable, but a few aren't

Abstract

Explores, for several classes of social choice rules, the distribution of the number of profiles at which a rule can be strategically manipulated. In this paper, we will do comparative social choice, looking for information about how social choice rules compare in their vulnerability to strategic misrepresentation of preferences.

The Geometry of Manipulation: A Quantitative Proof of the Gibbard-Satterthwaite Theorem

“…However these constructions considered worst case analysis-they did not rule out the possibility that on average, finding a manipulation may be easy. Indeed, some results showed that finding manipulations is easy on average for certain restricted classes of social choice functions [PR06,CS06,Kel93] (see also the survey [FP10]). …”

On the Average Minimum Size of a Manipulating Coalition

“…To answer this question, various indices of manipulability of voting rules have been introduced and studied [1,8,14,20,21] and various models introduced [2,21]. Among the models the following two have gained the lion's share of attention.…”

Strategyproof Social Choice

“…One of the concepts that have been used is that of susceptibility to manipulation. In fact, the idea that there one can measure the degree of manipulability of di¤erent rules was developed by Kelly (1993) and further studied by Aleskerov and Kurbanov (1999). These works concentrate on the relative size of the subdomains where the rules do satisfy the exact version of strategy-proofness.…”