Making a voting system depend only on orders of preference reduces its manipulability rate

François Durand 1, 2 Fabien Mathieu 1, 3 Ludovic Noirie 1, 3
2 GANG - Networks, Graphs and Algorithms
LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications, Inria Paris-Rocquencourt
Abstract : For any non-trivial voting system, there exists manipulable situations where a coalition of voters, by casting an insincere ballot, may secure an outcome that is better from their point of view. In this paper, we investigate how it is possible to reduce the manipulability rate, which is the probability of such situations in a given culture, i.e. a probabilistic structure of the population. We prove that when electors are independent, the culture meets a condition that we call decomposability. And when this condition is met, for any voting system that uses more complex ballots than orders of preferences (for example grades), there exists a "reasonable" voting system that depends only on orders of preference and whose manipulability rate is at most as high. Combining this result with Condorcification theorem from Durand et al. (2014) and Green-Armytage et al. (2014), we conclude that when searching for a "reasonable" voting system whose manipulability is minimal, one can restrict to those that depend only on orders of preference and meet the Condorcet criterion.
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François Durand, Fabien Mathieu, Ludovic Noirie. Making a voting system depend only on orders of preference reduces its manipulability rate. [Research Report] 2014, pp.26. ⟨hal-01009136⟩

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