Voting Rules

May's theorem famously shows that, in social decisions between two options, simple majority rule uniquely satisfies four appealing conditions. Although this result is often cited in support of majority rule, it has never been extended beyond decisions based on pairwise comparisons of options. We generalize May's theorem to many-option decisions where voters each cast one vote. Surprisingly, plurality rule uniquely satisfies May's conditions. This suggests a conditional defense of plurality rule: If a society's balloting procedure collects only a single vote from each voter, then plurality rule is the uniquely compelling electoral procedure. To illustrate the conditional nature of this claim, we also identify a richer informational environment in which approval voting, not plurality rule, is supported by a May-style argument.
Preprint: http://eprints.lse.ac.uk/5818/1/A_conditional_defense_of_plurality_rule_%28LSERO%29.pdf

"Supermajorities have their advantage as well as their disadvantage: they provide an hedge against being in the minority, but they make being in the majority less likely. We characterize this trade-off and compute the most preferred majority threshold. The relevant parameters are voting power, risk aversion and pessimism. People who feel powerful prefer low thresholds. High thresholds are preferred by risk averters or by those who are pessimistic about being in the majority.
Further we study constitutional agreements on the voting rule. Members of the constituent assembly are heterogeneous in the parameters above. We show that weak and minority members succeed in pushing forward on high and protective rule"

""We study political distortions that emerge in situations where agents' political power is disproportionate with respect to their economic power. We provide a specific definition which adopts the same measure unit, the Shapley value, to evaluate both the economic and the political power. We show that usual weighted majority voting cannot prevent political distortions from emerging in a huge mass of situations. We propose an alternative voting method based on random assignments of voting rights. Agents are given chances to vote instead of weights. If chances are computed according to a specific formula, no political distortion occurs.
As an application, we analyze the rotation voting system recently adopted by the European Central Bank. We find that this system yields an enormous amount of political distortion. Then we compute the voting chances that should be assigned to countries in order to eliminate it..""

" Elections européennes : l'option du vote préférentiel ", Note à l'attention de M. Alain Tourret, rapporteur pour la commission des Lois de l'Assemblée nationale du projet de loi relatif à l'élection des représentants au Parlement européen (n° 539), 23 janvier 2018, 3 pages.

The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections. The Condorcet efficiency of a voting procedure is the conditional probability that it will elect the Condorcet winner, given that a Condorcet winner exists. The study considers the Condorcet efficiency of weighted scoring rules (WSR’s) on three candidates for large electorates when voter indifference between candidates is allowed. It is shown that increasing the proportion of voters who have partial indifference will increase the probability that a Condorcet winner exists, and will also increase the Condorcet efficiency of all WSR’s. The same observation is observed when the proportion of voters with complete preferences on candidates is reduced. Borda Rule is shown to be the WSR with maximum Condorcet efficiency over a broad range of assumptions related to voter preferences. The result of forcing voters to completely rank all candidates, by random...