Measuring majority power and veto power of voting rules

Abstract

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful, and whether minorities can veto the candidates they do not prefer. For a given voting rule, the minimal share of voters that guarantees a victory to one of their most preferred candidates is the measure of majority power, and the minimal share of voters that allows them to veto each of their least preferred candidates is the measure of veto power. We find tight bounds on these minimal shares for voting rules that are popular in the literature and in real elections. We order these rules according to majority power and veto power. The instant-runoff voting has both the highest majority power and the highest veto power and the plurality rule has the lowest. In general, the higher the majority power of a voting rule is, the higher its veto power. The three exceptions are: voting with proportional veto power, Black's rule, and Borda rule, which have a relatively low level of majority power and a high level of veto power and thus provide minority protection. Our results can shed light on how voting rules provide different incentives for voter participation and candidate nomination.

An integrated probabilistic linguistic projection method for MCGDM based on ELECTRE III and the weighted convex median voting rule

“…Liao, Wu, et al (2019) improved the Borda rule with the weights of decision makers and introduced the weighted Borda rule to obtain the rankings of alternatives. Borda rule, as one of various positional voting methods, often has different results from other methods (Kondratev & Nesterov, 2018). To arrive at a reasonable result, we explore the convex median voting rule and improve it by using the weight of decision makers.…”

“…Convex median voting rule is based on truncated Borda scores, convex scoring rules and the WMM criterion (Kondratev, 2018). Convex median voting rule is defined as follows.Definition (Kondratev & Nesterov, 2018). Let n i ( a j ) represent the number of alternatives, a j , in the i th position in descending order.…”

“…The best alternative is the candidate with the highest score of the weighted convex median. Convex median is an extension of the Borda rule, which meets positional dominance, positive responsiveness and WMM (Kondratev & Nesterov, 2018).…”

“…The best one is selected by comparing the scores among alternatives. This approach not only compensates for the shortcomings of Black's rule, but also meets the WMM (Kondratev & Nesterov, 2018).…”

“…The Black's rule, a combination of the Borda rule and the majority rule (Kondratev, 2018), can obtain more reasonable results than the Borda rule. Convex median voting rule, an improvement on the Black's rule, satisfies weak mutual majority (WMM) (Kondratev & Nesterov, 2018). Thus, convex median voting rule is chosen to aggregate the ranking results.…”