Single transferable vote

Abstract: A simple model is used to compare, under different electoral systems, the incentives for candidates to create inequalities among otherwise homogeneous voters, by making campaign promises that favor small groups, rather than appealing equally to all voters. In this game model, each candidate generates offers for voters independently out of a distribution that is chosen by the candidate, subject only to the constraints that offers must be nonnegative and have mean 1. Symmetric equilibria with sincere voting are analyzed for two-candidate elections and for multicandidate elections under rank-scoring rules, approval voting, and single transferable vote. Voting rules that can guarantee representation for minorities in multiseat elections generate, in this model, the most severely unequal campaign promises.

Abstract: We give evidence that Single Tranferable Vote (STV) is computationally resistant to manipulation: It is NP-complete to determine whether there exists a (possibly insincere) preference that will elect a favored candidate, even in an election for a single seat. Thus strategic voting under STV is qualitatively more dicult than under other commonly-used voting schemes. Furthermore, this resistance to manipulation is inherent to STV and does not depend on hopeful extraneous assumptions like the presumed diculty of learning the preferences of the other voters. We also prove that it is NP-complete to recognize when an STV election violates monotonicity. This suggests that non-monotonicity in STV elections might be perceived as less threatening since it is in eect “hidden” and hard to exploit for strategic advantage.

Abstract: In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using protocols where determining a beneficial manipulation is hard. Especially among computational agents, it is reasonable to measure this hardness by computational complexity. Some earlier work has been done in this area, but it was assumed that the number of voters and candidates is unbounded. Such hardness results lose relevance when the number of candidates is small, because manipulation algorithms that are exponential only in the number of candidates (and only slightly so) might be available. We give such an algorithm for an individual agent to manipulate the Single Transferable Vote (STV) protocol, which has been shown hard to manipulate in the above sense. This motivates the core of this article, which derives hardness results for realistic elections where the number of candidates is a small constant (but the number of voters can be large).The main manipulation question we study is that of coalitional manipulation by weighted voters. (We show that for simpler manipulation problems, manipulation cannot be hard with few candidates.) We study both constructive manipulation (making a given candidate win) and destructive manipulation (making a given candidate not win). We characterize the exact number of candidates for which manipulation becomes hard for the plurality, Borda, STV, Copeland, maximin, veto, plurality with runoff, regular cup, and randomized cup protocols. We also show that hardness of manipulation in this setting implies hardness of manipulation by an individual in unweighted settings when there is uncertainty about the others' votes (but not vice-versa). To our knowledge, these are the first results on the hardness of manipulation when there is uncertainty about the others' votes.

Abstract: The relationship between electoral systems can be examined on a number of dimensions. Seat allocation methods are conveniently divided into two groups: those based on largest remainders and those based on highest averages. The single transferable vote has its own distinct characteristics. Focusing on certain elements – the quota, thresholds, paradoxes and the conditions under which a majority of seats can be won – enables comparisons to be drawn between seat allocation methods. Certain seat allocation methods conventionally seen as variants of proportional representation (PR) cannot be regarded as such. PR methods can be rank ordered according to whether, when complete proportionality is not attainable, they display electoral bias towards larger or smaller parties. However, a definitive ordering is elusive, since some methods that are generally more favourable to larger parties can in some circumstances set lower thresholds of representation than methods generally favourable to smaller parties.