Distances in Voting and Committee Election Rules for General Preference Types

摘要

Distances have a major role in voting theory. They can determine the outcome of an election or ways to influence elections via manipulation or bribery. In the first part of this abstract, previotus results concerning distance-based committee election rules are summarized, while current research questions are introduced in the second part. There is detailed work on elections where the desirable outcome of an election is a single winner. However, in many situations a group of candidates is supposed to be elected, such as a group of people for a certain project, a delegation of politicians, or a selection of food for a party. Here we use a setting in which the size of the committee is fixed, such that a committee election is defined by a tuple (C, V, k), where C = {c_1,..., c_m} is the set of candidates, V = (v_1,... v_n) a list of all votes given by the voters in the set {1,..., n}, and k the committee size. As election rules the minisum- and minimax approaches are used. Brams et al. [5] studied these procedures regarding approval voting and Baumeister and Dennisen [3] enlarged on this matter by also considering trichotomous votes, incomplete-, and complete linear orders. The complexity of winner determination and manipulation of these different variations was studied by Baumeister et al. [4].