Catálogo de publicaciones - libros

A set of new power indices is introduced extending Banzhaf power index and taking into account agents’ preferences to coalesce. An axiomatic characterization of intensity functions representing a desire of agents to coalesce is given. A set of axioms for new power indices is presented and discussed. An example of use of these indices for Russian parliament is given.

Gerrymandering - the artful and partisan manipulation of electoral districts - is a well known pathology of electoral systems, especially majoritarian ones. In this paper, we try to give theoretical and experimental answers to the following questions: 1) How much biased can the assignment of seats be under the effect of gerrymandering? 2) How effective is compactness as a remedy against gerrymandering? Accordingly, the paper is divided into two parts. In the first one, a highly stylized combinatorial model of gerrymandering is studied; in the second one, a more realistic multiobjective graph-partitioning model is adopted and local search techniques are exploited in order to find satisfactory district designs. In a nutshell, our results for the theoretical model mean that gerrymandering is as bad as one can think of and that compactness is as good as one can think of. These conclusions are confirmed to a large extent by the experimental results obtained with the latter model on some medium-large real-life test problems.

This paper characterizes divisor methods for vector and matrix apportion problems with very simple properties. For the vector problem—a vector gives the votes of parties or the populations of states, a single number the size of the house—they are shown to be the only methods that are the definition of the corresponding divisor method when applied to only two states or parties. For the matrix problem—rows correspond to districts, columns to parties, entries to votes for party-lists, and the number of seats due to each row (or district) and each column (or party) is known—one extra property is necessary. The method must be : it must give identical answers to a problem obtained by re-scaling any rows and/or any columns of the matrix of votes.

This note presents an algorithm for computing the minimum total deviation apportionment. Some properties of this apportionment are also explored. This particular apportionment arises from the jurisprudential concern that total deviation is the appropriate measure for the harm caused by malapportionment of the United States House of Representatives.

Simulation may be a useful tool to address some basic problems concerning the choice of the electoral system. A case study is analyzed as an example. The utility of including power indices is discussed. A simulation program is illustrated.

Approval balloting is applied to the problem of electing a representative committee. We demonstrate several procedures for determining a committee based on approval ballots, paying particular attention to weighting methods that can reduce the influence of voters with extreme views. We show that a general class of voting systems based on approval ballots can be implemented through analysis of appropriate tables. A by-product of this procedure is a clarification of the complexity of these systems.

This paper investigates the relationship between Kemeny-type distance functions on the set of choice functions and the original Kemeny distances on the set of binary relations with special emphasis on the set of linear orders. First, it will be shown in what way such distances differ. Second, for the Kemeny-type distance function on the set of choice functions we will provide an explicit expression in terms of the linear orders that rationalize them.

For the biproportional apportionment problem two algorithms are discussed, that are implemented in the Augsburg BAZI program, the alternating scaling algorithm and the tie-and-transfer algorithm of . The goal is to determine an integer-valued apportionment matrix that is “proportional to” a matrix of input weights (e.g. vote counts) and that at the same time achieves prespecified row and column marginals. The alternating scaling algorithm finds the solution of most of the practical problems very efficiently. However, it is possible to create examples for which the procedure fails. The tie-and-transfer algorithm converges always, though convergence may be slow. In order to make use of the benefits of both algorithms, a hybrid version is proposed.

Social choice theory deals with aggregating individual opinions into social choices. Over the past decades a large number of choice methods have been evaluated in terms of various criteria of performance. We focus on methods that can be viewed as distance minimizing ones in the sense that they can be analyzed in terms of a goal state of consensus and the methods themselves can be seen as minimizing the distance of the observed profile from that consensus. The methods, thus, provide a way of measuring the degree of disagreement prevailing in the profile.

Problems of multi-candidate races in U.S. presidential elections—exemplified by Ralph Nader’s spoiler effect in 2000—motivated the modern invention and advocacy of approval voting; but it has not previously been recognized that the first four U.S. presidential elections (1788–1800) were conducted using a variant of approval voting. That experiment ended disastrously in 1800 with an infamous Electoral College tie between Thomas Jefferson and Aaron Burr. The tie, this paper shows, resulted less from miscalculation than from a strategic tension built into approval voting, which forces two leaders appealing to the same voters to play a game of Chicken. All outcomes are possible, but none is satisfactory- mutual cooperation produces a tie, while all-out competition degrades the system to single-vote plurality, which approval voting was designed to replace. In between are two Nash equilibria that give the advantage to whichever candidate enjoys an initial lead or, in the case of initial parity, to the candidate who is less cooperative and more treacherous.