A minimax procedure for electing committees

A new voting procedure for electing committees, called the minimax procedure, is described. Based on approval balloting, it chooses the committee that minimizes the maximum Hamming distance to voters’ ballots, where these ballots are weighted by their proximity to other voters’ ballots. This minimax outcome may be diametrically opposed to the outcome obtained by aggregating approval votes in the usual manner, which minimizes the sum of the Hamming distances and is called the minisum outcome. The manipulability of these procedures, and their applicability when election outcomes are restricted in various ways, are also investigated. The minimax procedure is applied to the 2003 Game Theory Society election of a council of 12 new members from a list of 24 candidates. By rendering outlying voters less influential and not antagonizing any voters too much, it arguably would have produced a committee more representative of the interests of all voters than the minisum committee that was elected.     

Dead Heat: The 2006 Public Choice Society Election

In 2006, the Public Choice Society chose a new president using approval voting. There were five candidates, and the election was extremely close. We indicate the sources of support of the different candidates, based in part on spectral analysis, by voters who cast between one and five votes. Using preference information that was also gathered, we show that two candidates different from the approval voting winner, including the apparent Condorcet winner, might have won under different voting systems. Because most voters did not indicate their complete preference rankings, however, these differences are hardly robust, especially since the outcome was essentially a dead heat.     

Efficacy,power and equity under approval voting

Approval voting allows each voter to vote for as many candidates as he wishes in a multicandidate election. Previous studies show that approval voting compares favorably with other practicable election systems. The present study examines the extent to which votes for different numbers of candidates can affect the outcome. It also considers generic powers of voters and the extent to which approval voting treats voters equitably. If there are three candidates, votes for one or two candidates are equally efficacious in large electorates. For four or more candidates, votes for about half the candidates are most efficacious. Although inequities among voters can arise under approval voting, the common plurality voting system is considerably less equitable than approval voting.     

The paradox of grading systems

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, using two or more grades. In approval voting, voters can assign two grades only—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.     

Multiwinner approval voting: an apportionment approach

Public Choice - To ameliorate ideological or partisan cleavages in councils and legislatures, we propose modifications of approval voting in order to elect multiple winners, who may be either...     

Influence in Terrorist Networks: From Undirected to Directed Graphs

A methodology for converting terrorist networks from undirected graphs to simplified directed graphs (or digraphs), and mapping the flow of influence in them, is described. It is based on an “influence assumption”—that important persons with more links influence less important persons with fewer links. This methodology, which was previously used to analyze the structure of influence relationships in Communist-bloc countries and the international system, is illustrated by its application to two terrorist networks constructed after 9/11. In the second more complex network, the hierarchy sheds light on the leadership and likely terrorist cells embedded in the network. Refined data and alternative assumptions about influence could provide additional insights into the structure of terrorist networks.     

Coalition formation on the U.S. Supreme Court: 1969–2009

We apply a fallback model of coalition formation to decisions of the U.S. Supreme Court, focusing on the seven natural courts, which had the same members for at least two terms, between 1969 and 2009. The predictions of majority coalitions on each of the courts are generally borne out by the 5–4 decisions, whereas the predictions of the Martin-Quinn (Political Analysis 10(2):134–153, 2002) model, which assumes a single underlying dimension along which the justices can be ordered, are not. The present model also provides insight into the dynamic process by which subcoalitions build up into majority coalitions and, in addition, identifies “kingmakers” and “leaders” on the natural courts. Furthermore, it provides evidence, from coalitional memberships, that a few justices shifted over time from one ideological camp to another.