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The Faroese electoral system uses a method of proportional representation for distributing the seats in the Faroese Parliament (The Løgting). The electoral formulae attempt to give each political party a number of seats that is close to its vote share. In addition, each district should receive a number of delegates that is proportional to the number of voters in the district. We show that the current electoral formula has significant weaknesses, and propose 7 alternative electoral formulae which consider various subsets of constraints — such as lower bounds on the number of seats in districts and electoral thresholds. Numerical simulations with the current and proposed electoral formulae on the elections from 1978 to 2004, and on randomly generated election results, are presented. The results show that some of the proposed alternatives clearly are superior to the current electoral formula with respect to well-known quality measures. [ABSTRACT FROM AUTHOR]

The complexities of voting theory are captured by Arrow's Impossibility Theorem and McKelvey's chaos result in spatial voting. A careful analysis of Arrow's theorem, however, proves that not all of the supplied information is used by the decision rule. As such, not only does this seminal result admit a benign interpretation, but there are several ways to sidestep Arrow's negative conclusion. McKelvey's result is described in terms of more general voting rules. Then a new solution concept, called the ‘finesse point', is introduced. This centrally located point generalizes the core and minimizes what it takes to respond to any proposal by another person. [ABSTRACT FROM AUTHOR]

In this work we present several methods for distributing the seats of the European Parliament amongst the States of the European Union, in accordance with the restrictions established in article I-20 of the projected European Constitution. The proposed methods can be applied to the current composition of the EU, but also if there is a change in the number of states or their populations. They are based on adjusting the quotas of every country so that they verify the constitutional restrictions, and so that their rounding to an integer number will constitute an allotment of the seats of the Parliament. [ABSTRACT FROM AUTHOR]

The divisor method with standard rounding (Sainte-Laguë/Schepers) is amended by a gentle majority clause, in order to map the government majority in parliament into a seat majority in committees. [ABSTRACT FROM AUTHOR]

In this paper we show results for some unipersonal and pluripersonal elections in Ecuador and in Spain, observing that the used methods can be replaced by better ones. We present a method for individual elections based on one-on-one comparisons, and preferential voting. This method verifies CONDORCET and PARETO, and it is furthermore better than the Two Round method. For multicandidate elections we give proportional and monotone methods based on preferential vote. We also analyse the electoral system of Ecuador and propose alternatives for it. [ABSTRACT FROM AUTHOR]

Three apportionment problems are addressed that are of current interest in Germany and Switzerland: the assignment of committee seats in a way that preserves the parliamentary majority-minority relation, the introduction of minimum restrictions in a two-ballot system to accommodate the direct seats won by the constituency ballots, and biproportional apportionment methods for systems with multiple districts so as to achieve proportionality between party votes as well as between district populations. [ABSTRACT FROM AUTHOR]

There is a serious technical flaw in the newly approved Italian electoral law. The flaw lies in the method used to allocate the Chamber of Deputies seats to parties (or coalitions) within multi-member regional constituencies. The procedure stated in the law could produce contradictory results: it could end up assigning a party more (or less) seats than it is entitled to receive on the basis of the same law. At least two types of paradoxes may occur. Although they have been utterly overlooked in the debate over electoral reform, they can be critical in practice when trying to determine the actual seat allocation. The failure of the current Italian electoral law was inherited from the previous one but the consequences are worse. Moreover, a correction mechanism introduced into the law at the last-minute does not prevent it from producing contradictory results. The paradoxes that undermine the Italian electoral law are pointed out and a solution is proposed. A broad conclusion is that a more extensive use of mathematics in the design and evaluation of electoral systems would help identify flaws and deliver more transparent, logical and fairer electoral laws. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 Balinski and Demange (1989b). 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 coherent with 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 proportional: it must give identical answers to a problem obtained by re-scaling any rows and/or any columns of the matrix of votes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]