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We provide a general analytic approach for calculating the Threshold of Exclusion (TE) for the single-seat and the multi-seat versions of all scoring rules , an infinitely large class of voting systems (Fishburn, 1973; Young, 1975; Saari, 1994, 1995). We offer specific results for two rules used for parliamentary elections at the national level: Borda (Black, 1958), used for national elections to special reserved seats for Hungarian and Italian ethnic minorities in Slovenia, and the unique and little known electoral system used for legislative elections on the Pacific Island state of Nauru, the Dowdall rule . When voters are required to provide a complete ranking of all candidates, we find that Borda does not, in general, operate as a majoritarian system in that a supermajority of roughly 2/3 rd is required to guarantee electing a candidate of choice. In contrast, we find that, as district magnitude increases, the Threshold of Exclusion for the Dowdall rule tends to zero, in the same way as do list systems of proportional representation (PR). However, in contrast to the case for list PR rules, TE for Dowdall can still be relatively close to 1 2 for small district magnitudes. [ABSTRACT FROM AUTHOR]

The Laakso-Taagepera index (Laakso and Taagepera, 1979) has become the most commonly used measure to specify the 'effective' number of political parties in a party system where parties vary substantially in their vote and/or seat shares. It is well known that the Laakso-Taagepera index is the inverse of the even more widely used Herfindahl-Hirschman index of concentration (Hirschman, 1945; Herfindahl, 1950; cf. Taagepera and Grofman, 1981). Drawing on little known work by Feld and Grofman (1977, 1980) on the so called 'class-size paradox', it can also be shown that both indices may be re-expressed as simple functions of a distribution's mean and variance. As far as we can judge, these latter relationships appear to be unknown in the party and electoral systems literatures. By expressing the Herfindahl-Hirschman index and the Laakso-Taagepera index in terms of means and variances we can see that each index has a 'natural' interpretation in terms of well known statistical parameters which allows their fundamental mathematical properties to be more clearly revealed. [ABSTRACT FROM AUTHOR]

We consider four factors relevant to picking a voting rule to be used to select a single candidate from among a set of choices: (1) avoidance of Condorcet losers, (2) choice of Condorcet winners, (3) resistance to manipulability via strategic voting, (4) simplicity. However, we do not try to evaluate all voting rules that might be used to select a single alternative. Rather, our focus is restricted to a comparison between a rule which, under the name ‘instant runoff,’ has recently been pushed by electoral reformers in the US to replace plurality-based elections, and which has been advocated for use in plural societies as a means of mitigating ethnic conflict; and another similar rule, the ‘Coombs rule.’ In both rules, voters are required to rank order candidates. Using the instant runoff, the candidate with the fewest first place votes is eliminated; while under the Coombs rule, the candidate with the most last place votes is eliminated. The instant runoff is familiar to electoral system specialists under the name ‘alternative vote’ (i.e., the single transferable vote restricted to choice of a single candidate). The Coombs rule has gone virtually unmentioned in the electoral systems literature (see, however, ). Rather than considering the properties of these two rules in the abstract, we evaluate them in the politically realistic situations where voters are posited to have (at least on balance) single-peaked preferences over alternatives. Evaluating the two rules under this assumption, we argue that the Coombs rule is directly comparable in that Coombs is always as good as AV with respect to two of our four criteria and it is clearly superior to AV with respect to one of the four criteria, namely criterion (2), and is potentially inferior only with respect to criterion (3). Key to this argument are two new propositions. The first new result shows that, under the posited assumption, for four alternatives or fewer, AV is always as likely or more likely to select the Condorcet winner than plurality. The second new result shows that, under the same assumptions, the Coombs rule will always select the Condorcet winner regardless of the number of alternatives. [Copyright &y& Elsevier]

Presents an intuitive geometric approach to necessary and sufficient conditions for a majority winner in n-dimensional spatial voting games. 'Demystification' of social choice theory; Construction of agenda manipulating trajectories; Offer of lemmas to help understand the basic dynamics of spatial voting games; Black's (1948, 1958) 'median voter.'

Niemi (1969), in an important but neglected paper, found that when orderings were drawn from a simulation based on the impartial culture, the greater the proportion of voter orderings that were single-peaked (a condition he called partial single-peakedness), the more likely was there to be a transitive group ordering. Niemi also found that the likelihood of transitivity increased with n, group size - approaching one as n grew large. Niemi's simulation was restricted to the case of three alternatives. Also, he provided no theoretical explanation for the results of his simulation. Here we provide a theoretical explanation for Niemi's results in terms of a model based on the idea of net preferences, and we extend his results for the general case of any finite number of alternatives, m, for electorates that are large relative to the number of alternatives being considered. In addition to providing a rationale for Niemi's (1969) simulation results, the ideas of net preferences and opposite preference we make use of have a wide range of potential applications. [ABSTRACT FROM AUTHOR]

Discusses the accuracy of group majority decisions in groups with assess members. Practical problem in collective decision making; Definition of an average competence of a group; Propositions about the relationship between individual and group competence.

In the spatial context, when preferences can be characterized by circular indifference curves, we show that we can derive all the information about the majority preference relationship In a space from the win-set of any single point. Furthermore, the size of win sets increases for points along any ray outward from a central point in the space, the point that is the center of the yolk. To prove these results we employ a useful new geometric construction, the half-win set. The implication of these results is that embedding choice in a continuous n-dimensional space imposes great constraints on the nature of the majority-preference relationship. [ABSTRACT FROM AUTHOR]

We consider a new solution set for majority voting tournaments recently proposed by Banks (1985), and we examine its internal structure. In particular, we demonstrate that, in the absence of a Condorcet winner, there is always a cycle including precisely the points in the Banks set. We introduce the concept of "external stability" in order to facilitate analysis. [ABSTRACT FROM AUTHOR]

We present some basic results concerning the spatial theory of voting in such a way that the theorems and their proofs should be accessible to a broad audience of political scientists. We do this by making the presentation essentially geometrical. We present the following results in particular: Plott's 'pairwise symmetry' condition for an unbeaten point; McKelvey's 'global cycling' theorem; Ferejohn, McKelvey and Packel's cardioid construction for establishing bounds on a 'win set'; and McKelvey's circular bound on the 'uncovered set' of points [ABSTRACT FROM AUTHOR]