Pairwise Majority Research Articles

Popular support for progressive taxation and the relative income hypothesis

We show that a marginal rate progressive tax always defeats a marginal rate regressive tax under pairwise majority voting (so long as the latter collects at least as much revenue as the former one) irrespective of whether the voters care at all about their relative incomes or not.

Paradoxes of voting in list systems of proportional representation

Three voting paradoxes for list systems of proportional representation are presented. The first paradox shows that a party may be preferred by a majority to another party and yet receive fewer seats. The second paradox illustrates that a party which is majority-preferred to every other party may not get the greatest number of seats. Actually, such a party may even be not represented at all in the legislative body. The third paradox shows that a party which is beaten by every other party in a pairwise majority comparison may become the largest party while a party which is majoritypreferred to every other party may become the smallest one.

The effect of social homogeneity on coincidence probabilities for pairwise proportional lottery and simple majority rules

The Condorcet efficiency of Pairwise Proportional Lottery Rules (PPLR) is considered under various assumptions concerning the likelihood that given voters' preference profiles are observed on three alternatives. Representations are developed for the expected Condorcet efficiency under impartial culture, impartial anonymous culture, and a generalization to Polya-Eggenberger distributions. PPLR is shown to be equivalent to a random selection process in the limit of voters under impartial culture. However, relatively small increases in social homogeneity, as measured by Kendall's Coefficient of Concordance, cause significant increases in the Condorcet efficiency of PPLR.

Probability calculations for transitivity of simple majority rule with anonymous voters

Let P(n, 4) denote the probability that there is a pairwise simple majority rule winner on four candidates with n voters under the impartial anonymous culture condition. Similarly, let Pt(n, 4) denote the probability that the complete ranking obtained by pairwise simple majority voting on four candidates with n voters is transitive under the impartial anonymous culture condition. We obtain representations for P(n, 4) and Pt(n, 4), and computed values for each for odd n with 3 ≤ n ≤ 19.

Social decision schemes and choice shift: An analysis of group decisions among bets

The present study analyzes group decisions in terms of current models of social decision scheme (SDS) research and in terms of two new models which simulate pairwise majority voting over all alternatives, the full paired comparison (FPC) and the reduced paired comparison (RPC) models. The latter two models take into account the subjects' rank orders over all alternatives (i.e., they are Condorcet functions). On the basis of their individual preferences in the preexperimental phase, 275 subjects were systematically assigned to 55 five-person groups according to theoretically useful configurations of occupancy numbers. Each five-person group had to choose one of six different bets with equal expected values. In the P-condition the probabilities for the bets were equally spaced; in the M-condition the distances between the money values were kept constant. The results show systematic deviations in at least one condition for all models except the best fitting RPC model. Furthermore a comparison with regard to the precision of the models indicates that RPC is significantly more precise than various other models, whereas no other model does significantly better than RPC. For the RPC model neither systematic bias nor precision varied with condition (P vs M). In addition the RPC model can account for risky shift and general choice shift both on the individual and on the group level. Results are discussed within the framework of SDS and choice-shift research.

Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule

The development of social choice theory over the past three decades has brought many new insights into democratic theory. Surprisingly, the theory of representation has gone almost untouched by social choice theorists. This article redresses this neglect and provides an axiomatic study of one means of implementing proportional representation.The distinguishing feature of proportional representation is its concern for the representativeness of deliberations as well as decisions. We define a representative in a way that is particularly attentive to this feature and then define a method of selecting representatives (a variant of the Borda rule) which selects a maximally representative body. We also prove that this method of selection meets four social choice axioms that are met by a number of other important social choice functions (including pairwise majority decision and the Borda rule).

Preference ranking models: Conditions for equivalence

This paper examines three established consensus methods used to aggregate ordinal rankings—pairwise majority rule, the Borda‐Kendall mean and the Kemeny‐Snell median. It is shown that when voter responses produce a certain form of transitivity, the three approaches result in the same consensus. The necessary transitivity condition is established when voter responses are described by the Dirichlet distribution.

VOTING FOR PUBLIC ALTERNATIVES: SOME NOTES ON MAJORITY RULE

MAJORITY common to voting almost is all an democratic institution co on o lmo t ll democrat c societies, but, as a method of social decision-making, it is vulnerable to attack on several fronts. In this paper I examine some of the well-known shortcomings of majority voting: intransitivity, indecisiveness, and susceptibility to strategic manipulation. Most important, I consider the assertion that majority rule is Pareto inefficient and show that this inefficiency is related to the shape of individuals' utility functions. I also present a result which enables one to predict the direction in which the inefficiency lies. Finally, I show that rank-order voting is likely to improve efficiency. One weakness of majority voting, first enunciated by Condorcet, is its failure, in general, to generate a transitive social ordering of alternatives. Given three alternatives, a, b, and c, a majority of the electorate may prefer a to b and b to c and yet c to a.1 This flaw is far from unique to decision-making by majority rule. As Arrow [1951] has demonstrated, the problem plagues any social choice procedure that satisfies several reasonable conditions. More seriously, majority voting may be non-decisive; a vote may fail to produce a majority winner at all. Non-decisiveness has two possible senses. One is simply that, with more than two candidates on the ballot, none may capture over fifty percent of the vote. Thus, there was concern in the 1968 U.S. Presidential election that George Wallace's presence would prevent either of the real contenders, Richard Nixon and Hubert Humphrey, from obtaining a majority. A second interpretation is that no candidate may emerge victorious even in pair-wise competition against the other alternatives. A pair-wise majority winner was presumably not absent in the 1968 election. That is, most likely Nixon would