Majority voting solution concepts and redistributive taxation

Strong assumptions are usually needed to guarantee the existence of a Condorcet winner in majority voting games. The theoretical literature has developed various solution concepts to accommodate the general absence of Condorcet winner, but very little is known on their economic implications. In this paper, I select three such concepts (the uncovered set, the bipartisan set and the minmax set), defined as game-theoretical solution concepts applied to a Downsian electoral competition game. These concepts are then computed by means of simulations in a simple model of purely redistributive taxation, where factor supply varies with net factor rewards. All three concepts give rather sharp predictions and are not too sensitive to small variations of the preference profiles. Received: 29 December 1997/Accepted: 26 August 1999     

Majority voting rules and the union success rate in national labor relations board representation elections

This paper simulates how the union success rate in representation elections would be affected if the NLRB reverted from its current simple-majority voting rule to its original majority-in-unit voting rule. Such a rule change would have altered 21 percent of decertification and 16 percent of certification victories over the period 1977–81, resulting in the loss of 180,400 actual or potential bargaining unit members for the union movement. Abstentions play an important role in election outcomes. Under the present voting rule unions have no clear advantage to “get out the vote” in decertification elections, but a clear disadvantage in certification elections. Under a majority-in-unit rule unions hold an advantage when they “get out the vote” in all representation elections. I would like to thank Mike Bognanno, Jim Dworkin, Paul Schumann, two reviewers, and the editor for helpful comments and David Wilson for excellent research assistance. I would also like to thank the NLRB for providing the election data tape.     

Yes-no voting

Yes-No (Y-N) voting is a voting method for choosing a governing coalition in a parliament after the seating of its members. Each member can designate a party to be Y (it must be included in the governing coalition), N (it must be excluded from the governing coalition), or neither (it may be either in or out of the governing coalition). The majority coalition acceptable to the most voters, because it includes all parties that these voters designate Y and no parties that they designate N, is given the first opportunity to form a government. Possible combinations of majority coalitions that a member might vote for are derived, including ones based on consistent and interval voting strategies. Examples illustrate a number of different phenomena, such as when a rational voter might not be loyal to his or her party by designating it Y.     

Inequality in voting power

This paper deals with the assessment of inequality in the distribution of voting power. Voting power is evaluated through a general concept of power measurement based on both the voting rule and the probability distribution over vote configurations. This general concept includes as particular cases the most usual power indices and other extensions of this traditional concept. Thus no particular power index is privileged in our approach. An inequality index over the class of all power profiles with a given number of voters generated by this general measure is then singled out by requiring reasonable properties. In order to compare profiles with different numbers of voters, two alternative principles are considered, which extend the said index consistently in two ways.Previous versions of this work were circulated under different titles. We gratefully acknowledge financial support from the Spanish Ministerio de Ciencia y Tecnología under the Ramón y Cajal programme and under projects PB96-0247 and BEC2000-0875; from the European Commission under the Training and Mobility of Researchers programme (contract FMRX - CT966-0055); and from the Instituto Valenciano de Investigaciones Económicas. We also thank two anonymous referees for their comments.2 October 2001     

Majority rule in multi-dimensional spatial models

A sufficient condition is derived for a policy y to be a Condorcet winner, when the set of feasible policies is some subsety ofR ^N with non-empty interior. Voters are assumed to differ in some scalar characteristic w. The sufficient condition refers only to voters' preferences over the set of preferred policies (of the various other voters). This set is a one-dimensional curve inR ^N> . The condition is that the indifference curves of each typew through the preferred policyy ^* (v) of any typev all be collinear. If the condition holds, then the preferred policyy ^* (m) of the median type of voter will be a Condorcet winner. If there are only three types of voter, then the above condition is also necessary for the existence of a Condorcet winner.This paper is a revision of the first part of my earlier Majority Rule with Multidimensional Economic Choices. I thank Ted Bergstrom, David Donaldson, and Greg Dow for very valuable comments on versions of that earlier paper, without implicating them in this current incarnation.     

Iterative elimination of weakly dominated strategies in binary voting agendas with sequential voting

This paper describes the correspondences between the results given by backward induction (BI) and iterative elimination of weakly dominated strategies (IEWDS) in binary voting agendas with sequential voting. When the voters have strict preferences over all candidates, the strategies that survive IEWDS all select the unique candidate selected by the BI strategy profiles. But if some voters are indifferent, this result no longer holds. However, when there are only two candidates, it is possible to demonstrate strong relationships between the results given by BI and IEWDS, even when some voters have indifferences.     

Strategic voting in repeated referenda

This paper analyzes learning and voting strategy when a budget maximizing bureaucrat has several chances to obtain referendum approval. The process is modeled as a sequential game with a continuum of heterogeneous voters and a dominant bureaucrat in which all agents are uncertain about the true distribution of voter preferences. The equilibrium concept is perfect Bayes Nash, so voting is strategic in the sense of foresighted but nevertheless noncooperative.Thanks to R. Gretlein, J. Hamilton, T. Palfrey, T. Romer, H. Rosenthal, S. Slutsky and the referees of this journal for their comments and encouragement. They are not responsible for any errors or omissions.     

Fairness and voting

In this paper we present a two-period model in which we examine how concern about fairness might affect voter behavior. We show that in the first period politicians choose the median voter’s position even if this does not correspond to their bliss points and neither they nor the voters can commit to a particular action. Moreover, concern about fairness creates substantial incumbency advantages. Our results hold even if voters care very little about fairness.     

Visible Minorities and Majority Giving

We examine if the presence of minority individuals in the community affects the decision to give to charities by majority individuals. We focus on two giving decisions by the majority population. The first is giving to any charitable organization; the second is giving to organizations geared to international causes. We also examine these two decisions when the sample is split into religious and non-religious individuals. We find that the larger the proportion of minorities in a given community, the less likely that members of the majority group give to charity in general—supporting the idea that heterogeneous communities deter outreach—but the more likely they are to give to international causes, giving credence to Allport’s ‘contact’ hypothesis.     

Majority vote following a debate

Voters determine their preferences over alternatives based on cases (or arguments) that are raised in the public debate. Each voter is characterized by a matrix, measuring how much support each case lends to each alternative, and her ranking is additive in cases. We show that the majority vote in such a society can be any function from sets of cases to binary relations over alternatives. A similar result holds for voting with quota in the case of two alternatives.We wish to thank Enriqueta Aragones, Jean-Francois Laslier, Andrew Postlewaite, and David Schmeidler for the comments and discussions. We thank Lada Burde for her help in proofreading.     

Powers of subgroups in voting bodies

This paper discusses the power p _n of an n-member subgroup B _n of an N-member voting body, N odd and 1 n N. In contrast to bloc voting, we assume that the members vote independently with equal probability for and against a given issue. Power p _n is defined as the probability that the outcome of a vote changes if all members of B _n reverse their votes. Theorems: p _{n + 1} = _n for odd n < N; p _n + p _{N – n} = 1; P _m + p _n > p _{m + n} if m + n < N; p _{n + 1}/p _n (n + 1)/n as N for fixed even n; for rational 0 > > 1, p _N 2^–1 sin^{–1 1/2} as N . A simple summation formula is given for p _n .     

Approval voting and positional voting methods: Inference,relationship, examples

Approval voting is the voting method recently adopted by the Society for Social Choice and Welfare. Positional voting methods include the famous plurality, antiplurality, and Borda methods. We extend the inference framework of Tsetlin and Regenwetter (2003) from majority rule to approval voting and all positional voting methods. We also establish a link between approval voting and positional voting methods whenever Falmagne et al.s (1996) size-independent model of approval voting holds: In all such cases, approval voting mimics some positional voting method. We illustrate our inference framework by analyzing approval voting and ranking data, with and without the assumption of the size-independent model. For many of the existing data, including the Society for Social Choice and Welfare election analyzed by Brams and Fishburn (2001) and Saari (2001), low turnout implies that inferences drawn from such elections carry low (statistical) confidence. Whenever solid inferences are possible, we find that, under certain statistical assumptions, approval voting tends to agree with positional voting methods, and with Borda, in particular.Michel Regenwetter thanks the National Science Foundation for funding this research through NSF grant SBR 97-30076. Both authors thank the Fuqua School of Business for financially supporting their collaboration. Most of this research was done while Regenwetter was a faculty member at Fuqua. We thank Prof. Steven Brams for his valuable comments as a discussant of a previous version of this paper, given at the 2002 Public Choice meeting, and Prof. Donald Saari for his helpful comments in conversations and on another draft. We also thank the editor in charge and a referee for their valuable comments. Tsetlin acknowledges the support of the Centre for Decision Making and Risk Analysis at INSEAD.     

Pareto optimality in spatial voting models

This paper studies the Pareto optimality properties of policy proposals that are made byk(k2) strategic candidates that face uncertainty about the choices that the voters will make. Our first theorem shows that, under very general conditions, any proposal that is a best reply for a candidate is necessarily Pareto optimal. This theorem, in turn, implies that, under slightly stronger conditions, all candidate proposals that are made in a Nash equilibrium or sequentially are necessarily Pareto optimal. Our second theorem shows that, when these conditions are themselves slightly strengthened, any proposal outside of the Pareto set is strictly dominated by at least one proposal inside the Pareto set.We would like to acknowledge helpful comments and suggestions provided by Otto Davis and Richard McKelvey     

Strategy versus sincerity in mean voting

This paper focuses on the mean vote procedure for choosing the quantity of a public good, a social choice rule that selects the mean of the quantities voted for. The available theoretical models of mean voting give rise to conflicting predictions about the extent of the strategic bias that might arise in the individual vote. An experiment has been run in order to assess whether the participants disclose their (induced) preferences in voting or whether they strategically manipulate their vote, and in the latter case, which variables impact upon the likelihood of strategic bias and to what extent.     

Probabilistic Borda rule voting

An alternative voting system, referred to as probabilistic Borda rule, is developed and analyzed. The winning alternative under this system is chosen by lottery where the weights are determined from each alternatives Borda score relative to all Borda points possible. Advantages of the lottery include the elimination of strategic voting on the set of alternatives under consideration and breaking the tyranny of majority coalitions. Disadvantages include an increased incentive for strategic introduction of new alternatives to alter the lottery weights, and the possible selection of a Condorcet loser. Normative axiomatic properties of the system are also considered. It is shown this system satisfies the axiomatic properties of the standard Borda procedure in a probabilistic fashion.I thank Nic Tideman and Andrew Yates for helpful comments and especially appreciate detailed criticism from Keith Dougherty which greatly improved the exposition of the text. In addition, Don Saari, in his role as editor, suggested a number of clarifications and an important extension for which I am grateful. I accept full responsibility for any remaining shortcomings.     

Equal representation in two-tier voting systems

The paper investigates how voting weights should be assigned to differently sized constituencies of an assembly. The one-person, one-vote principle is interpreted as calling for a priori equal indirect influence on decisions. The latter are elements of a one-dimensional convex policy space and may result from strategic behavior consistent with the median voter theorem. Numerous artificial constituency configurations, the EU and the US are investigated by Monte–Carlo simulations. Penrose’s square root rule, which originally applies to preference-free dichotomous decision environments and holds only under very specific conditions, comes close to ensuring equal representation. It is thus more robust than previously suggested.     

Constructions of Europe in the run-up to the EU referendum in the UK

The paper reports findings from a focus group study on representations of Europe, conducted in England in the run-up to the UK EU referendum. Four themes were identified in the analysis: ‘cultured Europe’; ‘little Europe/global Britain’; ‘Europe as a cultural threat’; and ‘Eastern vs. Western Europe’. Analysis of these themes showed that Europe was an ambivalent identity category that could encapsulate contrary ideas such as cosmopolitanism/isolationism and cultural enrichment/undermining. Europe’s relation to Britain was also ambivalent in the data. Britain could be positioned as superior to Europe, sometimes being seen as closer to the ‘European essence’ in the context of the EU’s eastward expansion, which was seen as diluting European culture. But, Britain could also be seen as backward compared to the idea of cosmopolitan continental Europe. These different lines of argument and their ideological underpinnings are explored in the discussion of the findings.     

On power distribution in weighted voting

We study here the strategic possibilities in a voting system where, in weight terms, there is a single main agent and the others are equivalent. As an alternative to the coalition formation, we suggest for the minor agents a more discreet, anonymous and solidary behavior based on commitments referred to the size of the coalitions that they would agree to form. In order to analyze, in a coherent way, the effects of such commitments on the a priori power distribution, we use as measures of power the Shapley value and a certain class of semivalues closely related to it.Research partially supported by Grant BFM 2003–01314 of the Science and Technology Spanish Ministry. The authors wish to thank Professor Maurice Salles and two anonymous referees for their stimulating comments.     

Strategic voting and nomination

Using computer simulations based on three separate data generating processes, I estimate the fraction of elections in which sincere voting is a core equilibrium given each of eight single-winner voting rules. Additionally, I determine how often each rule is vulnerable to simple voting strategies such as ‘burying’ and ‘compromising’, and how often each rule gives an incentive for non-winning candidates to enter or leave races. I find that Hare is least vulnerable to strategic voting in general, whereas Borda, Coombs, approval, and range are most vulnerable. I find that plurality is most vulnerable to compromising and strategic exit (causing an unusually strong tendency toward two-party systems), and that Borda is most vulnerable to strategic entry. I use analytical proofs to provide further intuition for some of my key results.