Voting schemes for which it can be difficult to tell who won the election

We show that a voting scheme suggested by Lewis Carroll can be impractical in that it can be computationally prohibitive (specifically, NP-hard) to determine whether any particular candidate has won an election. We also suggest a class of impracticality theorems which say that any fair voting scheme must, in the worst-case, require excessive computation to determine a winner.Presented at Purdue University, March 1987; at the University of Arizona, April 1987; at Massachusetts Institute of Technology, April 1987; at Yale University, November 1987; at Centre International de Rencontres Mathematiques, Marseille-Luminy, April 1988. This research was supported in part by Presidential Young Investigator Awards from the National Science Foundation to the first two authors (ECS-8351313 and ECS-8451032), and by grant N00014-86-K-0173 from the Office of Naval Research.The authors thank the editor and three anonymous referees for many helpful suggestions.     

Recognizing majority-rule equilibrium in spatial voting games

It is provably difficult (NP-complete) to determine whether a given point can be defeated in a majority-rule spatial voting game. Nevertheless, one can easily generate a point with the property that if any point cannot be defeated, then this point cannot be defeated. Our results suggest that majority-rule equilibrium can exist as a purely practical matter: when the number of voters and the dimension of the policy space are both large, it can be too difficult to find an alternative to defeat the status quo. It is also computationally difficult to determine the radius of the yolk or the Nakamura number of a weighted voting game.We are grateful to Norman Schofield and an anonymous referee for many helpful suggestions.The first author was supported in part by a Presidential Young Investigator Award from the National Science Foundation (ECS-8351313) and by the Office of Naval Research (N00014-85-K-0147). The third author was supported in part by a Presendential Young Investigator Award from the National Science Foundation (ECS-8451032).     

Partially efficient voting by committees

On the separable preference domain, voting by committees is the only class of voting rules that satisfy strategy-proofness and unanimity, and dictatorial rules are the only ones that are strategy-proof and Pareto efficient. To fill the gap, we define a sequence of efficiency conditions. We prove that for strategy-proof rules on the separable preference domain, the various notions of efficiency reduce to three: unanimity, partial efficiency, and Pareto efficiency. We also show that on the domain, strategy-proofness and partial efficiency characterize the class of voting rules represented as simple games which are independent of objects, proper and strong. We call such rules voting by stable committee.The author is deeply indebted to William Thomson for many helpful discussions on an earlier draft. The current version is greatly benefited from detailed comments of an anonymous referee. Thanks are also due to Jeffrey Banks, Salvador Barberà, Marcus Berliant, Ryo-ichi Nagahisa, Takehiko Yamato, and participants in a seminar at Rochester in 1992, the 1992 Midwest Conference at Michigan State, and the 1993 Summer Meeting of Econometric Society at Boston University for conversations and suggestions.     

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.     

Gambling: The shaping of an opinion

Examining historical and contemporary writings, the authors show that many of the negative arguments about gambling spring from selfish interests in the business and political sectors. The stigma associated with gambling turns out to be a method of preventing competition from gambling, and leads to misguided social policies.The authors are, respectively, associate professor of economics at the Business School of the University of Montreal (HEC), and professor of economics in the department of economics of the University of Montreal. The paper draws on our recently published bookGambling and Speculation (Cambridge University Press, 1990), as well as on events that took place since we finished writing it. We thank Loto-Québec for its financial support.     

Enlargement and the balance of power: an experimental study

Theoretical analysis suggests that enlargement of a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the existing voters may actually gain, a phenomenon known as the paradox of new members. We test for this effect using laboratory experiments. Participants propose and vote on how to divide a budget according to weighted majority voting rules, and we measure the voting power of a player by his average payoff in the experiment. By comparing voting power across voting bodies of varying size, we find empirical support for the paradox of new members.     

Challenges to professionalism and union voting intentions: The case of pharmacists

Using data from a national survey of pharmacists who are members of the American Pharmaceutical Association, we examine the union voting intentions of employee pharmacists. We find that union instrumentality regarding professionalism is a primary predictor of union voting intent among these employees. In addition, this predictor mediates the relationship between the level of professionalism at a pharmacist’s current employment situation and his or her expected union vote. Also important to union voting intent are respondent beliefs about union instrumentality regarding pecuniary issues, prior union experience, as well as overall job satisfaction. Implications for employers, unions, and researchers are drawn. We thank Mary Graham, Jann Skelton, Paul Swiercz, Terry Thomason, and participants at the Seventh Bar-gaining Group Conference at Michigan State University for their comments on earlier versions of this paper. This research was made possible by a grant from the American Pharmaceutical Association.     

Media,migrants and human rights in the cultural history. Dialogue with Lynn Hunt

Lynn Hunt is an American historian and writer; she is Distinguished Research Professor at the University of California in Los Angeles (U.C.L.A.), and before coming to U.C.L.A., she taught at the University of Pennsylvania (1987–1998) and at the University of California, Berkeley (1974–1987). She is known for her studies in European Cultural History, and in 2007 she published the book Inventing Human Rights, where she examines the rise of the human rights in the eighteenth century.

We are specifically interested in her work because it gives us the chance to create a dialogue and disclose the moment we are living in comparing it with the cultural history and the role the media can have during a humanitarian crisis.

Therefore, we ask Lynn Hunt to explain how the exodus of migrants can be interpreted in light of the meta-narrative model, and to make clear what is and what will be the role of the cultural historians in offering us an interpretation of this historical moment. According to what the writer says in Writing History in the Global Era (2014), Hunt also deals with the importance of the relationship between means of communication, development of empathy and the emergence of human rights. For this reason, we asked the researcher, What is the role of the media today in mapping a humanitarian crisis?     

Limiting median lines do not suffice to determine the yolk

The yolk, an important concept in the spatial model of voting, is defined in two dimensions as the smallest circle intersecting all median lines. In the literature one finds the assumption that the limiting median lines, i.e., those that pass through two voter ideal points, suffice to determine the yolk. Counterex-amples are given here which invalidate this assumption.This work was done while the second author held a Research Associateship from the National Research Council at the Naval Postgraduate School, and a Presidential Young Investigator Award from the National Science Foundation, ECS-8451032.     

How the size of a coalition affects its chances to influence an election

Since voting rules are prototypes for many aggregation procedures, they also illuminate problems faced by economics and decision sciences. In this paper we are trying to answer the question: How large should a coalition be to have a chance to influence an election? We answer this question for all scoring rules and multistage elimination rules, under the Impartial Anonymous Culture assumption. We show that, when the number of participating agents n tends to infinity, the ratio of voting situations that can be influenced by a coalition of k voters to all voting situations is no greater than $D_{m} \frac{k}{n}Since voting rules are prototypes for many aggregation procedures, they also illuminate problems faced by economics and decision sciences. In this paper we are trying to answer the question: How large should a coalition be to have a chance to influence an election? We answer this question for all scoring rules and multistage elimination rules, under the Impartial Anonymous Culture assumption. We show that, when the number of participating agents n tends to infinity, the ratio of voting situations that can be influenced by a coalition of k voters to all voting situations is no greater than , where D _m is a constant which depends only on the number m of alternatives but not on k and n. Recent results on individual manipulability in three alternative elections show that this estimate is exact for k=1 and m=3.

Arkadii SlinkoEmail:

     

A personal account of developing preventive approaches to the problem of child sexual abuse in the UK

Abstract

This paper is a revised version of a keynote address on Child Sexual Abuse Prevention presented by Carolyn Okell Jones at the first European Congress on Child Abuse and Neglect, Rhodes, Greece 6-10 April 1987, but developed by both authors.     

Limiting distributions for continuous state Markov voting models

This paper proves the existence of a stationary distribution for a class of Markov voting models. We assume that alternatives to replace the current status quo arise probabilistically, with the probability distribution at time t+1 having support set equal to the set of alternatives that defeat, according to some voting rule, the current status quo at time t. When preferences are based on Euclidean distance, it is shown that for a wide class of voting rules, a limiting distribution exists. For the special case of majority rule, not only does a limiting distribution always exist, but we obtain bounds for the concentration of the limiting distribution around a centrally located set. The implications are that under Markov voting models, small deviations from the conditions for a core point will still leave the limiting distribution quite concentrated around a generalized median point. Even though the majority relation is totally cyclic in such situations, our results show that such chaos is not probabilistically significant.We acknowledge the support of NSF Grants #SOC79-21588, SES-8106215 and SES-8106212.     

General Feelings Toward Unions and Employers as Predictors of Union Voting Intent

The union voting intention literature shows that many nonunion employees who indicate that they think unions are instrumental in increasing wages, benefits, and working conditions would vote against forming a union. Although American workers have often been characterized as pragmatic with regard to their support for unions, the “disconnect” between union beliefs and union voting intentions just described suggests that more subtle forces are at work. In this paper, it is shown empirically that union instrumentality is a limited predictor of union voting intentions for a recent national cross-section of workers. Rather, more general feelings toward unions and employers are primary. These accounted for a large portion of the variance in union voting intentions, with general feelings towards unions by far the most critical predictor. A concluding section discusses whether the results may reflect changes in union power and changes in employee views of unions. Areas for future research are discussed.     

Monotonicity properties and their adaptation to irresolute social choice rules

What is a monotonicity property? How should such a property be recast, so as to apply to voting rules that allow ties in the outcome? Our original interest was in the second question, as applied to six related properties for voting rules: monotonicity, participation, one-way monotonicity, half-way monotonicity, Maskin monotonicity, and strategy-proofness. This question has been considered for some of these properties: by Peleg and Barberà for monotonicity, by Moulin and Pérez et?al, for participation, and by many authors for strategy-proofness. Our approach, however, is comparative; we examine the behavior of all six properties, under three general methods for handling ties: applying a set extension principle (in particular, G?rdenfors’ sure-thing principle), using a tie-breaking agenda to break ties, and rephrasing properties via the “t-a-t” approach, so that only two alternatives are considered at a time. In attempting to explain the patterns of similarities and differences we discovered, we found ourselves obliged to confront the issue of what it is, exactly, that identifies these properties as a class. We propose a distinction between two such classes: the “tame” monotonicity properties (which include participation, half-way monotonicity, and strategy proofness) and the strictly broader class of “normal” monotonicity properties (which include monotonicity and one-way monotonicity, but not Maskin monotonicity). We explain why the tie-breaking agenda, t-a-t, and G?rdenfors methods are equivalent for tame monotonicities, and how, for properties that are normal but not tame, set-extension methods can fail to be equivalent to the other two (and may fail to make sense at all).     

Costly voting when both information and preferences differ: is turnout too high or too low?

We study a model of costly voting over two alternatives, where agents’ preferences are determined by both (i) a private preference in favour of one alternative e.g. candidates’ policies, and (ii) heterogeneous information in the form of noisy signals about a commonly valued state of the world e.g. candidate competence. We show that depending on the level of the personal bias (weight on private preference), voting is either according to private preferences or according to signals. When voting takes place according to private preferences, there is an unique equilibrium with inefficiently high turnout. In contrast, when voting takes place according to signals, turnout is locally too low. Multiple Pareto-ranked voting equilibria may exist and in particular, compulsory voting may Pareto dominate voluntary voting. Moreover, an increase in personal bias can cause turnout to rise or fall, and an increase in the accuracy of information may cause a switch to voting on the basis of signals and thus lower turnout, even though it increases welfare. This is a substantially revised version of Department of Economics University of Warwick Working Paper 670, “Information Aggregation, Costly Voting and Common Values”, January 2003. We would like to thank B. Dutta, M. Morelli, C. Perrroni, V. Bhaskar and seminar participants at Warwick, Nottingham and the ESRC Workshop in Game Theory for their comments. We would also like to thank the editor and an anonymous referee for their comments.     

Subgame perfect implementation of voting rules via randomized mechanisms

We characterize completely ordinal and onto choice rules that are subgame perfect of Nash equilibrium (SPE) implementable via randomized mechanisms under strict preferences. The characterization is very operationalizable, and allows us to analyse SPE implementability of voting rules. We show that no scoring rule is SPE implementable. However, the top-cycle and the uncovered correspondences as well as plurality with runoff and any strongly Condorcet consistent voting rule can be SPE implemented. Therefore our results are favourable to majority based voting rules over scoring rules. Nevertheless, we show that many interesting Condorcet consistent but not strongly Condorcet consistent rules, such as the Copeland rule, the Kramer rule and the Simpson rule, cannot be SPE implemented.     

Unlikelihood of Condorcet’s paradox in a large society

We provide intuitive, formal, and computational evidence that in a large society Condorcet’s paradox (the intransitivity of social preference obtained by pairwise vote) can hardly occur. For that purpose, we compare two models of social choice, one based on voting and another one based on summing individual cardinal utilities, expressed either in reals, or integers. We show that in a probabilistic model with a large number of independent individuals both models, almost surely, provide the same decision results. This implies that Condorcet’s and Borda’s methods tend to give the same decisions as the number of voters increases. Therefore, in the model with a large number of voters, the transitivity of the Borda preference is inherent in a majority preference as well. Received: 26 June 1998/Accepted: 16 April 1999     

Alienation,indifference and the choice of ideological position

In this paper we describe a simple model of individual voting behavior and present its implications for the candidate positioning problem under both vote and plurality maximization. Under our assumptions, some voters at the extremes of the ideological spectrum typically will not vote because they are alienated by the equilibrium location of candidates. There will also be some voters in the middle of the ideological spectrum who will not vote because they are indifferent between the equilibrium locations of the candidates. Both the abstention from alienation and from indifference arise explicitly from utility maximization. Once we allow for alienation and indifference, the two alternative candidate objective functions (vote maximization and plurality maximization) yield different outcomes. In particular, we show that under vote maximization the Median Voter (or Minimum Differentiation) outcome will not arise. On the other hand, under plurality maximization, the Median Voter outcome may or may not hold, depending on the distribution of voter preferences.We should like to thank Jerry Fusselman, Jon Hamilton, Mel Hinich, Charlie Holt and participants at seminars at the University of Virginia, Northwestern University and the 1989 Meetings of the Public Choice Society and the Economic Science Association for their helpful comments.     

Why Kohut endures

Both critics and followers of Kohut's ideas have often misunderstood the true significance of self-psychology within the context of the history of psychoanalytic psychology and clinical practice. Self-psychology has frequently been equated with the discovery of the narcissistic personality disorders and thus critiqued by those who insist on the clinical and theoretical usefulness of the concept of the psychoneuroses. When the importance of the empathic mode itselfis recognized, however, empathy is often misunderstood and thus not seen as a significant and lasting clinical contribution. By tracing the development of Kohut's thinking, with special emphasis on the interweaving of his views on empathy and his metapsychology, and by examining the ramifications of the use of empathy in actual clinical practice, it is hoped that the reader will more fully appreciate its crucial and central importance for psychoanalytic psychotherapy.An earlier version of this paper was presented to the Graduate Clinical Psychology Department at Xavier University on April 30, 1987.