Relationships between Borda voting and Zermelo ranking

There are many situations wherein a group of individuals (e.g., voters, experts, sports writers) must produce an ordered list of ‘best’ alternatives selected from a given group of alternatives (e.g., candidates, proposals, sports teams). Two long established mechanisms that have been used for this task are ‘Zermelo’s Ranking Method’ (1929) and ‘Borda’s Voting Scheme’ (1781). The main purpose of this paper is to point out that they are, under certain common circumstances, identical. We then show that Zermelo’s Method can be used in situations that Borda’s Method is not designed to handle.     

Top-Pair and Top-Triple Monotonicity

We say that a social choice function (SCF) satisfies Top-k Monotonicity if the following holds. Suppose the outcome of the SCF at a preference profile is one of the top k-ranked alternatives for voter i. Let the set of these k alternatives be denoted by B. Suppose that i’s preference ordering changes in such a way that the set of first k-ranked alternatives remains the set B. Then the outcome at the new profile must belong to B. This definition of monotonicity arises naturally from considerations of set “improvements” and is weaker than the axioms of strong positive association and Maskin Monotonicity. Our main results are that if there are two voters then a SCF satisfies unanimity and Top-2 or Top-pair Monotonicity if and only if it is dictatorial. If there are more than two voters, then Top-pair Monotonicity must be replaced by Top-3 Monotonicity (or Top-triple Monotonicity) for the analogous result. Our results demonstrate that connection between dictatorship and “improvement” axioms is stronger than that suggested by the Muller–Satterthwaite result (Muller and Satterthwaite in J Econ Theory 14:412–418, 1977) and the Gibbard–Sattherthwaite theorem.     

Hansson’s theorem for generalized social welfare functions: an extension

 Hansson (1969) sets forth four conditions satisfied by no generalized social welfare function (GSWF), a mapping from profiles of individual preferences to arbitrary social preference relations. Though transitivity is not imposed on social preferences, one of Hansson’s conditions requires that socially maximal alternatives always exist. Of course, this condition is not satisfied by the majority GSWF. We prove a generalization of Hansson’s theorem that requires the existence of maximal alternatives only in very special cases. Our result applies to the majority GSWF and a large class of other GSWFs that sometimes produce no maximal alternatives. Received: 10 July 1995/Accepted: 4 March 1996     

The Chairman’s Paradox Revisited

This paper re-examines the so-called ‘chairman’s paradox‘ that was first noticed by Farquharson in his path breaking tract on sophisticated voting, Theory of Voting (1969). The Chairman’s paradox is concerned with the case of a three member committee in which a particular player who has a regular and a tie-breaking vote – the ‘chairman’ – not only will do worse in specific instances under the plurality procedure for three alternatives than if he did not have such a vote, but will also do worse overall. That is, the chairman’s a priori probability of success (‘getting what one wants’) for all possible games with linear (strict) preference orders is lower than that of the two regular members. It is demonstrated that this result, which comes about if voters act strategically rather than sincerely, is not as robust as it has been thought to be. By merely replacing the standard assumption of linear preference orders with weak preference orders, which allow for indifference, we can escape from the paradox for the canonical case of three players and three alternatives. With weak preference orders, the a priori success of the chairman is now greater than that of the other two players. We also point to a new paradox of sophisticated voting.     

Interpretation of electoral mixed strategies

In this paper is remarked that “mixed” strategies in games of electoral competition do not need to be interpreted as random moves. There are two a priori symmetric parties, and a finite (non spatial) set of alternatives. Parties are allowed to take unclear positions, by campaining on a “platform” that is a mix of several alternatives. Each individual nevertheless identifies a party with a single alternative, the number of individuals who identify a party with a given alternative being proportional to the importance of that alternative in the party’s platform. Received: 24 March 1998/Accepted: 3 March 1999     

The stranger as seer or voyeur: A dilemma of the peep-show theory of knowledge

The belief that ‘the stranger’ (outsider, disinterested third party) sees things more clearly, i.e. is more “objective,” is seen to be a corner-stone of folk wisdom; underlying Western judicial thought and concepts of objectivity in the social sciences. The author raises the dilemma that both positivistic and humanistic sociologists accept this belief—suggesting 1) that it is a residue of positivism and a quest for certain knowledge, or 2) the possibility that ‘the stranger’ does gain deeper insight into group life than members. The paper examines the concept of the stranger, considering the aura of charisma that seems to have been attached to it in ordinary discourse as well as within the sociological dialogue. Two types of strangers are described: outsiders and enemies within. Finally, an attempt is made to examine the testimony of prominant strangers as they describe their marginal status and speculate on the ways that status has made them unusually perceptive observers of social phenomena.     

‘One and a Half Dimensional’ Preferences and Majority Rule

I examine a model of majority rule in which alternatives are described by two characteristics: (1) their position in a standard, left-right dimension, and (2) their position in a good-bad dimension, over which voters have identical preferences. I show that when voters’ preferences are single-peaked and concave over the first dimension, majority rule is transitive, and the majority’s preferences are identical to the median voter’s. Thus, Black’s (The theory of committees and elections, 1958) theorem extends to such a “one and a half” dimensional framework. Meanwhile, another well-known result of majority rule, Downs’ (An economic theory of democracy, 1957) electoral competition model, does not extend to the framework. The condition that preferences can be represented in a one-and-a-half-dimensional framework is strictly weaker than the condition that preferences be single-peaked and symmetric. The condition is strictly stronger than the condition that preferences be order-restricted, as defined by Rothstein (Soc Choice Welf 7:331–342;1990).     

Nash Implementation with Lottery Mechanisms

Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin in Rev Econ stud 66: 23–38, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackon and Palfrey in J Econ Theory 98: 1–25, 2001).I thank Toyo Sakai for his comments on a previous draft. I also thank two anonymous referees and an editor of this journal for helpful comments that improved this paper. A previous version circulated as “A note on Maskin monotonicity”. After the results presented here were obtained, I became aware of a new unpublished paper by Benoit and Ok (2004). The result of Theorem 2 and the discussion that follows is partially similar to their Theorem 1.     

Does majoritarian approval matter in selecting a social choice rule? An exploratory panel study

This study is an attempt to empirically detect the public opinion concerning majoritarian approval axiom. A social choice rule respects majoritarian approval iff it chooses only those alternatives which are regarded by a majority of “voters” to be among the “better half” of the candidates available. We focus on three social choice rules, the Majoritarian Compromise, Borda’s Rule and Condorcet’s Method, among which the Majoritarian Compromise is the only social choice rule always respecting majoritarian approval. We confronted each of our 288 subjects with four hypothetical preference profiles of a hypothetical electorate over some abstract set of four alternatives. At each hypothetical preference profile, two representing the preferences of five and two other of seven voters, the subject was asked to indicate, from an impartial viewpoint, which of the four alternatives should be chosen whose preference profile was presented, which if that is unavailable, then which if both of the above are unavailable, and finally which alternative should be avoided especially. In each of these profiles there is a Majoritarian Compromise-winner, a Borda-winner and a Condorcet-winner, and the Majoritarian Compromise-winner is always distinct from both the Borda-winner and the Condorcet-winner, while the Borda- and Condorcet-winners sometimes coincide. If the Borda- and Condorcet-winners coincide then there are two dummy candidates, otherwise only one, and dummies coincide with neither of the Majoritarian Compromise-, Borda- or Condorcet-winner. We presented our subjects with various types of hypothetical preference profiles, some where Borda respecting majoritarian approval, some where it failed to do so, then again for Condorcet, some profiles it respected majoritarian approval and some where it did not. The main thing we wanted to see was whether subjects’ support for Borda and Condorcet was higher when this social choice rule respected majoritarian approval than it did not. Our unambiguous overall empirical finding is that our subjects’ support for Borda and Condorcet was significantly stronger as they respect majoritarian approval.     

Reports of Wins and Risk Taking: An Investigation of the Mediating Effect of the Illusion of Control

Two experiments examined the relationships between the knowledge that another person has won in a gamble, the illusion of control and risk taking. Participants played a computer-simulated French roulette game individually. Before playing, some participants learnt that another person won a large amount of money. Results from a first experiment (n = 24) validated a causal model where the knowledge of another person’s win increased the illusion of control, measured with betting times, expectancy and self-reports on scales, which in turn encourages risk taking. In the second experiment (n = 36), some participants were told the previous player acknowledged the win to be fortuitous. The suppression of the belief that the previous winner had himself exerted control over the outcome resulted in lower rates of risk-taking behaviors. This suggests that it was not the knowledge of another person’s win in itself that increased risk taking, but rather, the belief that the other person had some control over the gamble’s outcome. Theoretical implications for the study of social mechanisms involved in gambling behavior are discussed.     

From government to grass-roots reform: the Ford Foundation's population programmes in South Asia, 1959–1981

This article traces the history of Ford's involvement in population work in South Asia from the 1950s to the mid-1980s. The primary focus is on the transition from large-scale technical assistance programmes rooted in government and academe, to work with grass-roots women's groups and community-based non-governmental organisations (NGOs). In the process, the Foundation also moved from quantitative efforts designed primarily to distribute contraceptives, to a more holistic approach focusing on maternal and child health. The article concludes by relating these trends to a larger shift from a belief in the power of ‘disinterested expertise’ and university-based policymaking that marked the efforts of the major American foundations since the Progressive era, to a new emphasis on ‘self-interested expertise’ and grass-roots social activist and development NGOs that emerged in the 1970s. Changing development paradigms, political trends and a growing disillusionment with large-scale technical assistance all contributed to this transition.     

On the manipulation of social choice correspondences

Duggan and Schwartz (Soc Choice and Welfare 17: 85–93, 2000) have proposed a generalization of the Gibbard–Satterthwaite Theorem to multivalued social choice rules. They show that only dictatorial rules are strategy-proof and satisfy citizens sovereignty and residual resoluteness. Citizens sovereignty requires that each alternative is chosen at some preference profile. Residual resoluteness compels the election to be single-valued when the preferences of the voters are “similar”. We propose an alternative proof to the Duggan and Schwartz’s Theorem. Our proof highlights the crucial role of residual resoluteness. In addition, we prove that every strategy-proof and onto social choice correspondence concentrates the social decision power in the hands of an arbitrary group of voters. Finally, we show that this result still holds in a more general framework in which voters report their preferences over sets of alternatives.     

The availability of child care centers,perceived search costs and parental life satisfaction

The supply of formal childcare has expanded in many developed countries. However, there is ambiguity in the theory whether the entry of care providers increases consumers’ surplus in a market with differentiated services, such as childcare. This study empirically investigates how perceived search costs and parental life satisfaction change when actual childcare availability is altered. It exploits the new panel data from Australia on the number of center-based childcare places per 100 children within a household’s residential area. The results show that an increase in the availability of center-based childcare is associated with a decrease in perceived difficulty in finding ‘good quality’ childcare, as well as an increase in mothers’ satisfaction with the amount of free time available. These findings imply that the local availability of center-based childcare has enhanced the subjective well-being of parents.     

By our bootstraps: Origins and effects of the high-wage doctrine and the minimum wage

Conclusion  Although the high-wage doctrine — the belief that the level of aggregate demand is determined by the level of wage rates — is most often associated with the Great Depression, the doctrine’s effects on wage policy go back at least two decades further. Rather than having been a product of desperate times, the doctrine gained wide acceptance during the prosperous 1920s as businessmen and economists, citing the success of Henry Ford's continuing high-wage policies, and the (supposedly counterproductive) wage deflation that had marked the steep depression of 1920-21, applied the doctrine's demand-enhancing logic to push for an economy-wide minimum wage. The authors thank Fred Bateman, Don Bellante, Roger Garrison, Peter Klein, and Anthony Patrick O’Brien for thoughtful comments and suggestions.     

Prophetic versus priestly sociology: The salient case study of Arthur K. Davis

Arthur K. Davis was President of the Canadian Sociology and Anthropology Association in 1975–1976 and in 1995 received the association’s Outstanding Contribution award. In Canada, he was particularly known for his article on “Canadian Society and History as Hinterland Versus Metropolis,” originally published in Ossenberg’s anthology of 1971. This article was frequently cited from 1972–1994 and was reprinted a number of times. Davis was also known for his articles on Thorstein Veblen, which continue to receive citation. Davis’ career merits careful study for at least two reasons. The first is that he was a Ph.D. product of the early Harvard sociology graduate program, which has received much less attention than it deserves from sociological historians (unlike the Chicago School). As such, Davis studied under of Talcott Parsons, Pitirim Sorokin, and Robert K. Merton. The second reason is that Davis’ career clearly illustrates the usefulness of Robert W. Friedrichs’ distinction between the priestly and prophetic roles that sociologists may fulfill. Davis’ career started under the influence of a priestly orientation (as symbolized by his doctoral supervisor Talcott Parsons) and then gravitated to a prophetic stance as influenced by Pitirim Sorokin, Paul M. Sweezy, and, more distantly, by Marx and Veblen. Since this transition took place just when the Cold War was falling, his career reveals some of the pitfalls that await the prophetic sociologist in times that favor security and conservatism rather than activism and change.     

Consistency between tastes and values: A universalization approach

The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that transform individuals ‘tastes’– which reflect the self-interested view point of the individuals – into (social) ranking of alternatives. In addition to her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of income inequality aversion, the so-called ‘ethics of responsibility’ and the aggregation of individual ranking of opportunity sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of ‘laundering’ individual preferences is also provided. Received: 25 June 1998/Accepted: 16 March 1999     

Is What’s Good for the Business,Good for the Family: A Financial Assessment

Small business prosperity doesn’t necessarily translate into family prosperity. This study utilizes the first and second waves of the National Family Business Survey to explore the influence of changes in key business financial measures on objective and subjective measures of family success. Increases in the available cash in the business from higher gross sales or net profits brings more cash into the household, while increases in the market value of the business increases the amount of money spent on other household assets. A more subjective assessment suggests that positive changes in the business financial measures create a more positive perception of the business’ success; however, these positive changes have no influence on a more positive perception of the family’s success.     

Flexibility of choice versus reduction of ambiguity

This paper explores the problem of a social planner willing to improve the welfare of individuals who are unable to compare all available alternatives. The optimal decision trades off the individuals’ desire for flexibility versus their aversion towards ambiguous choice situations. We introduce an axiom system that formalizes this idea. Our main result characterizes the preference maximizing opportunity set. It is a maximal set that consists of mutually comparable alternatives. It also has the property that it maximizes the sum of the distances between its ordered elements for some appropriate pseudometric imposed on the set of possible choices.     

Contraction consistent stochastic choice correspondence

We model a general choice environment via probabilistic choice correspondences, with (possibly) incomplete domain and infinite universal set of alternatives. We offer a consistency restriction regarding choice when the feasible set contracts. This condition, ‘contraction consistency’, subsumes earlier notions such as Chernoff’s Condition, Sen’s α and β, and regularity. We identify a restriction on the domain of the stochastic choice correspondence (SCC), under which contraction consistency is equivalent to the weak axiom of revealed preference in its most general form. When the universal set of alternatives is finite, this restriction is also necessary for such equivalence. Analogous domain restrictions are also identified for the special case where choice is deterministic but possibly multi-valued. Results due to Sen (Rev Econ Stud 38:307–317, 1971) and Dasgupta and Pattanaik (Econ Theory 31:35–50, 2007) fall out as corollaries. Thus, conditions are established, under which our notion of consistency, articulated only in reference to contractions of the feasible set, suffices as the axiomatic foundation for a general revealed preference theory of choice behaviour.     

Looking at Smelser’s Theory of Collective Behavior After Almost 50 Years: A Review and Appreciation

A half century has gone by since the publication of Neil Smelser’s classic book on the Theory of Collective Behavior. The re-issue of the book triggered these observations in which I reflect on the fate of old books; trace a bit of the book’s genealogy; note changes in the field; and argue that Smelser’s book is really four books in one with varying impact over the decades and likely to be of varying interest to current scholars—an application of Parsonian theory to conflict and change; an elaboration of key concepts found with collective behavior which involves “uninstitutionalized mobilization to reconstitute components of social action on the basis of a generalized belief”; an elaboration of variables such as objective conditions of the social order, perceptions and belief systems required to understand the topic; and a comprehensive summary and critique of relevant empirical and theoretical work on collective behavior through the 1950s. Based on criticisms of the book, I suggest some areas that should be addressed were the book to be revised.