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.     

Distribution of coalitional power in randomized multi-valued social choice

This paper considers the distribution of coalitional influence under probabilistic social choice functions which are randomized social choice rules that allow social indifference by mapping each combination of a preference profile and a feasible set to a social choice lottery over all possible choice sets from the feasible set. When there are at least four alternatives in the universal set and ex-post Pareto optimality, independence of irrelevant alternatives and regularity are imposed, we show that: (i) there is a system of additive coalitional weights such that the weight of each coalition is its power to be decisive in every two-alternative feasble set; and (ii) for each combination of a feasible proper subset of the universal set and a preference profile, the society can be partioned in such a way that for each coalition in this partition, the probability of society's choice set being contained in the union of the best sets of its members is equal to the coalition's power or weight. It is further shown that, for feasible proper subsets of the universal set, the probability of society's choice set containing a pair of alternatives that are not jointly present in anyone's best set is zero. Our results remain valid even when the universal set itself becomes feasible provided some additional conditions hold. Received: 10 May 1999/Accepted: 18 June 2000 I would like to thank Professor Prasanta Pattanaik for suggesting to me the line of investigation carried out in this paper. I am solely responsible for any remaining errors and omissions.     

On the selection of the same winner by all scoring rules

Different scoring rules can result in the selection of any of the k competing candidates, given the same preference profile, (Saari DG 2001, Chaotic elections! A mathematician looks at voting. American Mathematical Society, Providence, R.I.). It is also possible that a candidate, and even a Condorcet winning candidate, cannot be selected by any scoring rule, (Saari DG 2000 Econ Theory 15:55–101). These findings are balanced by Saari’s result (Saari DG 1992 Soc Choice Welf 9(4):277–306) that specifies the necessary and sufficient condition for the selection of the same candidate by all scoring rules. This condition is, however, indirect. We provide a sufficient condition that is stated directly in terms of the preference profile; therefore, its testability does not require the verdict of any voting rule.     

The replacement principle for the provision of multiple public goods on tree networks

This article considers the provision of two public goods on tree networks where each agent has a single-peaked preference. We show that if there are at least four agents, then no social choice rule exists that satisfies efficiency and replacement-domination. In fact, these properties are incompatible, even if agents’ preferences are restricted to a smaller domain of symmetric single-peaked preferences. However, for rules on an interval, we prove that Miyagawa’s (Soc Choice Welf 18:527–541, 2001) characterization that only the left-peaks rule and the right-peaks rule satisfy both of these properties also holds on the domain of symmetric single-peaked preferences. Moreover, if agents’ peak locations are restricted to either the nodes or the endpoints of trees, rules exist on a subclass of trees. We provide a characterization of a family of such rules for this tree subclass.     

Why do larger families reduce parental investments in child quality, but not child quality per se?

Becker’s Quantity–Quality model (Becker in Demographic and economic change in developed countries, Princeton University Press, Princeton, pp 209–240, 1960; Becker and Lewis in J Polit Econ 81(2): S279–S288, 1973; Becker and Tomes in J Polit Econ 84(4): S143–S162, 1976) suggests a trade-off between family size and parental investments in children. To date, only Cáceras-Delpiano (J Hum Resour 41(4): 738–754, 2006) tests this theory by considering private school enrolment. This study extends this work by using a unique data set containing a broader range of parental investments that are arguably linked to parental intentions for producing higher quality children, such as overall and non-sectarian private school enrolment, the number of computers in the home per child, and saving for the child’s education. Both studies find that fertility reduces parental investments. However, the literature generally finds that fertility has no impact on child outcomes. The study offers three potential explanations for this ‘puzzle’.     

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A _k is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B _l . If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained.     

Strategy-proof resolute social choice correspondences

We qualify a social choice correspondence as resolute when its set valued outcomes are interpreted as mutually compatible alternatives which are altogether chosen. We refer to such sets as “committees” and analyze the manipulability of resolute social choice correspondences which pick fixed size committees. When the domain of preferences over committees is unrestricted, the Gibbard–Satterthwaite theorem—naturally—applies. We show that in case we wish to “reasonably” relate preferences over committees to preferences over committee members, there is no domain restriction which allows escaping Gibbard–Satterthwaite type of impossibilities. We also consider a more general model where the range of the social choice rule is determined by imposing a lower and an upper bound on the cardinalities of the committees. The results are again of the Gibbard–Satterthwaite taste, though under more restrictive extension axioms.     

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     

A note on the stability of Chen’s Lindahl mechanism

There are no general theoretical results on the stability of the Lindahl mechanism introduced by Chen (Econ Theory 19:773–790, 2002). We show that despite not fitting the requirements of the Milgrom and Roberts 1990 stability result for supermodular games, if the Chen mechanism induces a supermodular game, then the best reply map is a contraction. This gives us an easy to identify sufficient condition for dynamic stability of equilibrium.     

Uncovered set choice rules

I study necessary and sufficient conditions for a choice function to be rationalized in the following sense: there exists a total asymmetric relation T (a tournament) such that, for each feasible (finite) set, the choice set coincides with the uncovered set of T restricted to that feasible set. This notion of ‘maximization’ offers testable restrictions on observable choice behavior.     

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 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.     

The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable

It is shown that the Majoritarian Compromise of Sertel (1986) is subgame-perfect implementable on the domain of strict preference profiles, although it fails to be Maskin-monotonic and is hence not implementable in Nash equilibrium. The Majoritarian Compromise is Pareto-optimal and obeys SNIP (strong no imposition power), i.e. never chooses a strict majority's worst candidate. In fact, it is “majoritarian approving” i.e. it always picks “what's good for a majority” (alternatives which some majority regards as among the better “effective” half of the available alternatives). Thus, being Pareto-optimal and majoritarian approving, it is majoritarian-optimal. Finally, the Majoritarian Compromise is measured against various criteria, such as consistency and Condorcet-consistency. Received: 31 January 1995/Accepted: 22 July 1998     

Internalities and paternalism: applying the compensation criterion to multiple selves across time

One reason to call an activity a vice and suppress it is that it reduces a person’s future happiness more than it increases his present happiness. Gruber and Koszegi (Q J Econ 116(4):1261–1303, 2001) show how a vice tax can increase a person’s welfare in a model of multiple selves with hyperbolic preferences across time. The present paper shows that an interself analogy of the compensation criterion can justify a vice ban whether preferences are hyperbolic or exponential, but subject to the caveat that the person has a binding constraint on borrowing.     

Opportunity sets and individual well-being

 An opportunity set ranking rule assigns an ordering of opportunity sets to each individual utility function (defined on the universal set of alternatives) within the domain of this rule. Using an axiomatic approach, this paper characterizes a general class of opportunity set ranking rules which are based on the utilities associated with the elements of an opportunity set. It is argued that the addition of an alternative to a given opportunity set is not necessarily desirable in terms of overall well-being, and this position is reflected in replacing a commonly used monotonicity axiom with an alternative condition. Received: 15 May 1995/Accepted: 14 December 1995     

Assessing the Reliability of the Gambling Functional Assessment: Revised

Dixon and Johnson (Anal Gambl Behav 1: 44–49, 2007) proposed the Gambling Functional Assessment as a tool to identify the consequences maintaining the respondent’s gambling behavior, but subsequent studies on its psychometric properties suggested that it could use improvement. The present study investigated the internal consistency of the Gambling Functional Assessment—Revised using the responses of 1,060 undergraduate students. Temporal reliability was assessed by a second administration of the measure four (n = 87) or twelve (n = 98) weeks after the first administration. Temporal reliability was also compared to the South Oaks Gambling Screen (Lesieur and Blume in Am J Psychiatry 144: 1184–1188, 1987), which was also administered at both time points. Internal consistency measures were good to excellent, even when potential non-gamblers were excluded from the analyses. Temporal stability was also very good, with the possible exception of the consequence of “escape” at 12 weeks. The Gambling Functional Assessment—Revised represents a potentially useful tool for researchers and therapists interested in why respondents are gambling.     

On probabilistic rationalizability

This paper examines the problem of rationalizability of a choice system without imposing restrictions on the universal set of alternatives and the family of feasible sets. A choice system is the probabilistic counterpart of a choice function which is basic to much of the theory of individual choice behaviour in economics. We provide a necessary and sufficient condition for a choice system to be induced by a probability measure on a set of utility functions. I would like to thank the editor and two anonymous referees for helpful comments.     

Examining Community Life “in the Making”: Emile Durkheim’s <Emphasis Type="Italic">Moral Education</Emphasis>

Although often overlooked in sociological circles, Emile Durkheim’s (1902–1903) Moral Education provides an important cornerstone in the quest to understand community life. Not only does Moral Education give a vibrant realism to the sociological venture in ways that Durkheim’s earlier works (1893, 1895, 1897) fail to achieve, but in addressing discipline, devotion, and informed reasoning as humanly engaged, collectively accomplished fields of activity Emile Durkheim also provides an exceptionally consequential baseline analysis of human knowing and acting. Notably as well, focusing on the organizational, intersubjectively achieved features of elementary education, Durkheim’s Moral Education lays bare the interactional nature of the moral order of community life. Indeed, as a sustained analysis of the way of life of a group of people collectively participating in the educational process, this text addresses the most basic features of people’s relations to one another and the broader society in which they find themselves. Much more than an account of childhood socialization, Durkheim’s Moral Education also presages the more thoroughly humanist sociology that Durkheim develops in The Evolution of Educational Thought (1904–1905), The Elementary Forms of the Religious Life (1912) and Pragmatism and Sociology (1913–1914).     

Cohabitation Premium in Men’s Earnings: Testing the Joint Human Capital Hypothesis

This paper provides new evidence on the increase in wage earnings for men due to marriage and cohabitation (in the literature, commonly referred to as marital and cohabitation wage premiums for men). Using data for a sample of white men from the National Longitudinal Survey of Youth 1979, the paper shows that even after accounting for potential selection bias there is a cohabitation wage premium for men, albeit smaller than the marriage premium. Our analysis shows that a joint human capital hypothesis (a la Benham in J Polit Econ 82(2, Part 2):S57–71, 1974) with intra-household spillover effects of partner’s education can explain the existence of the wage premiums. Our estimates provide some empirical support for the joint human capital hypothesis.