Smallest tournaments not realizable by $${\frac{2}{3}}$$-majority voting

Define the predictability number α(T) of a tournament T to be the largest supermajority threshold for which T could represent the pairwise voting outcomes from some population of voter preference orders. We establish that the predictability number always exists and is rational. Only acyclic tournaments have predictability 1; the Condorcet voting paradox tournament has predictability ; Gilboa has found a tournament on 54 alternatives (i.e. vertices) that has predictability less than , and has asked whether a smaller such tournament exists. We exhibit an 8-vertex tournament that has predictability , and prove that it is the smallest tournament with predictability <  . Our methodology is to formulate the problem as a finite set of two-person zero-sum games, employ the minimax duality and linear programming basic solution theorems, and solve using rational arithmetic. D. Shepardson was supported by a NSF Graduate Research Fellowship during the course of this work.     

The NIP graph of a social welfare function

We consider the fraction of pairs of m distinct alternatives on which a social welfare function f may be nondictatorially independent and Pareto when the domain of f satisfies the free k-tuple property. When k = 4 we improve the existing upper bound to . When there are at least 26 alternatives and we obtain an original upper bound, . To obtain these results we define and analyze the graph formed from the nondictatorial independent and Pareto pairs and combine the results of this analysis with known results from extremal graph theory. The authors extend special thanks to the two reviewers and the editor for their comments.     

Arrovian impossibilities in aggregating preferences over non-resolute outcomes

Let A be a set of alternatives whose power set is . Elements of are interpreted as non-resolute outcomes. We consider the aggregation of preference profiles over into a (social) preference over . In case we allow individuals to have any complete and transitive preference over , Arrow’s impossibility theorem naturally applies. However, the Arrovian impossibility prevails, even when the set of admissible preferences over is severely restricted. In fact, we identify a mild “regularity” condition which ensures the dictatoriality of a domain. Regularity is compatible with almost all standard extension axioms of the literature. Thus, we interpret our results as the strong prevalence of Arrow’s impossibility theorem in aggregating preferences over non-resolute outcomes. This paper is part of a project entitled “Social Perception—A Social Choice Perspective”, supported by Istanbul Bilgi University Research Fund. It has been completed while Remzi Sanver was visiting Ecole Polytechnique, Paris. We are grateful to both institutions. We thank Nick Baigent, two anonymous referees and an anonymous associate editor for their valuable comments.     

On the leximin and utilitarian overtaking criteria with extended anonymity

We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S{\mathcal{S}}-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S{\mathcal{S}}-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S{\mathcal{S}}-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.     

Marriage matching and gender satisfaction

The performance of the Gale–Shapley marriage matching algorithm (Am Math Mon 16:217–222, 1962) has been studied extensively in the special case of men’s and women’s preferences random. We drop the assumption that women’s preferences are random and show that , where R _n is the men’s expected level of satisfaction, that is, the expected sum of men’s rankings of their assigned mates, when the men-propose Gale–Shapley algorithm is used to match n men with n women. This is a step towards establishing a conjecture of Knuth (Mariages Stables et leurs relations avec d’ autres problémes combinatoires, 1976, CRM Proceedings and Lecture Notes, Vol 10, 1997) of 30 years standing. Under the same assumptions, we also establish bounds on the expected rankings by women of their assigned mates.     

Reproduction, juvenile survival and retention in an urban fox squirrel population

Fox squirrels in an urban environment had an average litter size of 2.83 (95% CI 2.5, 3.16) which was similar to rural populations. Nonetheless, the proportion of squirrels reproductively active during the summer/fall breeding season (0.73) and annually (spring + summer/fall) was higher (1.23) than previously recorded for non-manipulated rural populations. The average monthly survival rate () of urban juvenile fox squirrels during the first 14 weeks of life was higher than reported for adult populations in the area. High rates of reproduction and juvenile survival yielded high juvenile to adult ratios (juveniles/adults) averaging 0.44. Retention of juveniles after 6 months (15%) was significantly less (χ ² = 7.24, p = 0.0071) than adults/subadults (40%). Results suggest that the urban environment provides quality habitat for fox squirrels and fox squirrels in urban environments have the potential to be a source population for surrounding suburban and rural environments.     

Characterizing Paretian preferences

A characterization of a property of binary relations is of type M if it can be stated in terms of ordered M-tuples of alternatives. A characterization of finite type provides an easy test of whether preferences over a large set of alternatives possesses the property characterized. Unfortunately, there is no characterization of finite type for Pareto representability in . A partial result along the same lines is obtained for Pareto representability in , k>2.

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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.     

Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters

In this paper I examine single member, simple plurality elections with n ≥ 3 probabilistic voters and show that the maximization of expected vote share and maximization of probability of victory are “generically different” in a specific sense. More specifically, I first describe finite shyness (Anderson and Zame in Adv Theor Econ 1:1–62, 2000), a notion of genericity for infinite dimensional spaces. Using this notion, I show that, for any policy in the interior of the policy space and any candidate j, the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which simultaneously satisfies the first and second order conditions for maximization of j’s probability of victory and j’s expected vote share at is finitely shy with respect to the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which satisfies the first and second order conditions for maximization of j’s expected vote share.     

Continuity and egalitarianism in the evaluation of infinite utility streams

There exists a utilitarian tradition à la Sidgwick of treating equal generations equally. Diamond showed that there exists no social evaluation ordering over infinite utility streams in the presence of the Pareto principle, the Sidgwick principle, and continuity. Instead of requiring the Sidgwick principle of procedural fairness, we focus on two principles of distributional egalitarianism along the line of the Pigou–Dalton transfer principle and the Lorenz domination principle, and show that there exists no social evaluation relation satisfying one of these egalitarian principles and the weakened continuity and rationality axioms even in the absence of the Pareto principle. This paper is a substantially revised version of our foregoing paper, “On the Possibility of Continuous, Paretian and Egalitarian Evaluation of Infinite Utility Streams,” which was based on our joint research conducted as a part of the Project on Intergenerational Equity under the auspices of the Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Thanks are due to Geir Asheim, Kaushik Basu, Walter Bossert, Hajime Hori, Tomoki Inoue, Mitsunori Noguchi and Koichi Tadenuma with whom we had several discussions on this and related issues. We are also grateful to the anonymous referees and the Associate Editor in charge of our earlier paper for their helpful comments and suggestions. Needless to say, no one other than ourselves should be held responsible for any remaining defect of this paper.     

Fair Groves mechanisms

We study allocation problems in which a costly task is to be assigned and money transfers are used to achieve fairness among agents. We consider a series of fairness notions (k-fairness for where n is the number of agents) of decreasing restrictiveness that are based on Rawls’ maximin equity criterion and impose welfare lower bounds. These fairness notions were introduced by Porter et al. (J Econ Theory 118:209–228, 2004) who also introduced two classes of Groves mechanisms that are 1-fair and 3-fair, respectively, and generate deficits that are bounded above. We show that these classes are the largest such classes of Groves mechanisms. We generalize these mechanisms for each and show that the corresponding mechanisms generate the smallest deficit for each economy among all k-fair Groves mechanisms. The first draft of this paper was written while we were Ph.D. students at the University of Rochester. We are grateful to William Thomson for his guidance and advice. We also thank two referees and the associate editor for their comments.     

Existence of a multicameral core

When a single group uses majority rule to select a set of policies from an n-dimensional compact and convex set, a core generally exists if and only if n = 1. Finding analogous conditions for core existence when an n-dimensional action requires agreement from m groups has been an open problem. This paper provides a solution to this problem by establishing sufficient conditions for core existence and characterizing the location and dimensionality of the core for settings in which voters have Euclidean preferences. The conditions establish that a core may exist in any number of dimensions whenever n ≤ m as long as there is sufficient preference homogeneity within groups and heterogeneity between groups. With m > 1 the core is however generically empty for . These results provide a generalization of the median voter theorem and of non-existence results for contexts of concern to students of multiparty negotiation, comparative politics and international relations.     

A Geometric Study of Shareholders’ Voting in Incomplete Markets: Multivariate Median and Mean Shareholder Theorems

A simple parametric general equilibrium model with S states of nature and K < S firms is considered. Since markets are incomplete, at a (financial) equilibrium shareholders typically disagree on whether to keep or not the status quo production plans. Hence each firm faces a genuine problem of social choice. The setup proposed in the present paper allows to study these problems within a classical (Downsian) spatial voting model. Given the multidimensional nature of the latter, super majority rules with rate are needed to guarantee existence of politically stable production plans. A simple geometric argument is proposed showing why a 50%-majority stable production equilibrium exists when K=S−1. When the degree of incompleteness is more severe, under more restrictive assumptions on agents’ preferences and the distribution of agents’ types, equilibria are shown to exist for rates ρ smaller than Caplin and Nalebuff (Econometrica 59: 1–23, 1991) bound of 0.64: they obtain for production plans whose span contains the ‘ideal securities’ of all K mean shareholders.Hervé Crès is a member of the GREGHEC, unité CNRS, UMR 2959.     

Identifying habitat sinks: a case study of Cooper’s hawks in an urban environment

We studied a population of Cooper’s hawks (Accipiter cooperii) in Tucson, Arizona from 1994 to 2005. High rates of mortality of nestlings from an urban-related disease prompted speculation that the area represented an ecological trap and habitat sink for Cooper’s hawks. In this paper, we used estimates of survival and productivity from 11years of monitoring to develop an estimate of the rate of population change, λ, for Cooper’s hawks in the area. We used a Cormack–Jolly–Seber approach to estimate survival of breeding hawks, and a stochastic, stage-based matrix to estimate λ. Despite the urban-related disease, the estimate of λ indicated that the area does not function as a habitat sink for Cooper’s hawks (= 1.11 ± 0.047; P = 0.0073 for the null of λ ≤ 1). Because data required to reliably identify habitat sinks are extensive and difficult to acquire, we suggest that the concept of habitat sinks be applied cautiously until substantiated with reliable empirical evidence.     

Gray squirrel density,habitat suitability,and behavior in urban parks

Increased density, increased intraspecific aggression, and a reduced fear of humans have been suggested as the more observable and frequently described characteristics of wildlife species undergoing synurbization, the process of becoming urbanized. The relationship among these variables and how they may be related to environmental variables that change with urbanization is poorly understood. In this paper we explore the relationship between density, intraspecific aggression, and reduced fear of humans in urban populations of gray squirrel. In the summer and fall of 2003 and 2004, we studied a park with a documented high density of gray squirrels, Lafayette Park, Washington, DC, and six urban parks in Baltimore, MD with unknown squirrel densities. We used linear regression (SAS Institute, SAS/STAT user’s guide. SAS Institute, Cary, NC, 2005) to determine if there was a relationship (P < 0.05) between squirrel density and intraspecific aggression, squirrel density and reduced fear of humans (wariness), and squirrel density and habitat suitability. We found a positive association between density and intraspecific aggression (R ² = 0.81, P < 0.00). A negative relationship between density and wariness (, P < 0.00). However, no relationship was evident between habitat suitability and squirrel density (, P = 0.437).     

Self-Employment,Work–Family Fit and Mental Health Among Female Workers

We used the 2002 National Study of the Changing Workforce to investigate the effects of work type on women’s lives. Specifically, we hypothesized that self-employed women have better work–family fit than organizationally employed women. We also hypothesized that as a result of better work–family fit, self-employed women would report better mental health than organizationally employed women. The analysis shows limited support for the hypotheses. Of the different dimensions of work–family fit, self-employment directly influenced only job to home facilitation. Work type had no direct influence on mental health. It appears that work type may indirectly influence work–family fit and mental health through higher job satisfaction and increased autonomy.

Does Nominal Devaluation Precede Real Devaluation? The Case of The Philippines

This paper attempts to examine the link between nominal devaluation and real devaluation with special reference to the Philippines. In doing so, we have used log linear relationship between the variables and have employed some sophisticated tests such as Ng–Perron unit root test, autoregressive distributive lag model, and dynamic ordinary least squares test for the long run correlation. The findings of the study with the Philippino quarterly data suggest that not only in the long run, but also in the short run, nominal devaluation leads to real devaluation.

Rapid Economic Development and Job Segregation in Taiwan

Most segregation studies have focused on industrialized nations where the economic structure is stable. However, when an economy experiences rapid development, the changing nature of industries and occupations may have a profound impact on gender segregation. This study uses a rapidly developing economy—Taiwan—to examine this issue. Based on the Yearbook of Manpower Survey Statistics, the gender representation was stable across industries and job status during the study period (1978–1997). However, occupation segregation increased dramatically. Rather than signaling a rise in discrimination, we find evidence that points to a benign, welfare improving self-selection, rather than gender discrimination. We speculate that this demonstrates occupation choice of women is more family-oriented when economic growth and development allows them this luxury.