Manipulability, unanimity, anonymity and merging functions

A merging (or assessment aggregation) function (see [7]) is a rule that synthesizes several individual assessments, or numerical judgements, by creating a unique “collective” assessment. Individual i can manipulate assessment aggregation if the change in the merged assessment due to a change in i's assessment from x to y depends solely on x and y. Some assumptions on the functional form capturing this dependence are put forward and their effects on aggregation investigated under unanimity and anonymity conditions using a functional equation approach. Attention is restricted to three types of results: the merging function does not exist; it is the arithmetic mean; it is dictatorial. Received: 21 November 1997/Accepted: 31 May 1999     

Comparison functions and choice correspondences

In this paper, we introduce the concept of a comparison function, which is a mapping g that assigns numbers to ordered pairs of alternatives (x,y) with the property that g(x,y)=−g(y,x). The paper discusses how some well-known choice correspondences on tournaments such as the uncovered set, the minimal covering set and the bipartisan set can be extended to this general framework. Axiomatic characterizations and properties are studied for these correspondences. Received: 4 November 1996/Accepted: 13 April 1998     

An extension of a theorem on the aggregation of separable preferences

An Excess-Voting Function relative to a profile π assigns to each pair of alternatives (x,y), the number of voters who prefer x to y minus the number of voters who prefer y to x. It is shown that any non-binary separable Excess-Voting Function can be achieved from a preferences profile when individuals are endowed with separable preferences. This result is an extension of Hollard and Le Breton (1996). Received: 16 December 1996 / Accepted: 8 October 1997     

Positional information and preference aggregation

A new version of independence (I⁺) is proposed for social welfare functions based on the following notion of agreement. Two weak orders R and R’ on a finite set S agree on a pair {x,y}, denoted byif R|_{x,y} = R’|_{x,y} and [z R*x and z R*y for some z∈S] if and only if [z’ (R’)* x and z’(R’)*y for some z’∈S]. The last part says that x and y are strictly under z with respect to R exactly when x and y are strictly under z’ with respect to R’. Some examples and results on social welfare functions that satisfy (I⁺), Pareto, and nondictatorship are given.I am grateful for the comments and suggestions made by an anonymous referee on an earlier version of this paper.     

The sensitivity of weight selection for scoring rules to profile proximity to single-peaked preferences

Niemi (Am Polit Sci Rev 63:488–497, 1969) proposed a simple measure of the cohesiveness of a group of n voters’ preferences that reflects the proximity of their preferences to single-peakedness. For three-candidate elections, this measure, k, reduces to the minimum number of voters who rank one of the candidates as being least preferred. The current study develops closed form representations for the conditional probability, PASW(n,IAC|k), that all weighted scoring rules will elect the Condorcet winner in an election, given a specified value of k. Results show a very strong relationship between PASW(n,IAC|k) and k, such that the determination of the voting rule to be used in an election becomes significantly less critical relative to the likelihood of electing the Condorcet winner as voters in a society have more structured preferences. As voters’ preferences become more unstructured as measured by their distance from single-peakedness, it becomes much more likely that different voting rules will select different winners.A preliminary version of this paper was presented at the European Public Choice Society Conference in Berlin, Germany, April 15–18, 2004.     

Does the Borda rule provide more than a ranking?

Consider the following problem: a set of candidates {x, y, z} has to be ranked from best to worse by a committee. Each member of the committee provides his own ranking of the three candidates and you decide to use the Borda method to aggregate the rankings. The resulting scores are as follows: 107 for x, 106 for y and 51 for z. Would you conclude that x is better than y? Probably not, because the difference between the scores of x and y is small. The only conclusion you would draw is that z definitely is the worst candidate. But, is it meaningful to consider differences of Borda scores? We characterize the Borda method in this new framework and find conditions that are very close to those characterizing the classical Borda method. Throughout our paper, we consider a generalization of the Borda method designed to aggregate fuzzy relations. Received: 2 March 1998/Accepted: 5 May 1999     

Ranking profiles of capability sets

In this paper, we present an innovative approach for ranking profiles of capability sets on the basis of equity. An interesting way of capturing the notion of equity is to take into account the extent to which each of the different functioning vectors is shared by the population under consideration (of size n). This is done by defining the ‘common capability sets’ enjoyed by k individuals as the set of functioning vectors simultaneously available to at least k individuals (1 ≤ k ≤ n). These sets are closely related to the original capability sets and have some interesting properties that are examined throughout the paper. We define and axiomatically characterize a capability profile ranking that lexicographically compares the different common capability sets. We would like to thank for helpful discussion and comments to Jorge Alcalde-Unzu, Ritxar Arlegi, Miguel A. Ballester, Jose Enrique Galdón, Antonio Nicolò, Jorge Nieto, Prasanta Pattanaik, John Weymark and the anonymous referees of this paper. The project is supported by Spanish’ Comision Interministerial de Ciencia y Technologia (SEC2003-08105) and by the European Commission (MRTN-CT-2003-504796).     

Egalitarian-equivalence and the Pareto principle for social preferences

The Pareto principle is often in conflict with the equity criteria in construction of social preferences: there exist two allocations x and y such that x Pareto dominates y, but y is an equitable allocation whereas x is not. The efficiency-first principle requires to rank an allocation x higher than y if (i) x Pareto dominates y or (ii) x and y are Pareto-noncomparable and x is equitable whereas y is not. The equity-first principle reverses the order of application of the two criteria. Adopting egalitarian-equivalence as the notion of equity, we examine rationality of the social preference functions based on the efficiency-first or the equity-first principle. The degrees of rationality vary widely depending on which principle is adopted, and depending on the range of egalitarian-reference bundles. We show several impossibility and possibility results as well as a characterization of the social preference function introduced by Pazner and Schmeidler (1978). We also identify the sets of maximal elements of the social preference relations in the set of feasible allocations. The results are contrasted with those in the case where no-envy is the notion of equity.This paper is a much extended version of a part of Tadenuma (1998). The author is grateful to Marc Fleurbaey, Serge-Chiristophe Kolm, Kotaro Suzumura, and William Thomson for helpful comments on the earlier version of the paper. ‘‘Financial support from the Ministry of Education, Culture, Sports, Science and Technology of Japan for the 21st Century Center of Excellence Project on the Normative Evaluation and Social Choice of Contemporary Economic Systems is gratefully acknowledged’’.     

Covering relations,closest orderings and hamiltonian bypaths in tournaments

We show that the Slater's set of a tournament, i.e. the set of the top elements of the closest orderings, is a subset of the top cycle of the uncovered set of the tournament. We also show that the covering relation is related to the hamiltonian bypaths of a strong tournament in that if x covers y, then there exists an hamiltonian bypath from x to y.We thank B. Monjardet and an anonymous editor for helpful suggestions.     

Intermediate inequality and welfare

We introduce a new centrist or intermediate inequality concept, between the usual relative and absolute notions, which is shown to be a variant of the α-ray invariant inequality measures in Pfingsten and Seidl (1997). We say that distributions x and y have the same (x, π)-inequality if the total income difference between them is allocated among the individuals as follows: 100π% preserving income shares in x, and 100(1−π)% in equal absolute amounts. This notion can be made as operational as current standard methods in Shorrocks (1983). Received: 13 May 1998/Accepted: 25 January 1999     

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.     

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).     

Welfarist-consequentialism,similarity of attitudes,and Arrow’s general impossibility theorem

Two features of Arrows social choice theory are critically scrutinized. The first feature is the welfarist-consequentialism, which not only bases social judgements about right or wrong actions on the assessment of their consequences, but also assesses consequences in terms of peoples welfare and nothing else. The second feature is a similarity of peoples attitudes towards social outcomes as a possible resolvent of the Arrow impossibility theorem. Two extended frameworks, one consequentialist and the other non-consequentialist, are developed. Both frameworks are shown to admit some interesting resolutions of Arrows general impossibility theorem, which are rather sharply contrasting with Arrows own perspective.     

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.     

A Note on the Separability Principle in Economies with Single-Peaked Preferences

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and Ω-continuity. We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of Ω-continuity. Furthermore, we prove that the equal division lower bound and separability imply no-envy. Using this result, we strengthen one of Chun’s (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, the equal division lower bound, separability, and either Ω-continuity or duplication-invariance.     

Visual Dominance and Visual Egalitarianism: Individual and Group-Level Influences of Sex and Status in Group Interactions

This study investigated visual dominance and visual egalitarianism of men and women (N = 94; 17 teams) in team meetings at diverse workplaces. Two novel gaze-related measures were developed: (a) a group visual dominance ratio (group-VDR) assessing each member’s visual dominance vis-à-vis all other members, and (b) a gaze distribution index (GDI) assessing each member’s visual egalitarianism to all group members. Multilevel analyses were conducted to account for influences of the team members’ sex and status on the individual level and for influences of sex and status composition of the teams, and the team leaders’ sex on the group level. Results suggested that high-status individuals displayed more visual dominance than low-status individuals. The significant interaction of individuals’ sex and status indicated that the positive relationship of status and visual dominance applied particularly to women. The more women in a team, the more visual dominance was displayed. The team leader’s sex significantly influenced visual egalitarianism: Gaze distribution was less egalitarian when the team leader was male.     

Improvement indices of well-being

In recent years, various classes of indices measuring the improvement of well-being have been suggested. Formally, an improvement index is a function Q* (x ₁, x ₂), where x _t is the level of some attribute of well-being, e.g., life expectancy, in period t. This paper extends previous works on improvement indices by introducing a class of multidimensional indices which aggregates the improvement of a group of attributes of well-being. We propose a set of axioms which leads inexorably to a multidimensional generalization of Kakwani's class of improvement indices of well-being (Kakwani 1993).Financial support from the Social Science and Education Panel of the Chinese University of Hong Kong (research grant account no: 220201620) is gratefully acknowledged     

Parental religiosity and daughters’ fertility: the case of Catholics in southern Europe

Preferences, including preferences for children, are shaped during the formative years of childhood. It is therefore essential to include exposure to religious practice during childhood in an attempt to establish a link between religiosity and fertility. This path has not been explored in the documented literature that looks at the relationship between current religiosity and fertility. The International Social Survey Programme: Religion II (ISSP) provides the data base. It includes information on maternal/paternal/own mass participation when the respondent was a child (nine levels each), as well as on his current churchgoing (six levels) and prayer habits (eleven levels). These variables are included as explanatory variables in ‘fertility equations’ that explain the number of children of Catholic women in Spain and Italy. The core findings are that exposure to religiosity during the formative years of childhood, has a pronounced effect on women’s ‘taste for children’ that later on translates into the number of her offspring. In Spain, the two parents have major opposite effects on women. Most striking is the negative effect of the mother’s intensity of church attendance on her daughter’s fertility: Women who were raised by an intensively practicing mother have on average one child less that their counterparts who were raised by a less religious mother. On the other hand, an intensively practicing father encourages the daughter to have more children (by about 0.8, on average). The Italian sample confirms the statistically significant negative effect of the mother’s religiosity. The father’s religious conduct has apparently no effect on Italian women’s birth rates. Current religiosity seems to be irrelevant, both in Spain and in Italy. It follows that religiosity and fertility are interrelated but the mechanism is probably different from the simplistic causality that is suggested in the literature.

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.