Showing papers in "Mathematical Social Sciences in 1991"

TL;DR: The difference measure of predictive success for area theories introduced by Selten and Krischker (1983) is the difference between hit rate and area as mentioned in this paper, which is defined as the relative frequency of successful predictions and the relative size of the predicted region within the set of all possible outcomes.

TL;DR: In this paper, the authors take the analytic framework developed to measure inequality in the distribution of income and extend it to the problem of measuring inequality in people across population groups (e.g. inequality of women across occupations).

TL;DR: The role colouring of a graph is an assignment of colours to the vertices which obeys the rule that two vertices are coloured the same only if their neighbourhoods have the same colour set as discussed by the authors.

TL;DR: In this article, the authors give several sets of axioms on a consensus function that characterize the plurality function, and also investigate the plurality functions for related consensus functions, such as the consensus function for voting.

TL;DR: In this paper, the Borda Dominance decomposition is used to derive necessary and sufficient conditions for various degrees of transitivity of majority preference, and Sen's well-known sufficiency theorem, together with some stronger theorems, are shown to depend upon a strong double form of the masking phenomenon.

TL;DR: The main theorem of as discussed by the authors generalizes the Eilenberg-Debreu theorems for the connected case of the problem of defining a topology t on an arbitrary set to be "useful".

TL;DR: The following axioms are imposed on aggregations of choice functions: Unrestricted Domain (U), Neutrality (N), Independence of Symmetric Substitutions (ISS), Anonymity (A) and Positive Response (PR) as mentioned in this paper.

TL;DR: In this article, the authors characterize sets of mutually acceptable pairs of individuals in the stable matching problem for which a stable matching exists under all preference profiles and show that the corresponding acceptability graph is bipartite.

TL;DR: In this article, a generalization of Rotondo's choice model is presented and several additional incomplete characterizations of the model are also presented; the class of random advantage models is related to the generalized Rotondo model.

TL;DR: In this article, the consequences of dropping the homogeneity axiom of equal absolute sharing and proportional sharing are examined and two characterizations of a class of sharing methods are provided, which contains equal absolute and proportional shares as polar (and in fact as the only homogeneous) cases.

TL;DR: In this article, a lexicographic equal-loss solution for Nash's bargaining problem is proposed, which equalizes across agents the losses from the ideal point to satisfy Pareto optimality.

TL;DR: In this article, a characterization of the plurality function interpreted as giving a vector of 0's and 1's, with the 1 representing membership in the consensus subset, is given, which leads to the problem of solving an interesting new functional equation.

TL;DR: In this article, the authors considered the class of partitioning games, which includes the assignment game, the consecutive game, and the m-sided assignment game and provided necessary and sufficient conditions for existence of the core in these games.

TL;DR: In this article, two independent methods to restrict simple games are given, one related to graph restriction theory for general games and the other related to a graph-restriction theory for simple games.

TL;DR: In this paper, it was shown that an upper-hemicontinuous correspondence, with nonempty, compact andconvex values, applying the cartesian product of an arbitrary number of simplexes on the corresponding space, has aquasi-diagonal image.

TL;DR: In this paper, the authors formalize the game situation in terms of an infinitary first-order predicate logic and give an axiom for final decisions, which takes the form of the common knowledge of the above requirement by its very nature.

TL;DR: In this paper, the problem of designing Nash allocations whose Nash allocations coincide with the Lindahl allocations for public goods economies with any number of private and public goods is dealt with. And the mechanism presented here improves the previous mechanisms by introducing two new features: one is that the mechanism is balanced (not merely weakly balanced), and the other is provided with the marginal cost pricing rule for both equilibrium and disequilibrium messages.

TL;DR: In this paper, it was shown that Debreu's theorem on the representation of preferences by a utility function is essentially nonconstructive, and it is shown that preference representation can be expressed as a function.

TL;DR: In this paper, a simple model of a multi-party political system is considered consisting of a distribution in Euclidean n-space, Rn the distribution of voters' political views, and of k parties, determined at every time instant through their policies, k points in the same space Rn.

TL;DR: A careful mathematical treatment of two majority voting procedures in which a voting agenda is utilized: sincere voting and sophisticated voting is given.

TL;DR: In this article, three classically equivalent notions - classical preference relation, weak preference relation, and preference relation - are discussed within the framework of recursive constructive mathematics, and it is shown that the implications preference relation ⇒ weak preference relations ⇒ classical preference relations are the best possible in that framework; but that under certain conditions, including two (openness and local nonsatiation) that arise naturally in economic theory, a strong preference relation is a preference relation.

TL;DR: The authors show that a variety of fairness axioms far more stringent than equal treatment are embraced by replicant refinements of the core and adopt an average perspective on the core allocation.

TL;DR: In this paper, the authors axiomatize three increasingly restrictive representations for a preference relation on a mixture set that presume neither transitivity nor an Archimedean condition, which are necessary and sufficient for the representations.

TL;DR: In this paper, a new algorithm for reconstructing a skew-symmetric utility function is proposed, which is asymptotically optimal in the sense that the number of binary (yes-no) questions that one has to ask to determine the values of F with given precision is of minimal possible order.

TL;DR: Theorem 3 as discussed by the authors examines the extent to which asymptotic verifications of Edgeworth's Conjecture for sequences of exchange economies can be verified effectively using a model-theoretic argument due to Compton (1980).

TL;DR: In this article, a class of social choice problems with a fixed set of alternatives was considered and the existence and the general form of continuous, proper and anonymous social choice functions were investigated.

TL;DR: In this paper, the authors analyzed a winner-take-all patent race where the time of success is a random variable directly related to the level of effort, a firm decision variable, and derived the characteristics of optimal patent life, fee for entry, and cost-sharing subsidy.

TL;DR: The purely set-theoretical equivalence of an iterative definition and a set theoretical definition of common knowledge is proved without any assumption on the cardinalities of the information partitions as mentioned in this paper.

TL;DR: In this paper, a framework for investigating the discrete/continuous choice of economic modeling is developed, where an essential economic unit (EU) is defined such that each (decision) variable is constructed in terms of the EU multiplied by an integer.