On rationalizability of choice functions: A characterization of the median

In this paper we characterize choice behaviour that picks the median element from a set of feasible alternatives. It is easily seen that this choice behaviour violates most of the standard consistency conditions for set contraction and set expansion. The paper offers a complete characterization in terms of pure choice function conditions, and contrasts the new axiom set with the traditional consistency conditions. It also suggests alternative external references which could explain the choice of the median. Received: 2 June 1997/Accepted: 27 July 1998     

A probabilistic synopsis of binary decision rules

Decision rules for Yes–No voting systems are placed in a probabilistic framework. Selfdual and permutationally invariant distributions are introduced. Under such distributions, the mean success margin of the majority rule and of the unanimity rule are shown to bound the mean success margin of all other decision rules. For bloc decision rules in the Penrose/Banzhaf model, a product formula for the voters’ influence probabilities is derived. Other indices and the Shapley/Shubik model are also discussed.     

Policy convergence in a two-candidate probabilistic voting model

We propose a generalization of the probabilistic voting model in two-candidate elections. We allow the candidates have general von Neumann–Morgenstern utility functions defined over the voting outcomes. We show that the candidates will choose identical policy positions only if the electoral competition game is constant-sum, such as when both candidates are probability-of-win maximizers or vote share maximizers, or for a small set of functions that for each voter define the probability of voting for each candidate, given candidate policy positions. At the same time, a pure-strategy local Nash equilibrium (in which the candidates do not necessarily choose identical positions) exists for a large set of such functions. Hence, if the candidate payoffs are unrestricted, the “mean voter theorem” for probabilistic voting models is shown to hold only for a small set of probability of vote functions.     

The structure of coalitional power under probabilistic voting procedures

We consider probabilistic voting procedures which map each feasible set of alternatives and each utility profile to a social choice lottery over the feasible set. It is shown that if we impose: (i) a probabilistic collective rationality condition known as regularity; (ii) probabilistic counterpart of Arrow's independence of irrelevant alternatives and citizens' sovereignty; (iii) a probabilistic positive association condition called monotonicity; then the coalitional power structure under a probabilistic voting procedure is characterized by weak random dictatorship. Received: 1 March 1999/Accepted: 21 May 2001     

Discontinuity and non-existence of equilibrium in the probabilistic spatial voting model

This paper shows that in the simplest one-dimensional, two-candidate probabilistic spatial voting model (PSVM), a pure strategy Nash equilibrium may fail to exist. The existence problem studied here is the result of a discontinuity in the function mapping the candidates' platforms into their probabilities of winning. Proposition 1 of the paper shows that, whenever this probability of winning function satisfies a certain monotonicity property, it must be discontinuous on the diagonal. As an immediate consequence of the discontinuity in the probability of winning function, the candidates' objective functions are discontinuous as well. It is therefore impossible to invoke standard theorems guaranteeing the existence of a pure strategy equilibrium, and an example is developed in which in fact there is no pure strategy equilibrium. Finally, however, it is demonstrated that, for a large class of probability of winning functions, the PSVM satisfies all the conditions of a theorem of Dasgupta and Maskin (1986a) which guarantees that it will always have an equilibrium in mixed strategies. Received: 31 December 1996/Accepted: 12 May 1998     

Maximal domain for strategy-proof probabilistic rules in economies with one public good

We consider the problem of choosing a level of a public good on an interval of the real line among a group of agents. A probabilistic rule chooses a probability distribution over the interval for each preference profile. We investigate strategy-proof probabilistic rules in the case where distributions are compared based on stochastic dominance relations. First, on a “minimally rich domain”, we characterize the so-called probabilistic generalized median rules (Ehlers et al., J Econ Theory 105:408–434, 2002) by means of stochastic-dominance (sd) strategy-proofness and ontoness. Next, we study how much we can enlarge a domain to allow for the existence of sd-strategy-proof probabilistic rules that satisfy ontoness and the no-vetoer condition. We establish that the domain of “convex” preferences is the unique maximal domain including a minimally rich domain for these properties.     

Deterministic versus probabilistic consequences of trust and trustworthiness: An experimental investigation

There is overwhelming evidence of reciprocal behavior, driven by intentions. However, the role of consequences is less clear cut. Experimentally manipulating how efficient trust and reciprocity can be in deterministic and uncertain environments allows us to study how payoff consequences of trust and trustworthiness affect reciprocity. According to the results for our modified Investment Game, trustees reward trust more when trust is more efficient but do not adjust rewards when the efficiency of rewarding is varied. Furthermore, higher deterministic benefits result in higher levels of reciprocity for all trust levels, whereas an uncertain environment diminishes reciprocity.     

For a probabilistic sociology: A history of concept formation with Pierre Bourdieu

Theory and Society - This article uses a history of concept formation focused on Pierre Bourdieu’s probabilism to provide the groundwork for a probabilistic sociology. We argue that not only...     

Dictator game variants with probabilistic (and cost-saving) payoffs: A systematic test

Driven by methodological concerns, theoretical considerations, and previous evidence, I systematically test the validity of common dictator game variants with probabilistic payoffs. Using a unified experimental framework, I include four approaches and compare them to a standard dictator game: involving fewer receivers than dictators, paying only some players, paying only some decisions, and role uncertainty. I also relate transfers in the dictator game variants to established complementary individual difference measures of prosociality: social value orientation, personal values, a donation to charity, and the Big Five personality factor agreeableness. My data shows that the standard dictator game presents the expected correlations with the complementary measures of prosociality. Involving fewer receivers yields comparably valid results. By contrast, when only some players or decisions are paid or, particularly, when subjects face role uncertainty, the expected associations with complementary prosociality measures are distorted. Under role uncertainty, generosity is also significantly biased upward. I conclude that the validity of dictator game outcomes is highly sensitive to the applied methods. Not all dictator game variants can be recommended for the valid measurement of social preferences.     

Choosing subsets: a size-independent probabilistic model and the quest for a social welfare ordering

“Subset voting” denotes a choice situation where one fixed set of choice alternatives (candidates, products) is offered to a group of decision makers, each of whom is requested to pick a subset containing any number of alternatives. In the context of subset voting we merge three choice paradigms, “approval voting“ from political science, the “weak utility model” from mathematical psychology, and “social welfare orderings” from social choice theory. We use a probabilistic choice model proposed by Falmagne and Regenwetter (1996) built upon the notion that each voter has a personal ranking of the alternatives and chooses a subset at the top of the ranking. Using an extension of Sen's (1966) theorem about value restriction, we provide necessary and sufficient conditions for this empirically testable choice model to yield a social welfare ordering. Furthermore, we develop a method to compute Borda scores and Condorcet winners from subset choice probabilities. The technique is illustrated on an election of the Mathematical Association of America (Brams, 1988). Received: 18 August 1995 / Accepted: 13 February 1997     

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.     

On Boundaries

In this essay, I discuss the consequences of establishing boundaries and categories and the consequences for peoples, the need to consider insider and outsider categories in the sociological endeavor, and some of the current problems in our society that have been revealed by research and the communication of boundary research.     

On trial

As researchers uncover basic mechanisms that underlie aging, they hope that lessons learned from mice, worms, flies, and other lab denizens will apply to people. Making that leap requires a new set of scientific approaches, from observational studies to the most rigorous of tests, the double-blind, randomized, placebo-controlled clinical trial. Navigating this unique scientific terrain presents new obstacles for basic-science researchers but can provide the ultimate payoff.     

伊斯兰新柏拉图主义研究

伊斯兰新柏拉图主义是在阿拉伯翻译家翻译希腊哲学过程中形成和发展起来的哲学思想。其代表人物在“第一”、“灵魂”和“人”这些哲学基本问题上进行了创造性的思维,表现出伊斯兰新柏拉图主义的一些共同特征:重视理性,研究理性和非理性认知的关系及作用;通过灵魂的修养和完善及个人与社会环境的关系及构建等表现哲学和宗教的调和。这些特征展示了伊斯兰新柏拉图主义哲学和神学(宗教)相结合,理性思维方式和非理性思维的内容统一。研究伊斯兰新柏拉图主义可拓宽我们思考生存与和谐问题的视域,为自身哲学应对外来文化冲击提供一个理论参考。