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Publications | The Federmann Center for the Study of Rationality

Publications

1992
Maya Bar-Hillel, Menahem Yaari . Judgments Of Distributive Justice. Discussion Papers 1992. Web. Publisher's VersionAbstract
The basic rule of distributive justice is the proportionality rule, which states that "Distributive justice involves a relationship between ... two persons, P1 and P2 one of whom can be assessed as higher than, or lower than, the other; and their two shares, or ... rewards, R1 and R2. The condition of distributive justice is satisfied when ... : P1/P2=R1/R2". (Homans, 1961). We studied this rule, in survey style, using cases such as the following: "suppose you have 12 grapefruit which you divide between Jones and Smith in as just a manner as possible. How should this be done ?". in our problems, either one or two goods were to be allocated between two recipients who differed on at most one dimension, either needs (e.g, Smith requires more grapefruit than Jones), beliefs (e.g, Smith believes that grapefruit are less nutritious than Jones believes them to be), or tastes (e.g, Smith enjoys grapefruit more than Jones). the results show that it is very hard to be more specific than the general formulation above without being ad hoc. For example, most people wish to allocate proportionately to need, only a minority wish to allocate proportionately to beliefs, and insofar as people wish to take tastes into consideration, they do so in a non-compensatory fashion. In other words, with regard to needs, less efficient extractors are awarded larger shares, but with regard to pleasure, more efficient extractors are awarded larger shares. Since real world distribution problems don't come neatly labelled as needs, tastes, etc., it is hard to predict or theorize what would be "just" in them.
Winter, Eyal . Mechanism Robustness In Multilateral Bargaining. Discussion Papers 1992. Web. Publisher's VersionAbstract
We describe a non-cooperative bargaining model for games in coalition form without transferable utility. In this model random moves determine the order by which the players take their actions. the specific assignment of probability distributions to these chance moves is called the mechanics of the bargaining. Within this framework we examine the relation between the property of mechanism robustness, and coalition stability of the bargaining outcome, by showing that these two properties boil down to be the same.
Shmida, Uzi Motro, and Avi. Near-Far Search: An Evolutionarily Stable Foraging Strategy. Discussion Papers 1992. Web. Publisher's VersionAbstract
This study addresses the momentary rules of foraging behavior on carpet inflorescences. It has long been suggested that patchiness in the distribution of nectar can give an advantage to near-far type of foraging strategies, that is, to foragers which search "near" (in the neighborhood of the last visited flower) as long as the nectar yield is high enough, and go "far" otherwise. Here we show that under certain conditions, such a strategy can be evolutionary stable. Furthermore, prior patchiness in the nectar distribution is not a necessary condition for the evolutionary stability of a near-far search. It turns out that during near-far foraging, some patchiness is created by the foraging process itself, which the near-far forager can exploit later on. To show the evolutionary stability of near-far search, various foraging strategies were compared, according to two, slightly different optimality criteria : the number of flowers emptied during a fixed length bout, and the number of flowers visited until total extraction of the entire inflorescence. We find that long enough bouts (in the case of a single forager) or a substantial probability of revisits to the same inflorescence (in the case of multipleforagers) are necessary for near-far to be an ESS.
Hart, Sergiu . On Prize Games. Discussion Papers 1992. Web. Publisher's VersionAbstract
We consider the class of hyperplane coalition games (H-games): the feasible set of each coalition is a half-space, with a slope that may vary from one coalition to another. H-games have turned out in various approaches to the value of general non-transferable utility (NTU) games. In this paper we introduce a simple model – prize games – that generates the hyperplane games. next, we provide an axiomatization for the Maschler & Owen (1989) consistent value of H-games.
Shmida, James W. Friedman, and Avi. Pollination, Gathering Nectar, And The Distribution Of Flower Species. Discussion Papers 1992. Web. Publisher's VersionAbstract
We present here a model of pollination having one species of bees and several species of flowers. Each flower species is distinguished by its rate of nectar production and the resources it devotes to display. The flowers and bees are assumed to have identical lifetimes that comprise a number of days within a single year. At the start of the year the bees in their naive phase are attracted to flowers according to the relative sizes of the flowers' displays; however, the bees soon become experienced and continually monitor the amounts of the nectar standing crops of each species, altering their visiting habits over time so that they always tend to visit most frequently the flower species having the largest nectar standing crop. This, in turn, tends equalize the nectar standing crop across species. From one year to the next the relative abundance of the flower species can change in accordance with the reproductive success of each species. This, in turn, depends upon the number of visits by bees to the flowers of each species, the amount of energy devoted to reproduction, and the relative abundance of each species in the preceding year. The model described below has been programmed so that it is possible to run simulations. We make no attempt to model the absolute number of bees or of flowers, but do assume the ratio of bees to flowers is the same from one season to the next. Within this model systematic deviations by the bees from apparently optimal foraging policies can be seen, due to monitoring by the bees, and also the ability to survive of large display flowers that produce no nectar ("cheaters") can be explained.
Peleg, Avi Shmida, and Bezalel. Strict And Symmetric Correlated Equilibria Are The Distributions Of The Ess's Of Biological Conflicts With Asymmetric Roles. Discussion Papers 1992. Web. Publisher's VersionAbstract
We investigate the ESS's of payoff-irrelevant asymmetric animal conflicts in Selten's (1980) model. We show that these are determined by the symmetric and strict correlated equilibria of the underlying (symmetric) two-person game. More precisely, the set of distributions (on the strategy space) of ESS's coincides with the set of strict and symmetric correlated equilibria (described as distributions). Our result enables us to predict all possible stable payoffs in payoff-irrelevant asymmetric animal conflicts using Aumann's correlated equilibria. Italso enables us to interpret correlated equilibria as solutions to biological conflicts: Nature supplies the correlation device as a phenotypic conditional behavior.
David Budescu, Maya Bar-Hillel . To Guess Or Not To Guess. Discussion Papers 1992. Web. Publisher's VersionAbstract
Multiple choice tests that are scored by formula scoring typically include instructions that discourage guessing. In this paper we look at test taking from the normative and descriptive perspectives of judgment and decision theory. We show that for a rational test taker, whose goal is the maximization of expected score, answering is either superior or equivalent to omitting – a fact which follows from the scoring formula. For test takers who are not fully rational, or have goals other than the maximization of expected score, it is very hard to give adequate formula scoring instructions, and the recommen-dation to answer under partial knowledge is problematic (though generally beneficial). Our analysis derives from a critical look at standard assumptions about the epistemic states, response strategies, and strategic motivations of test takers. In conclusion, we endorse the "number right" scoring rule, which discourages omissions, and is robust against variability in respondent motivations, limitations in judgments of uncertainty, and item vagaries.