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Publications | The Federmann Center for the Study of Rationality

Publications

2009
Tamar Keasar, Ally R. Harar, Guido Sabatinelli Denis Keith Amots Dafni Ofrit Shavit Assaph Zylbertal, and Avi Shmida. Red Anemone Guild Flowers As Focal Places For Mating And Feeding Of Mediterranean Glaphyrid Beetles. Discussion Papers 2009. Web. Publisher's VersionAbstract
Several species of glaphyrid beetles forage and mate on Mediterranean red flowers. In red anemones and poppies in Israel, female beetles occupy only bowl-shaped a subset of the flowers, do not aggregate, and are hidden below the petals. This raises the question how males find their mates. The possibility that males and females orient to similar plant- generated cues, thereby increasing their mate encounter prospects, was investigated. Beetle attraction to red models increased with display area in previous studies. Choice tests with flowers and with models indicate that both male and female beetles prefer large displays to smaller ones. In anemones, beetles rest, feed and mate mainly on male- phase flowers, which are larger than female- phase flowers. Poppies that contain beetles are larger than the population average. These findings support the hypothesis that males and females meet by orienting to large red displays. Corolla size correlates with pollen reward in both plant species, suggesting that visits to large flowers also yield foraging benefits. Male beetles often jump rapidly among adjacent flowers. In contrast to the preference for large flowers by stationary individuals, these jumps sequences are random with respect to flower (in anemone) and size (in poppy). They may enable males to detect females at sex-phase close range. We hypothesize that males employ a mixed mate- searching strategy, combining orientation to floral signals and to female- produced cues. The glaphyrids' preference for large flowers may have selected for extraordinarily large displays within the "red anemone" pollination guild of the Levant.
Bavli, Hillel . Rule-Rationality And The Evolutionary Foundations Of Hyperbolic Discounting. Discussion Papers 2009. Web. Publisher's VersionAbstract
Recent studies involving intertemporal choice have prompted many economists to abandon the classical exponential discount utility function in favor of one characterized by hyperbolic discounting. Hyperbolic discounting, however, implies a reversal of preferences over time that is often described as dynamically inconsistent and ultimately irrational. We analyze hyperbolic discounting and its characteristic preference reversal in the context of rule-rationality, an evolutionary approach to rationality that proposes that people do not maximize utility in each of their acts; rather, they adopt rules of behavior that maximize utility in the aggregate, over all decisions to which an adopted rule applies. In this sense, people maximize over rules rather than acts. Rule-rationality provides a framework through which we may examine the rational basis for hyperbolic discounting in fundamental terms, and in terms of its evolutionary foundations. We conclude that although aspects of hyperbolic discounting may contain a certain destructive potential, it is likely that its evolutionary foundations are sound – and its application may well be as justified and rational today as it was for our foraging ancestors.
Samuel-Cahn, Abba M. Krieger, and Ester. Secretary Problem Of Minimizing Expected Rank: A Simple Suboptimal Approach With Generalizations, The. Discussion Papers 2009. Web. Publisher's VersionAbstract
The secretary problem for selecting one item so as to minimize its expected rank, based on observing the relative ranks only, is revisited. A simple suboptimal rule, which performs almost as well as the optimal rule, is given. The rule stops with the smallest i such that Ri
Jay Bartroff, Larry Goldstein, Yosef Rinott, and Ester Samuel-Cahn. Spend-It-All Region And Small Time Results For The Continuous Bomber Problem, The. Discussion Papers 2009. Web. Publisher's VersionAbstract
A problem of optimally allocating partially effective ammunition x to be used on randomly arriving enemies in order to maximize an aircraft's probability of surviving for time t, known as the Bomber Problem, was first posed by Klinger and Brown (1968). They conjectured a set of apparently obvious monotonicity properties of the optimal allocation function K(x,t). Although some of these conjectures, and versions thereof, have been proved or disproved by other authors since then, the remaining central question, that K(x,t) is nondecreasing in x, remains unsettled. After reviewing the problem and summarizing the state of these conjectures, in the setting where x is continuous we prove the existence of a "spend-it-all" region in which K(x,t) = x and find its boundary, inside of which the long-standing, unproven conjecture of monotonicity of K(.,t) holds. A new approach is then taken of directly estimating K(x,t) for small t, providing a complete small-t asymptotic description of K(x,t) and the optimal probability of survival.
Levy, Yehuda (John) . Stochastic Games With Information Lag. Discussion Papers 2009. Web. Publisher's VersionAbstract
Two-player zero-sum stochastic games with finite state and action spaces, as well as two-player zero-sum absorbing games with compact metric action spaces, are known to have undiscounted values. We study such games under the assumption that one or both players observe the actions of their opponent after some time-dependent delay. We develop criteria for the rate of growth of the delay such that a player subject to such an information lag can still guarantee himself in the undiscounted game as much as he could have with perfect monitoring. We also demonstrate that the player in the Big Match with the absorbing action subject to information lags which grow too rapidly, according to certain criteria, will not be able to guarantee as much as he could have in the game with perfect monitoring. toring.
Sheshinski, Eytan . Uncertain Longevity And Investment In Education. Discussion Papers 2009. Web. Publisher's VersionAbstract
It has been argued that increased life expectancy raises the rate of return on education, causing a rise in the investment in education followed by an increase in lifetime labor supply. Empirical evidence of these relations is rather weak. Building on a lifecycle model with uncertain longevity, this paper shows that increased life expectancy does not suffice to warrant the above hypotheses. We provide assumptions about the change in survival probabilities, specifically about the age dependence of hazard rates, which determine individuals' behavioral response w.r.t. education, work and age of retirement. Comparison is made between the case when individuals have access to a competitive annuity market and the case of no insurance.
Neyman, Abraham . Value Of Two-Person Zero-Sum Repeated Games With Incomplete Information And Uncertain Duration, The. Discussion Papers 2009. Web. Publisher's VersionAbstract
It is known that the value of a zero-sum infinitely repeated game with incomplete information on both sides need not exist [Aumann Maschler 95]. It is proved that any number between the minmax and the maxmin of the zero-sum infinitely repeated game with incomplete information on both sides is the value of the long finitely repeated game where players' information about the uncertain number of repetitions is asymmetric.
2008
Ullmann-Margalit, Edna . "We The Big Brother" Or The Curious Incident Of The Camera In The Kitchen. Discussion Papers 2008. Web. Publisher's VersionAbstract
Last summer, a member of the Rationality Center at the Hebrew University of Jerusalem installed a closed-circuit TV camera in the Center's kitchen. An email explained that the camera was installed in an effort to keep the kitchen clean. By the time the camera was removed, a week later, the members of the Center exchanged close to 120 emails among themselves, expressing their opinions for and against the camera and discussing related issues.Taking off from this exchange, I explore the surprisingly rich set of normative concerns touched upon by the kitchen-camera incident. These include a host of issues regarding people's polarized attitudes toward public surveillance, the problem of the invasive gaze and the argument that "if you have nothing to hide you have nothing to worry," the efficacy of disciplining behavior through sanctions along with the problems related to shaming sanctions, the notion of privacy and its arguable relevance to the kitchen case, and more. Special attention is given to the notion ofcleanness and to its related norms.In an epilogue, I offer some reflections in the wake of the incident. I find that it is precisely the smallness, concreteness and seeming triviality of this incident that helps bring a large set of interconnected, vexing normative concerns into sharper relief.
Zultan, Andriy Zapechelnyuk, and Ro'i. Altruism, Partner Choice, And Fixed-Cost Signaling. Discussion Papers 2008. Web. Publisher's VersionAbstract
We consider a multitype population model with unobservable types, in which players are engaged in the `mutual help' game: each player can increase her partner's fitness at a cost to oneself. All individuals prefer free riding to cooperation, but some of them, helpers, can establish reciprocal cooperation in a long-term relationship. Such heterogeneity can drive cooperation through a partner selection mechanism under which helpers choose to interact with one another and shun non-helpers. However, in contrast to the existing literature, we assume that each individual is matched with an anonymous partner, and therefore, stable cooperation cannot be achieved by partner selection per se. We suggest that helpers can signal their type to one another in order to establish long-term relationships, and we show that a reliable signal always exists. Moreover, due to the difference in future benefits of a long-term relationship for helpers and non-helpers, the signal need not be a handicap, in the sense that the cost of the signal need not be correlated with type.
Zamir, Shmuel . Bayesian Games: Games With Incomplete Information. Discussion Papers 2008. Web. Publisher's VersionAbstract
An encyclopedia article on games with incomplete information. Table of contents:1. Definition of the subject and its importance2. Introduction: Modeling incomplete information3. Harsanyi s model: The notion of type4. Aumann s model5. Harsanyi s model and the hierarchies of beliefs6. The Universal Belief Space7. Belief subspaces8. Consistent beliefs and Common prior9. Bayesian games and Bayesian equilibrium10. Bayesian equilibrium and Correlated equilibrium11. Concluding remarks and future directions12. Bibliography
Zamir, Bezalel Peleg, and Shmuel. Condorcet Jury Theorem: The Dependent Case. Discussion Papers 2008. Web. Publisher's VersionAbstract
{We provide an extension of the Condorcet Theorem. Our model includes both the Nitzan-Paroush framework of unequal competencies  and Ladha s model of correlated voting by the jurors . We assume that the jurors behave informatively , that is, they do not make a strategic use of their information in voting. Formally, we consider a sequence of binary random variables X = (X1,X2, ...,Xn, ...) with range in 0,1 and a joint probability distribution P. The pair (X,P) is said to satisfy the Condorcet Jury Theorem (CJT) if limn†’ˆ\v zP(ˆ‘Xi>n/2)=1. For a general (dependent) distribution P we provide necessary as well as sufficient conditions for the CJT. Let pi = E(Xi)
Hart, Sergiu, and Andreu Mas-Colell. Cooperative Games In Strategic Form. Discussion Papers 2008. Web. Publisher's VersionAbstract
In this paper we view bargaining and cooperation as an interaction superimposed on a strategic form game. A multistage bargaining procedure for N players, the "proposer commitment" procedure, is presented. It is inspired by Nash's two-player variable-threat model; a key feature is the commitment to "threats." We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies the traditional coalitional function may not be adequate when utilities are not transferable.
Kahana, Alon Harel, and Tsvi. Easy Core Case For Judicial Review, The. Discussion Papers 2008. Web. Publisher's VersionAbstract
This paper defends judicial review on the grounds that judicial review is necessary for protecting a right to a hearing.  Judicial review is praised by its advocates on the basis of instrumentalist reasons, i.e., because of its desirable contingent consequences such as protecting rights, romoting democracy, maintaining stability, etc. We argue that instrumentalist easons for judicial review are bound to fail and that an adequate defense of udicial review requires justifying judicial review on non-instrumentalist grounds. A non-instrumentalist justification grounds judicial review in essential attributes of he judicial process. In searching for a non-instrumental justification we establish that judicial review is designed to protect the right to a hearing. The right to a hearing consists of hree components: the opportunity to voice a grievance, the opportunity to be rovided with a justification for a decision that impinges (or may have impinged) on one s rights and, last, the duty to reconsider the initial decision giving rise to the grievance. The right to a hearing is valued independently of the merit of the decisions generated by the judicial process. We also argue that the recent proposals to reinforce popular or democratic participation in shaping the Constitution are wrong because they are detrimental to the right to a hearing.
Kalai, Gil . Economics And Common Sense. Discussion Papers 2008. Web. Publisher's VersionAbstract
A review of Steven E. Landsburg's book More Sex is Safer Sex, the Unconventional Wisdom of Economics. The surprise 2005 best seller Freakonomics by Steven Levitt and Stephen Dubner launched a small genre of books by economists applying economic reasoning to everyday life and finding counterintuitive results. Mathematician and economist Steven Landsburg, whose online Slate column ``Everyday Economics predates the Levitt and Dubner volume, has now collected and expanded some of those columns to form the basis of his new book.In his book, Landsburg uses the ``weapons of evidence and logic, especially the logic of economics to draw surprising conclusions which run against common sense. ``If your common sense tells you otherwise, says Landsburg, ``remember that common sense also tells you the Earth is flat. In this review, scheduled to appear in the June/July 2008 issue of the Notices of the American Mathematical Society, we describe and discuss some of the issues and claims raised in Landsburg's book. For further discussion see the May 29 post in http://gilkalai.wordpress.com/ .
Ehud Friedgut, Gil Kalai, and Noam Nisan. Elections Can Be Manipulated Often. Discussion Papers 2008. Web. Publisher's VersionAbstract
The Gibbard-Satterthwaite theorem states that every non-trivial voting method between at least 3 alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random manipulation by a single random voter will succeed with non-negligible probability for every neutral voting method between 3 alternatives that is far from being a dictatorship.
Abba M. Krieger, Moshe Pollak, and Ester Samuel-Cahn. Extreme(Ly) Mean(Ingful): Sequential Formation Of A Quality Group (Revised April 2009). Discussion Papers 2008. Web. Publisher's VersionAbstract
The present paper studies the limiting behavior of the average score of a sequentially selected group of items or individuals, the underlying distribution of which, F, belongs to the Gumbel domain of attraction of extreme value distribution. This class contains the Normal, log Normal, Gamma, Weibull and many other distributions. The selection rules are the better than average  (² = 1) and the ²-better than average  rule, defined as follows. After the first item is selected, another item is admitted into the group if and only if its score is greater than ² times the average score of those already selected. Denote by Yk the average of the k first selected items, and by Tk the time it takes to amass them. Some of the key results obtained are: Under mild conditions, for the better than average rule, Yk less a suitable chosen function of log k converges almost surely to a finite random variable. When 1 ˆ’ F(x) = exp(-[x$\pm$ +h(x)]) , $\pm$>0 and h(x)/x$\pm$†’0 as x†’ˆ\v z, then Tk is of approximate order k2 . When ² > 1, the asymptotic results for Yk are of a completely different order of magnitude. Interestingly, for a class of distributions, Tk, suitably normalized, asymptotically approaches 1, almost surely for relatively small ² > 1, in probability for moderate sized ² and in distribution when ² is large.
Yehoram Leshem, Tamar Keasar, and Avi Shmida. Female-Biased Nectar Production In The Protandrous, Hermaphroditic Shrub Salvia Hierosolymitana: Possible Reasons And Consequences. Discussion Papers 2008. Web. Publisher's VersionAbstract
Sexual selection theory states that male reproductive success is commonly limited by opportunities for fertilization, while female reproductive success is more often resource-limited. This creates higher selective pressure on males to attract mating partners as compared with females. Similar reasoning, when applied to plant reproduction, predicts higher investment in pollinator-attracting traits, such as nectar production, in male flowers than in female flowers. Contrary to this prediction, nectar production by female-phase flowers in the protandrous hermaphrodite shrub Salvia hierosolymita (Boiss.) (Lamiaceae) was significantly higher than in male-phase flowers in two populations over three years. Female-biased nectar production may reflect selection for pollinator attraction by female-phase flowers, possibly due to pollen limitation. In support of this interpretation, (a) the number of pollen grains on female-phase stigmas was substantially higher than on male-phase stigmas, suggesting that the female phase received more insect visits ; (b) the number of germinating pollen grains in female-phase styles only slightly exceeded the number of ovules per flower, therefore pollen availability may restrict female fitness. Proportions of female-phase flowers decreased from the base of the inflorescences towards their top. This creates a vertical gradient of nectar production, which may help reduce geitonogamous pollination by effecting pollinator behavior.
Zultan, Andriy Zapechelnyuk, and Ro'i. Job Market Signaling And Job Search. Discussion Papers 2008. Web. Publisher's VersionAbstract
The high cost of searching for employers borne by prospective employees increases friction in the labor market and inhibits formation of efficient employer-employee relationships. It is conventionally agreed that mechanisms that reduce the search costs (e.g., internet portals for job search) lower unemployment and improve overall welfare. We demonstrate that a reduction of the search costs may have the converse effect. We consider a labor market in which workers can either establish a long-term relationship with an employer by being productive, or shirk and move from one employer to the next. In addition, the workers can signal to a potential employer their intention to be productive. We show that lower search costs lead to fewer employees willing to exert effort and, in a separating equilibrium, to more individuals opting to stay completely out of the job market and remain unemployed. Furthermore, we show that lower search costs not only deteriorate the market composition, but also impair efficiency by leading to more expensive signaling in a separating equilibrium.
Neyman, Abraham . Learning Effectiveness And Memory Size. Discussion Papers 2008. Web. Publisher's Version
Fink, Yevgeni Berzak, and Michael, Howlett. Manipulating Allocation Justice: How Framing Effects Can Increase The Prevalence Of The Talmudic Division Principle "Shnaim Ohazin". Discussion Papers 2008. Web. Publisher's VersionAbstract
In the role of judges in bankruptcy problems, people may prescribe various just divisions of the available goods to claimants who have rights for them. Two widespread division rules are equality and proportionality. A less known rule is the Talmudic "Shnaim Ohazin" principle, whose basic rationale is applying an equal division only to that part of the goods which is genuinely under dispute. This paper demonstrates that the ratio of subjects that prefer the "Shnaim Ohazin" principle over equality and proportionality can be increased by a simple framing manipulation. These results suggest that framing effects might be a prevalent factor in the realm of distributive justice.