The base-rate fallacy is people's tendency to ignore base rates in favor of, e.g., individuating information (when such is available), rather than integrate the two. This tendency has important implications for understanding judgment phenomena in many clinical, legal, and social-psychological settings. An explanation of this phenomenon is offered, according to which people order information by its perceived degree of relevance, and let high-relevance information dominate low-relevance information. Information is deemed more relevant when it relates more specifically to a judged target case. Specificity is achieved either by providing information on a smaller set than the overall population, of which the target case is a member, or when information can be coded, via causality, as information about the specific members of a given population. The base-rate fallacy is thus the result of pitting what seem to be merely coincidental, therefore low-relevance, base rates against more specific, or causal, information. A series of probabilistic inference problems is presented in which relevance was manipulated with the means described above, and the empirical results confirm the above account. In particular, base rates will be combined with other information when the two kinds of information are perceived as being equally relevant to the judged case.
Dean P. Foster Sergiu Hart. 2019. “Forecast-Hedging and Calibration”. Publisher's Version Abstract
Calibration means that for each forecast x the average of the realized actions in the periods in which the forecast was x is, in the long run, close to x. Calibration can always be guaranteed (Foster and Vohra 1998), but it requires the forecasting procedure to be stochastic. By contrast, smooth calibration, which combines in a continuous manner nearby forecasts, can be guaranteed by a deterministic procedure (Foster and Hart 2018). In the present paper we develop the concept of forecast-hedging, which consists of choosing the forecasts in such a way that, no matter what the realized action will be, the expected forecasting track record can only improve. This approach integrates the existing calibration results by obtaining them all from the same simple basic argument, and at the same time differentiates between them according to the forecast-hedging tools that are used: deterministic and fixed point-based vs. stochastic and minimax-based. Additional benefits are new calibration procedures in the one-dimensional case that are simpler than all known such procedures, and a short proof for deterministic smooth calibration, in contrast to the complicated existing proof.
A multi-item questionnaire concerning lay people's attitudes toward organ procurement without consent from executed prisoners was given to several hundred respondents. The items ranged from all-out condemnation ("It is tantamount to murder") to enthusiasm ("It is great to have this organ supply"). Overall, we found two guiding principles upheld by most respondents: (1) Convicts have as much a right to their bodies and organs as other people, so the practice should be judged by the same standards as those that guide organ procurement from any donor. Procuring organs without consent is wrong. (2) Benefiting from those organs should be held to more lenient standards than are demanded for their procurement. So, benefitting from these ill-gotten organs should be tolerated.
Bar-Hillel, Noah and Frederick (2018) studied a class of riddles they called stumpers, which have simple, but curiously elusive, solutions. A canonical example is: "Andy is Bobbie's brother, but Bobbie is not Andy's brother. How come?" Though not discussed there, we found that the ability to solve stumpers correlates significantly with performance on items resembling the CRT (Cognitive Reflection Test) but not with performance on items from the CRAT (Compound Remote Associates Test). We report those results here.
We consider the basic setup of one seller, one buyer, and one good, where the seller is risk averse, and characterize the mechanism that maximizes the seller's expected utility. In contrast to the risk-neutral case, where a single deterministic price is optimal, we show that in the risk averse case the optimal mechanism consists of a continuum of lotteries.
The Bayesian posterior probability of the true state is stochastically dominated by that same posterior under the probability law of the true state. This generalizes to notions of "optimism" about posterior probabilities.
This paper characterizes the preferences over bounded infinite utility streams that satisfy the time-value of money principle and an additivity property, and preferences that in addition are impatient. Based on this characterization, the paper introduces a concept of optimization that is robust to a small imprecision in the specification of the preference, and proves that the set of feasible streams of payoffs of a finite Markov decision process admits such a robust optimization.
Abraham Neyman Kristoffer Arnsfelt Hansen, Rasmus Ibsen-Jensen. 2018. “Big Match with a Clock and a Bit of Memory, The”. Publisher's Version Abstract
The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage.Blackwell and Ferguson (1968) give an $varepsilon$-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless.The present paper proves that there is such a strategy that is $varepsilon$-optimal. In fact, we show that just two states of memory are sufficient.
Capsule: Microclimatic conditions in the nest of the Lesser Kestrel (Falco naumanni), particularly the percentage of time of extremely low humidity, affect breeding success.Aim: (1) To study the effect of within-nest temperature and humidity on nest productivity, and the correlation between nest productivity and the order of dates on which nests were occupied by the parents. (2) To compare microclimatic conditions in the nest, breeding success and order of occupation between nests under tile roofs and artificial nest boxes.Methods: Three different Lesser Kestrel colonies in Israel "one rural, one urban and one in an open country habitat. Data loggers, that measure temperature and humidity, were put in 39 nests for the entire breeding period. The number of fledglings was recorded for each nest, as well as the date of occupation.Results: (1) Full microclimatic data from 35 nests suggest that percentage of time of extremely low humidity is the major predictor of nest productivity. (2) The urban colony had the lowest breeding success of the three colonies. (3) Sites of more successful nests were occupied earlier. (4) No significant difference in mean productivity between nests in roofs and nest boxes, but nests in roofs were occupied earlier.Conclusion: Nest microclimate affects nesting success in addition to colony location.
The effect of food supplement to Lesser Kestrel (Falco naumanni) nests during the nestling period (from hatching to fledging) was studied in two nesting colonies in Israel - Alona and Jerusalem. Our hypotheses was that food supplement will have a greater effect on fledgling success in the food-limited, urban colony of Jerusalem, than in the rural colony of Alona. Indeed, food supplement had a significantly positive effect on breeding success in both colonies. However, and contrary to our prediction, the decrease in chick mortality between supplemented and control nests in Jersualem was actually smaller than in Alona. This implies either that additional factors, possibly urbanization associated, other than food limitation, might be responsible for the difference in nesting success of Lesser Kestrels between Alona and Jersualem, and/or that the amount of additional food provided to supplemented nests (three mice per chick per week), was not enough.
We consider a standard model of judgment aggregation as presented, for example, in Dietrich (2015). For this model we introduce a sequential majority procedure (SMP) which uses the majority rule as much as possible. The ordering of the issues is assumed to be exogenous. The definition of SMP is given in Section 2. In Section 4 we construct an intuitive relevance relation for our model, closely related to conditional entailment, for our model. While in Dietrich (2015), the relevance relation is given exogenously as part of the model, we insist that the relevance relation be derived from the agenda. We prove that SMP has the property of independence of irrelevant issues (III) with respect to (the transitive closure of) our relevance relation. As III is weaker than the property of proposition-wise independence (PI) we do not run into impossibility results as does List (2004) who incorporates PI in some parts of his analysis. We proceed to characterize SMP by anonymity, restricted monotonicity, limited neutrality, restricted agenda property, and independence of past deliberations (see Section 3 for the precise details). SMP inherits the first three axioms from the Majority Rule. The axiom of restricted agenda property guarantees sequentiality. The most important axiom, independence of past deliberations (IPD), says that the choice at time (t+1) depends only on the choices in dates 1, ..., t and the judgments at (t +1) (and not on the judgments in dates 1, ..., t) . Also, we use this occasion to point out that Roberts (1991) characterization of choice by plurality voting may be adapted to our model.
Shane Frederick Maya Bar-Hillel, Tom Noah. 2018. “Learning Psychology from Riddles: The Case of Stumpers”. Publisher's Version Abstract
Riddles can teach us psychology when we stop to consider the psychological principles that make them work . This paper studies a particular class of riddles that we call stumpers, and provides analysis of the various principles (some familiar, some novel) that inhibit most people from finding the correct solution "or any solution "even though they find the answers obvious ex post. We restrict our analysis to four stumpers, propose the psychological antecedents of each, and provide experimental support for our conjectures
Yael Lubin Ally R. Harari Shevy Waner, Uzi Motro. 2018. “Male Mate Choice in a Sexually Cannibalistic Widow Spider”. Publisher's Version Abstract
Males of the brown widow spider,Latrodectusgeometricus(Theridiidae), invest energy in courtship displays and are often cannibalized after mating;accordingly, partial sex role reversal is expected. In this species, subadult females are able to mate and produce viable offspring. In contrast to mature females, these subadult females do not cannibalize their mates after copulation. Nevertheless, when given a choice, males preferred mature over subadult females and older over young mature females. We found no benefit for males in mating with the females of their choice. Older females weresignificantly less fecund than young mature females, and werenot more fecund than subadult females. We tested possible advantages in mating with cannibalistic (mature) females, such as an increased probability of plugging the female s genital duct or longer copulations,or disadvantages in mating with subadult females, such as higher remating risk. None of these explanations was supported. Thus, we lack an adaptive explanation for male preference for mature older females. We suggest that older females produce more pheromone to attract males and that males are thus misled into mating with older, more aggressive and less fecund females.
We survey the results on representations of committees and constitutions by game forms that possess some kind of equilibrium strategies for each profile of preferences of the players. The survey is restricted to discrete models, that is, we deal with finitely many players and alternatives. No prior knowledge of social choice is assumed: As far as definitions are concerned, the paper is self-contained. Section 2 supplies the necessary general tools for the rest of the paper. Each definition is followed by a simple (but nontrivial) example. In Section 3 we give a complete account of representations of committees (proper and monotonic simple games), by exactly and strongly consistent social choice functions. We start with Peleg's representations of weak games, and then provide a complete and detailed account of Holzman's solution of the representation problem for simple games without veto players. In Section 4 we deal with representations of constitutions by game forms. Following Grdenfors we model a constitution by a monotonic and super additive effectivity function. We fully characterize the representations for three kinds of equilibrium: Nash equilibrium; acceptable equilibrium (Pareto optimal Nash equilibrium); and strong Nash equilibrium. We conclude in Section 5 with a report on two recent works on representations of constitutions under incomplete information.
A social choice correspondence is self-implementable in strong equilibrium if it is implementable in strong equilibrium by a social choice function selecting from the correspondence itself as a game form. We characterize all social choice correspondences implementable this way by an anonymous social choice function satisfying no veto power, given that the number of agents is large relative to the number of alternatives. It turns out that these are exactly the social choice correspondences resulting from feasible elimination procedures as introduced in Peleg (1978).
Yonatan Loewenstein Lotem Elber-Dorozko. 2018. “Striatial Action-Value Neurons Reconsidered”. Publisher's Version Abstract
It is generally believed that during economic decisions, striatal neurons represent the values associated with different actions. This hypothesis is based on studies, in which the activity of striatal neurons was measured while the subject was learning to prefer the more rewarding action. Here we show that these publications are subject to at least one of two critical confounds. First, we show that even weak temporal correlations in the neuronal data may result in an erroneous identification of action-value representations. Second, we show that experiments and analyses designed to dissociate action-value representation from the representation of other decision variables cannot do so. We suggest solutions to identifying action-value representation that are not subject to these confounds. Applying one solution to previously identified action-value neurons in the basal ganglia we fail to detect action-value representations. We conclude that the claim that striatal neurons encode action-values must await new experiments and analyses.
In making an agreement with someone, I conditionally promise to perform a certain action, conditioning my obligation on their both making a corresponding promise and performing their action. What promise should I require? That they simply commit to perform is not enough. I should demand the kind of promise I am making myself, and they should demand the same of me. This makes our promises indirectly self-referential. Assuming the performance actions are specified, my promise can be characterized as a set of available promises, all those the other could make to activate my obligation. We have an agreement if each one s promise is a member of the other s promise. Assume that the set P of available promises satisfies (1) Aczel s axiom for circular sets; (2) transitivity: if the obligation of $p 'in P$ is activated by $p $, then $p 'in P$; and (3) superset closure: if $p 'in P$ is activated by $p $, $p$ is activated by any promise that implies (is a superset of) $p $. The focus is on bargaining procedures that treat the parties symmetrically (e.g., no specified offerer or accepter.) Each party chooses an agreement promise $p*$ such that (4) if both make $p*$ and one performs, the other is obligated to perform; (5) if one makes $p*$ and the other does not, the former is not unilaterally obligated. It is shown that among available promise sets of a given size, exactly one contains an agreement promise and contains exactly one of them.
Talk delivered at the opening of SPUDM 26, Haifa, Israel, August 2017.