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Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50 % of all inferences by Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference. Is the mind, by design, predisposed against performing Bayesian inference? The classical probabilists of the Enlightenment, including Condorcet, Poisson, and Laplace, equated probability theory with the common sense of educated people, who were known then as “hommes éclairés.” Laplace (1814/1951) declared that “the theory of probability is at bottom nothing more than good sense reduced to a calculus which evaluates that which good minds know by a sort of instinct,

e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determined by the prior information, independently of the choice of parameters. In a certain class of problems, therefore, the prior distributions may now be claimed to be fully as "objective" as the sampling distributions. I. Background of the problem Since the time of Laplace, applications of probability theory have been hampered by difficulties in the treatment of prior information. In realistic problems of decision or inference, we often have prior information which is highly relevant to the question being asked; to fail to take it into account is to commit the most obvious inconsistency of reasoning and may lead to absurd or dangerously misleading results. As an extreme examp

Inspired by game theory representations, Bayesian networks, influence diagrams, structured Markov decision process models, logic programming, and work in dynamical systems, the independent choice logic (ICL) is a semantic framework that allows for independent choices (made by various agents, including nature) and a logic program that gives the consequence of choices. This representation can be used as a specification for agents that act in a world, make observations of that world and have memory, as well as a modelling tool for dynamic environments with uncertainty. The rules specify the consequences of an action, what can be sensed and the utility of outcomes. This paper presents a possible-worlds semantics for ICL, and shows how to embed influence diagrams, structured Markov decision processes, and both the strategic (normal) form and extensive (game-tree) form of games within the Thanks to Craig Boutilier and Holger Hoos for detailed comments on this paper. This work was supporte...

This work proposes an axiomatic characterization of merging operators. It underlines the differences between arbitration operators and majority operators. A representation theorem is stated showing that each merging operator corresponds to a family of partial preorders on interpretations. Examples of operators are given. They show the consistency of the axiomatic characterization. A new merging operator 4GMax is provided. It is proved that it is actually an arbitration operator. 1 Introduction In a growing number of applications, we face conflicting information coming from several sources. The problem is to reach a coherent piece of information from these contradicting ones. A lot of different merging methods have already been given [BI84, LMa, BKM91, BKMS92, Sub94]. Instead of giving one particular merging method we propose, in this paper, a characterization of such methods following the rationality of the postulates they satisfy. We shall call merging operators those meth...

Graphical representations for probabilistic relationships have recently received considerable attention in A1. Qualitative probabilistic networks abstract from the usual numeric representations by encoding only qualitative relationships, which are inequality constraints on the joint probability distribution over the variables. Although these constraints are insufficient to determine probabilities uniquely, they are designed to justify the deduction of a class of relative likelihood conclusions that imply useful decision-making properties. Two types of qualitative relationship are defined, each a probabilistic form of monotonicity constraint over a group of variables. Qualitative influences describe the direction of the relationship between two variables. Qualitative synergies describe interactions among influences. The probabilistic definitions chosen justify sound and efficient inference procedures based on graphical manipulations of the network. These procedures answer queries about qualitative relationships among variables separated in the network and determine structural properties of optimal assignments to decision variables.

Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing notions of independence for utility functions in a multi-attribute space, and suggest that these can be used to achieve similar advantages. Our new results concern conditional additive independence, which we show always has a perfect representation as separation in an undirected graph (a Markov network). Conditional additive independencies entail a particular functional form for the utility function that is analogous to a product decomposition of a probability function, and confers analogous benefits. This functional form has been utilized in the Bayesian network and influence diagram literature, but generally without an explanation in terms of independence. The functional form yields a decomposition of the utility function that can greatly speed up e...

Economists have long been ambivalent about whether the discipline should focus on the analysis of markets or should be concerned with social interactions more generally. Recently the discipline has sought to broaden its scope while maintaining the rigor of modern economic analysis. Major theoretical developments in game theory, the economics of the family, and endogenous growth theory have taken place. Economists have also performed new empirical research on social interactions, but the empirical literature does not show progress comparable to that achieved in economic theory. This paper examines why and discusses how economists might make sustained contributions to the empirical analysis of social interactions.

The economic theory of rationality promises to equal mathematical logic in its importance for the mechanization of reasoning. We survey the growing literature on how the basic notions of probability, utility, and rational choice, coupled with practical limitations on information and resources, influence the design and analysis of reasoning and representation systems. 1 Introduction People make judgments of rationality all the time, usually in criticizing someone else's thoughts or deeds as irrational, or in defending their own as rational. Artificial intelligence researchers construct systems and theories to perform or describe rational thought and action, criticizing and defending these systems and theories in terms similar to but more formal than those of the man or woman on the street. Judgments of human rationality commonly involve several different conceptions of rationality, including a logical conception used to judge thoughts, and an economic one used to judge actions or...

Goals, as typically conceived in AI planning, provide an insufficient basis for choice of action, and hence are deficient as the sole expression of an agent's objectives. Decision-theoretic utilities offer a more adequate basis, yet lack many of the computational advantages of goals. We provide a preferential semantics for goals that grounds them in decision theory and preserves the validity of some, but not all, common goal operations performed in planning. This semantic account provides a criterion for verifying the design of goal-based planning strategies, thus providing a new framework for knowledge-level analysis of planning systems. Planning to achieve goals In the predominant AI planning paradigm, planners construct plans designed to produce states satisfying particular conditions called goals. Each goal represents a partition of possible states of the world into those satisfying and those not satisfying the goal. Though planners use goals to guide their reasoning, the crude b...