A qualitative logic of decision

An important aspect of intelligent behavior is the ability to reason, make decisions, and act in spite of uncertainty. This paper presents a qualitative logic of decision that supports decision-making under uncertainty. To be specific, the paper presents a knowledge representation language based upon subjective Bayesian decision theory that aims to capture some aspects of common-sense reasoning associated with making decisions about actions. The language addresses the problem of describing justifications of rational choices in situations where the alternatives involve trading off potential losses and gains. The logic and an associated qualitative arithmetic are implemented in an efficient PROLOG program. Examples illustrate their use in several concrete decision-making situations

Subjective Expected Utility Theory with “Small Worlds”

We model the notion of a "small world" as a context dependent state space embedded into the "grand world". For each situation the decision maker creates a "small world" reflecting the events perceived to be relevant for the act under consideration. The "grand world" is represented by an event space which is a more general construction than a state space. We retain preference axioms similar in spirit to the Savage axioms and obtain, without abandoning linearity of expectations, a subjective expected utility theory which allows for an intuitive distinction between risk and uncertainty. We also obtain separation of subjective probability and utility as in the state space models.subjective expected utility; decision making under uncertainty; uncertainty aversion; Ellsberg paradox

Foundations of Bayesian Theory

This paper states necessary and sufficient conditions for the existence, uniqueness, and updating according to Bayes?rule, of subjective probabilities representing individuals?beliefs. The approach is preference based, and the result is an axiomatic subjective expected utility model of Bayesian decision making under uncertainty with statedependent preferences. The theory provides foundations for the existence of prior probabilities representing decision makers?beliefs about the likely realization of events and for the updating of these probabilities according to Bayes?rule.

Recursive Smooth Ambiguity Preferences

This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in Klibanoff, Marinacci, and Mukerji (2005). A key feature of the model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. In applications one may thus specify/vary these two characteristics independent of each other, thereby facilitating richer comparative statics and modeling flexibility than possible under other models which accomodate ambiguity sensitive preferences. Another key feature is that the preferences are dynamically consistent and have a recursive representation. Therefore techniques of dynamic programming can be applied when using this model.Ambiguity, Uncertainty, Knightian Uncertainty, Ambiguity Aversion, Uncertainty Aversion, Ellsberg Paradox, Dynamic Decision Making, Dynamic Programming under Ambiguity, Smooth Ambiguity.

A Simple Agro-Economic Model for Optimal Farm Nitrogen Application under Yield Uncertainty

Farmers in the developed world tend to over-apply fertilizer, and we explore a model for decision-making under uncertainty in yields. This article proposes an agro-economic model for farmer decision-making based on subjective expected yield and crop response to fertilization. The model explores subjective yield probability distributions that are both better suited to subjective crop yields than the previously proposed probability distribution and is easier to extract from farmers. The model allows the analysis of the impact of changes in fertilizer price and variance of expected yields. The model result is consistent with observed farmer behavior based on the rule of “fertilizing for the good years” that appears, according to our model, as rational and consistent with expected profit maximization under yield uncertainty since the cost of over-application is lower than that of the opportunity cost of under-application. The goal of increasing the efficiency of nitrogen use requires both technical innovation and an expansion of the knowledge on the socioeconomic factors underlying excessive crop fertilization that must be improved both to meet future food demands and to prevent environmental degradation and climate change

Actions and Beliefs: Estimating Distribution-Based Preferences Using a Large Scale Experiment with Probability Questions on Expectations

We combine the choice data of proposers and responders in the ultimatum game, their expectations elicited in the form of subjective probability questions, and the choice data of proposers ("dictators") in a dictator game to estimate a structural model of decision making under uncertainty. We use a large and representative sample of subjects drawn from the Dutch population. Our results indicate that there is considerable heterogeneity in preferences for equity in the population. Changes in preferences have an important impact on decisions of dictators in the dictator game and responders in the ultimatum game, but a smaller impact on decisions of proposers in the ultimatum game, a result due to proposer's subjective expectations about resopnders' decisions. The model which uses subjective data on expectations has better predictive power and lower noise level than a model which assumes that players have rational expectations.Ultimatum game, inequity aversion, subjective expectations