scholarly journals UNACCEPTABLE RISKS AND THE CONTINUITY AXIOM

2012 ◽  
Vol 28 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Karsten Klint Jensen
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Extreme Case ◽  
Expected Utility Theory ◽  
Alternative Proof ◽  
Ordinal Ranking ◽  
Gains And Losses ◽  
Continuity Axiom

Consider a sequence of outcomes of descending value, A > B > C > . . . > Z. According to Larry Temkin, there are reasons to deny the continuity axiom in certain ‘extreme’ cases, i.e. cases of triplets of outcomes A, B and Z, where A and B differ little in value, but B and Z differ greatly. But, Temkin argues, if we assume continuity for ‘easy’ cases, i.e. cases where the loss is small, we can derive continuity for the ‘extreme’ case by applying the axiom of substitution and the axiom of transitivity. The rejection of continuity for ‘extreme’ cases therefore renders the triad of continuity in ‘easy’ cases, the axiom of substitution and the axiom of transitivity inconsistent.As shown by Arrhenius and Rabinowitz, Temkin's argument is flawed. I present a result which is stronger than their alternative proof of an inconsistency. However, this result is not quite what Temkin intends, because it only refers to an ordinal ranking of the outcomes in the sequence, whereas Temkin appeals to intuitions about the size of gains and losses. Against this background, it is argued that Temkin's trilemma never gets off the ground. This is because Temkin appeals to two mutually inconsistent conceptions of aggregation of value. Once these are clearly separated, it will transpire, in connection with each of them, that one of the principles to be rejected does not appear plausible. Hence, there is nothing surprising or challenging about the result; it is merely a corollary to Expected Utility Theory.

scholarly journals Nonhuman Primates Satisfy Utility Maximization in Compliance with the Continuity Axiom of Expected Utility Theory

2021 ◽  
Vol 41 (13) ◽  
pp. 2964-2979 ◽  
Author(s):  
Simone Ferrari-Toniolo ◽  
Philipe M. Bujold ◽  
Fabian Grabenhorst ◽  
Raymundo Báez-Mendoza ◽  
Wolfram Schultz
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Utility Maximization ◽  
Nonhuman Primates ◽  
Expected Utility Theory ◽  
Continuity Axiom

Compliance with the Continuity Axiom of Expected Utility Theory Supports Utility Maximization in Monkeys

2020 ◽  
Author(s):  
Simone Ferrari-Toniolo ◽  
Philipe M. Bujold ◽  
Fabian Grabenhorst ◽  
Raymundo Báez-Mendoza ◽  
Wolfram Schultz
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Utility Maximization ◽  
Expected Utility Theory ◽  
Continuity Axiom

scholarly journals Non-human primates satisfy utility maximization in compliance with the continuity axiom of Expected Utility Theory

2020 ◽  
Author(s):  
Simone Ferrari-Toniolo ◽  
Philipe M. Bujold ◽  
Fabian Grabenhorst ◽  
Raymundo Báez-Mendoza ◽  
Wolfram Schultz
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Utility Maximization ◽  
Expected Utility Theory ◽  
Decision Makers ◽  
Utility Measure ◽  
Trade Off ◽  
Subjective Value ◽  
Subjective Utility ◽  
Continuity Axiom

ABSTRACTExpected Utility Theory (EUT), the first axiomatic theory of risky choice, describes choices as a utility maximization process: decision makers assign a subjective value (utility) to each choice option and choose the one with the highest utility. The continuity axiom, central to EUT and its modifications, is a necessary and sufficient condition for the definition of numerical utilities. The axiom requires decision makers to be indifferent between a gamble and a specific probabilistic combination of a more preferred and a less preferred gamble. While previous studies demonstrated that monkeys choose according to combinations of objective reward magnitude and probability, a concept-driven experimental approach for assessing the axiomatically defined conditions for maximizing subjective utility by animals is missing. We experimentally tested the continuity axiom for a broad class of gamble types in four male rhesus macaque monkeys, showing that their choice behavior complied with the existence of a numerical utility measure as defined by the economic theory. We used the numerical quantity specified in the continuity axiom to characterize subjective preferences in a magnitude-probability space. This mapping highlighted a trade-off relation between reward magnitudes and probabilities, compatible with the existence of a utility function underlying subjective value computation. These results support the existence of a numerical utility function able to describe choices, allowing for the investigation of the neuronal substrates responsible for coding such rigorously defined quantity.SIGNIFICANCE STATEMENTA common assumption of several economic choice theories is that decisions result from the comparison of subjectively assigned values (utilities). This study demonstrated the compliance of monkey behavior with the continuity axiom of Expected Utility Theory, implying a subjective magnitude-probability trade-off relation which supports the existence of numerical subjective utility directly linked to the theoretical economic framework. We determined a numerical utility measure able to describe choices, which can serve as a correlate for the neuronal activity in the quest for brain structures and mechanisms guiding decisions.

scholarly journals Continuity and catastrophic risk

2021 ◽  
pp. 1-9
Author(s):  
H. Orri Stefánsson
Keyword(s):  
Social Welfare ◽  
Decision Maker ◽  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Continuity Condition ◽  
Trade Off ◽  
Catastrophic Risk ◽  
Lifetime Income ◽  
Continuity Axiom

Abstract Suppose that a decision-maker’s aim, under certainty, is to maximize some continuous value, such as lifetime income or continuous social welfare. Can such a decision-maker rationally satisfy what has been called ‘continuity for easy cases’ while at the same time satisfying what seems to be a widespread intuition against the full-blown continuity axiom of expected utility theory? In this note I argue that the answer is ‘no’: given transitivity and a weak trade-off principle, continuity for easy cases violates the anti-continuity intuition. I end the note by exploring an even weaker continuity condition that is consistent with the aforementioned intuition.

scholarly journals Cumulative Prospect Theory Version with Fuzzy Values of Outcome Estimates

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 72
Author(s):  
Oleg Uzhga-Rebrov ◽  
Peter Grabusts
Keyword(s):  
Prospect Theory ◽  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Cumulative Prospect Theory ◽  
Development History ◽  
Decisions Under Risk ◽  
History Of ◽  
Main Factors ◽  
Theoretical Foundations

Choosing solutions under risk and uncertainty requires the consideration of several factors. One of the main factors in choosing a solution is modeling the decision maker’s attitude to risk. The expected utility theory was the first approach that allowed to correctly model various nuances of the attitude to risk. Further research in this area has led to the emergence of even more effective approaches to solving this problem. Currently, the most developed theory of choice with respect to decisions under risk conditions is the cumulative prospect theory. This paper presents the development history of various extensions of the original expected utility theory, and the analysis of the main properties of the cumulative prospect theory. The main result of this work is a fuzzy version of the prospect theory, which allows handling fuzzy values of the decisions (prospects). The paper presents the theoretical foundations of the proposed version, an illustrative practical example, and conclusions based on the results obtained.

Norm-Endorsement Utilitarianism and the Nature of Utility

1996 ◽  
Vol 12 (2) ◽  
pp. 165-182 ◽  
Author(s):  
Jonathan Baron
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Interpersonal Comparison ◽  
Moral Norms ◽  
Moral Principles ◽  
Future Goals ◽  
Equal Consideration

In this article, I shall suggest an approach to the justification of normative moral principles which leads, I think, to utilitarianism. The approach is based on asking what moral norms we would each endorse if we had no prior moral commitments. I argue that we would endorse norms that lead to the satisfaction of all our nonmoral values or goals. The same approach leads to a view of utility as consisting of those goals that we would want satisfied. In the second half of the article, I examine the implication of this view for several issues about the nature of utility, such as the use of past and future goals. The argument for utilitarianism is not completed here. The rest of it requires a defense of expected-utility theory, of interpersonal comparison, and of equal consideration (see Baron, 1993; Broome, 1991).

Housing Market Search Behavior and Expected Utility Theory: 1. Measuring Preferences for Housing

1982 ◽  
Vol 14 (5) ◽  
pp. 681-698 ◽  
Author(s):  
T R Smith ◽  
W A V Clark
Keyword(s):  
Los Angeles ◽  
Housing Market ◽  
Expected Utility ◽  
Utility Theory ◽  
House Price ◽  
Expected Utility Theory ◽  
Utility Functions ◽  
Future Search ◽  
Space Construction ◽  
Market Search

This is the first of two papers examining housing market search in a Los Angeles market. In this paper, we derive and analyze utility functions for housing for each individual in two groups of subjects. The utility functions are derived from an experimental setting, in which house price, floor space, construction quality, and neighborhood quality are varied. The functions are found to be essentially compatible with a linear model. They are used to predict the ratings of real houses and the ratings of the expected value of future search. These ratings are compared with actual ratings obtained from subjects during search. The results suggest that the actual or predicted ratings may be employed in a direct test of a simple expected utility theory of search, and further research along these lines appears justified.

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