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 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 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 Desenvolvimento de uma Medida de Desempenho Comportamental

2012 ◽  
Vol 10 (3) ◽  
pp. 395
Author(s):  
Marcelo Cabus Klotzle ◽  
Leonardo Lima Gomes ◽  
Luiz Eduardo Teixeira Brandão ◽  
Antonio Carlos Figueiredo Pinto
Keyword(s):  
Prospect Theory ◽  
Decision Maker ◽  
Performance Measures ◽  
Behavioral Finance ◽  
Expected Utility ◽  
Loss Aversion ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Performance Measure ◽  
Uncertain Outcomes

Since the fifties, several measures have been developed in order to measure the performance of investments or choices involving uncertain outcomes. Much of these measures are based on Expected Utility Theory, but since the nineties a number of measures have been proposed based on Non-Expected Utility Theory. Among the Theories of Non-Expected Utility highlights Prospect Theory, which is the foundation of Behavioral Finance. Based on this theory this study proposes a new performance measure in which are embedded loss aversion along with the likelihood of distortions in the choice of alternatives. A hypothetical example is presented in which various performance measures, including the new measure are compared. The results showed that the ordering of the assets varied depending on the performance measure adopted. According to what was expected, the new performance measure clearly has captured the distortion of probabilities and loss aversion of the decision maker, ie, those assets with the greatest negative deviations from the target were those who had the worst performance.

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 Preferences for partial information and ambiguity

2020 ◽  
Vol 15 (3) ◽  
pp. 1059-1094 ◽  
Author(s):  
Jian Li
Keyword(s):  
Decision Maker ◽  
Expected Utility ◽  
Utility Theory ◽  
Ambiguity Aversion ◽  
Partial Information ◽  
Expected Utility Theory ◽  
Recursive Preferences ◽  
Recursive Model ◽  
Information Aversion ◽  
Free Information

We commonly think of information as an instrument for better decisions, yet evidence suggests that people often decline free information in nonstrategic scenarios. This paper provides a theory for how a dynamically‐consistent decision maker can be averse to partial information as a consequence of ambiguity aversion. It introduces a class of recursive preferences on an extended choice domain, which allows the preferences to depend on how information is dynamically revealed and to depart from the standard expected‐utility theory. A new notion of ambiguity aversion, called Event Complementarity, exactly characterizes aversion to partial information. Familiar static ambiguity‐averse preferences are embedded into the general recursive model, in which conditions for partial information aversion are identified. The findings suggest that Event Complementarity overlaps with yet still differs from the conventional notion of ambiguity aversion.

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.

Sign in / Sign up

Export Citation Format

Share Document