Understanding Expected Utility for Decision Making

De Finetti's concept of exchangeability provides a way to formalize the intuitive idea of similarity and its role as guide in decision making. His classic representation theorem states that exchangeable expected utility preferences can be expressed in terms of a subjective beliefs on parameters. De Finetti's representation is inextricably linked to expected utility as it simultaneously identifies the parameters and Bayesian beliefs about them. This paper studies the implications of exchangeability assuming that preferences are monotone, transitive and continuous, but otherwise incomplete and/or fail probabilistic sophistication. The central tool in our analysis is a new subjective ergodic theorem which takes as primitive preferences, rather than probabilities (as in standard ergodic theory). Using this theorem, we identify the i.i.d. parametrization as sufficient for all preferences in our class. A special case of the result is de Finetti's classic representation. We also prove: (1) a novel derivation of subjective probabilities based on frequencies;

ISIPTA, 2003

We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: r-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there ...

2003

Abstract Intelligent agents often need to assess user utility functions in order to make decisions on their behalf, or predict their behavior. When uncertainty exists over the precise nature of this utility function, one can model this uncertainty using a distribution over utility functions. This view lies at the core of games with incomplete information and, more recently, several proposals for incremental preference elicitation.

2000

Expected utility theory does not directly deal with the utility of chance. It has been suggested in the literature ) that this can be remedied by an approach which explicitly models the emotional consequences which give rise to the utility of chance. We refer to this as the elaborated outcomes approach. It is argued that the elaborated outcomes approach destroys the possibility of deriving a representation theorem based on the usual axioms of expected utility theory. This is shown with the help of an example due to Markowitz. It turns out that the space of conceivable lotteries over elaborated outcomes is too narrow to permit the application of the axioms. Moreover it is shown that a representation theorem does not hold for the example.

Synthese, 2018

In his classic book Savage (1954, 1972) develops a formal system of rational decision making. It is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems – without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of " idealized agent " that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent.

The Journal of Socio-Economics, 2010

Attachment values Allais paradox Insurance paradox Ellsberg paradox Coalescing paradox Violations of stochastic dominance Cash segregation paradox Risk preferences for losses paradox a b s t r a c t The expected utility (EU) model is widely used for predicting and describing choices under uncertainty. Its usefulness, however, is limited because of its widely acknowledged inconsistencies and paradoxes. This paper describes how important EU model paradoxes can be resolved by accounting for the influences of socio-emotional goods (SEGs) embedded in word and other symbolic frames.

Journal of Mathematical Psychology, 2011

This paper proposes a theory of subjective expected utility based on primitives only involving the fact that an act can be judged either "attractive" or "unattractive". We give conditions implying that there are a utility function on the set of consequences and a probability distribution on the set of states such that attractive acts have a subjective expected utility above some threshold. The numerical representation that is obtained has strong uniqueness properties.

Proceedings of the National Academy of Sciences, 2013

We consider decision makers who know that payo¤ relevant observations are generated by a process that belongs to a given class M , as postulated in Wald [36]. We incorporate this Waldean piece of objective information within an otherwise subjective setting a la Savage [33] and show that this leads to a two-stage subjective expected utility model that accounts for both state and model uncertainty.

The Review of Economic Studies, 1991

Erkenntnis, 1975

Indian Journal of Applied Research, 2011

The topic of this article is stochastic algorithms for evaluation of the utility and subjective probability based on the decision maker's preferences. The main direction of the presentation is toward development of mathematically grounded algorithms for subjective probability and expected utility evaluation as a function of both the probability and the rank of the alternative. The stochastic assessment is based on mathematically formulated axiomatic principles and stochastic procedures and on the utility theory without additivity. The uncertainty of the human preferences is eliminated as is typical for the stochastic programming. Numerical presentations are shown and discussed.

Theory and decision, 1988

Economic Theory, 2000

We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs.

Social Science Research Network, 2000

Noûs, 2018

This paper argues in favor of a particular account of decision‐making under normative uncertainty: that, when it is possible to do so, one should maximize expected choice‐worthiness . Though this position has been often suggested in the literature and is often taken to be the ‘default’ view, it has so far received little in the way of positive argument in its favor. After dealing with some preliminaries and giving the basic motivation for taking normative uncertainty into account in our decision‐making, we consider and provide new arguments against two rival accounts that have been offered—the accounts that we call ‘My Favorite Theory’ and ‘My Favorite Option’. We then give a novel argument for comparativism —the view that, under normative uncertainty, one should take into account both probabilities of different theories and magnitudes of choice‐worthiness. Finally, we further argue in favor of maximizing expected choice‐worthiness and consider and respond to five objections.