A substantial body of empirical evidence shows that individuals overweight extreme events and act in conflict with the expected utility theory. These findings were the primary motivation behind the development of a rank-dependent utility theory for choice under uncertainty. The purpose of this paper is to demonstrate that some simple empirical rules of thumb for choice under uncertainty are consistent with the rank-dependent utility theory.

Causal Decision Theory (CDT) cares only about the effects of a contemplated act, not its causes. The paper constructs a case in which CDT consequently recommends a bet that the agent is certain to lose, rather than a bet that she is certain to win. CDT is plainly giving wrong advice in this case. It therefore stands refuted.

One of the reasons for adopting hyperbolic discounting is to explain preference reversals. Another is that this value structure suggests an elegant theory of the will. I examine the capacity of the theory to solve Newcomb's problem. In addition, I compare Ainslie's account with other procedural theories of choice that seem at least equally capable of accommodating reversals of preference.

Consider a transitive value ordering of outcomes and lotteries on outcomes, which satisfies substitutivity of equivalents and obeys “continuity for easy cases,” i.e., allows compensating risks of small losses by chances of small improvements. Temkin (2001) has argued that such an ordering must also – rather counter-intuitively – allow chances of small improvements to compensate risks of huge losses. In this paper, we show that Temkin's argument is flawed but that a better proof is possible. However, it is more difficult (...) to determine what conclusions should be drawn from this result. Contrary to what Temkin suggests, substitutivity of equivalents is a notoriously controversial principle. But even in the absence of substitutivity, the counter-intuitive conclusion is derivable from a strengthened version of continuity for easy cases. The best move, therefore, might be to question the latter principle, even in its original simple version: as we argue, continuity for easy cases gives rise to a sorites. (shrink)

This sparkling collection of essays both defines and reassesses the concept of Utility. Using it as a touchstone for the consideration of the place of ethics in the recent history of design, the collection offers a way into the issues which concern design decision-makers today. It offers previously unpublished research into diverse topics such as the investigation into the hitherto undiscovered designs for a utility vehicle, and it reveals a fresh perspective on the philosophy behind the concept of Utility as (...) a design theory. (shrink)

We provide welfarist evaluations of decision rules for federations of states and consider models, under which the interests of people from different states are stochastically dependent. We concentrate on two welfarist standards; they require that the expected utility for the federation be maximized or that the expected utilities for people from different states be equal. We discuss an analytic result that characterizes the decision rule with maximum expected utility, set up a class of models that display interstate dependencies and run (...) simulations for different dependency scenarios in the European Union. We find that, under positive correlations, the welfare distribution tends to be less sensitive to the choice of the decision rule, whereas it can be important under negative correlations. The results that Beisbart and Bovens (SCW 29, p. 581, 2007) have found for two types of models without interstate dependencies are relatively stable. There are exceptions, though, under which the way the welfare distribution is shaped by a decision rule is significantly affected by dependencies. (shrink)

This paper contributes to the mathematical foundations of the model for utility theory developed by Richard Jeffrey in The Logic of Decision [5]. In it I discuss the relationship of Jeffrey's to classical models, state and interpret an existence theorem for numerical utilities and subjective probabilities and restate a theorem on their uniqueness.

Our aim in this paper was to establish an empirical evaluation for similarity effects modeled by Rubinstein; Azipurua et al.; Leland; and Sileo. These tests are conducted through a sensitivity analysis of two well-known examples of expected utility (EU) independence violations. We found that subjective similarity reported by respondents was explained very well by objective measures suggested in the similarity literature. The empirical results of this analysis also show that: (1) the likelihood of selection for the riskier choice increases as (...) the pair becomes more similar, (2) these choice patterns are consistent with well-known independence violations of expected utility, and (3) a significant proportion of individuals exhibit intransitive choice patterns predicted under similarity effects, but not allowed under generalized expected utility models for risky choice. (shrink)

In the present paper we study the framework of additive utility theory, obtaining new results derived from a concurrence of algebraic and topological techniques. Such techniques lean on the concept of a connected topological totally ordered semigroup. We achieve a general result concerning the existence of continuous and additive utility functions on completely preordered sets endowed with a binary operation ``+'', not necessarily being commutative or associative. In the final part of the paper we get some applications to expected utility (...) theory, and a representation theorem for a class of complete preorders on a quite general family of real mixture spaces. (shrink)

Prospect Relativity 2 Abstract In many theories of decision under risk (e.g., expected utility theory, rank dependent utility theory, and prospect theory) the utility or value of a prospect is independent of other prospects or options in the choice set. The experiments presented here show a large effect of the available options set, suggesting instead that prospects are valued relative to one another. The judged certainty equivalent is strongly influenced by the options available. Similarly, the selection of a preferred option (...) from a set of prospects is strongly influenced by the prospects available. Alternative theories of decision under risk (e.g., the stochastic difference model, multialternative decision field theory, and range frequency theory), where prospects themselves or prospect attributes are valued relative to one another, can provide an account of these context effects. (shrink)

This essay gives necessary and sufficient conditions for recovering expected utility from choice behavior in several popular models of uncertainty. In particular, these techniques handle a finite state model; a model for which the choice space consists of probability densities and the expected utility representation requires bounded, measurable utility; and a model for which the choice space consists of Borel probability measures and the expected utility representation requires bounded, continuous utility. The key result is the identification of the continuity condition (...) necessary for the revelation of linear utility. (shrink)

The results generated by experimentalists in psychology and economics haveled to numerous advances in the study of human decision making under risk.Camerer (1995) and Rabin (1998) provide excellent reviews of the relevantliterature. These results clearly display the gap between normative theoriesof ideal behavior and descriptive theories of observed behavior. The mostprominent result is loss aversion – the observation that a loss is given greatervalue than a gain of an equal size – and the resulting S-shaped utility function.Rabin puts the key (...) point as follows: ``Researchers have identified a pervasive feature of reference dependence: In a wide variety of domains, people are significantly more averse to losses than they are attracted to same size gains''(Rabin 1998, 13–14). In what follows, I will show that the ``wide variety of domains'' is wide indeed. In particular, I will review the effects of the S-shaped utility function on the resolution of the decision to commit a crime, to decision to violate professional ethics, and the decision to participate in a rebellion. (shrink)

Utilitarians are attracted to the idea that an act is morally right iff it leads to the best outcome. But critics have pointed out that in many cases we cannot determine which of our alternatives in fact would lead to the best outcome. So we can’t use the classic principle to determine what we should do. It’s not “practical”; it’s not “action-guiding”. Some take this to be a serious objection to utilitarianism, since they think a moral theory ought to be (...) practical and action-guiding. In response, some utilitarians propose to modify utilitarianism by replacing talk of actual utility with talk of expected utility. Others propose to leave the original utilitarian principle in place, but to combine it with a decision procedure involving expected utility. What all these philosophers have in common is this: they move toward expected utility in order to defend utilitarianism against the impracticality objection. My aim in this paper is to cast doubt on this way of replying to the objection. My central claim is that if utilitarians are worried about the impracticality objection, they should not turn to expected utility utilitarianism. That theory does not provide the basis for a cogent reply to the objection. (shrink)

a–b* c–d is taken to mean that your degree of preference for a over b is less than your degree of preference for c over d. Various properties of the strength-of-preference comparison relation * are examined along with properties of simple preferences defined from *. The investigation recognizes an individual's limited ability to make precise judgments. Several utility theorems relating a–b * c–d to u(a)–u(b) are included.

This paper formulates and axiomatizes utility models for denumerable time streams that make no commitment in regard to discounting future outcomes. The models address decision under certainty and decision under risk. Independence assumptions in both contexts lead to additive or multiplicative utilities over time periods that allow unambiguous comparisons of the relative importance of different periods. The models accommodate all patterns of future valuation. This discount-neutral feature is attained by restricting preference comparisons to outcome streams or probability distributions on outcome (...) streams that differ in at most a finite number of periods. (shrink)

- In decision theory, an agent is deciding how to value a gamble that results in different outcomes in different states. Each outcome gets a utility value for the agent.

A generalization of the usual approach to the expected utility theory is given, with the aim of representing the state of belief of an agent who may decline on grounds of ignorance to express a preference between a given pair of acts and would, therefore, be considered irrational from a Bayesian point of view. Taking state, act, and outcome as primitive concepts, a utility function on the outcomes is constructed in the usual way. Each act is represented by a utility-valued (...) function on the states — but not all such functions are taken to represent acts. A weaker than usual set of axioms on preferences between acts is now postulated. It is shown that any agent can be represented by a risk function that assigns to each (mixed) state a number that gives the maximum loss (in utility) the agent might expect should be the actual state of the world. The form of the risk function is determined, both in general and in important particular cases. The results show that any rational agent behaves as though he were acting under the guidance of a set of Bayesian (or, more generally, pseudo-Bayesian) advisors. (shrink)

Contrary to the received view, decision theory is not primarily devoted to instrumental (ends-to-means) reasoning. Instead, its major preoccupation is the derivation of ends from other ends. Given preferences over basic alternatives, it constructs preferences over alternatives that have been modified through the addition of value object modifiers (modes) that specify probability, uncertainty, distance in time etc. A typology of the decision-theoretical modes is offered. The modes do not have (even extrinsic) value, but they transform the value of objects to (...) which they are applied. A rational agent's total set of preferences should be coherent, but from this it does not follow that her preferences over mode-containing objects have to be derivable from her preferences over mode-free objects. (shrink)

The purpose of this paper is to show how some of the controversial questions concerning utilitarianism can be clarified by the modelling techniques and the other analytical tools of decision theory (and, sometimes, of game theory). It is suggested that the moral rules of utilitarian ethics have a logical status similar to that of the normative rules (theorems) of such formal normative disciplines as decision theory and game theory.The paper argues that social utility should be defined, not in hedonistic or (...) in ideal-utilitarian terms, but rather in terms of individual preferences, in accordance with the author's equiprobability model of moral value judgments. (shrink)

Ellsberg (The Quarterly Journal of Economics 75, 643–669 (1961); Risk, Ambiguity and Decision, Garland Publishing (2001)) argued that uncertainty is not reducible to risk. At the center of Ellsberg’s argument lies a thought experiment that has come to be known as the three-color example. It has been observed that a significant number of sophisticated decision makers violate the requirements of subjective expected utility theory when they are confronted with Ellsberg’s three-color example. More generally, such decision makers are in conflict with (...) either the ordering assumption or the independence assumption of subjective expected utility theory. While a clear majority of the theoretical responses to these violations have advocated maintaining ordering while relaxing independence, a persistent minority has advocated abandoning the ordering assumption. The purpose of this paper is to consider a similar dilemma that exists within the context of multiattribute models, where it arises by considering indeterminacy in the weighting of attributes rather than indeterminacy in the determination of probabilities as in Ellsberg’s example. (shrink)

This paper argues that any specific utility or disutility for gambling must be excluded from expected utility because such a theory is consequential while a pleasure or displeasure for gambling is a matter of process, not of consequences. A (dis)utility for gambling is modeled as a process utility which monotonically combines with expected utility restricted to consequences. This allows for a process (dis)utility for gambling to be revealed. As an illustration, the model shows how empirical observations in the Allais paradox (...) can reveal a process disutility of gambling. A more general model of rational behavior combining processes and consequences is then proposed and discussed. (shrink)

This paper proposes an exploration of the methodology of utility functions that distinguishes interpretation from representation. While representation univocally assigns numbers to the entities of the domain of utility functions, interpretation relates these entities with empirically observable objects of choice. This allows us to make explicit the standard interpretation of utility functions which assumes that two objects have the same utility if and only if the individual is indifferent among them. We explore the underlying assumptions of such an hypothesis and (...) propose a non-standard interpretation according to which objects of choice have a well-defined utility although individuals may vary in the way they treat these objects in a specific context. We provide examples of such a methodological approach that may explain some reversal of preferences and suggest possible mathematical formulations for further research. (shrink)

Suppose my utilities are representable by a set of utility assignments, each defined for atomic sentences; suppose my beliefs are representable by a set of probability assignments. Then each of my utility assignments together with each of my probability assignments will determine a utility assignment to non-atomic sentences, in a familiar way. This paper is concerned with the question, whether I am committed to all the utility assignments so constructible. Richard Jeffrey (1984) says (in effect) "no", Isaac Levi (1974) says (...) "yes". I argue for "no", and raise in passing a problem for Levi. (shrink)

On the orthodox view in economics, interpersonal comparisons of utilityare not empirically meaningful, and ``hence'' impossible. To reassess this view, this paper draws onthe parallels between the problem of interpersonal comparisons of utility and the problem of translation of linguisticmeaning, as explored by Quine. I discuss several cases of what the empirical evidence for interpersonal comparisonsof utility might be and show that, even on the strongest of these, interpersonal comparisons are empiricallyunderdetermined and, if we also deny any appropriate truth of (...) the matter, indeterminate. However, the underdeterminationcan be broken non-arbitrarily (though not purely empirically) if (i) we assign normative significance to certainstates of affairs or (ii) we posit a fixed connection between certain empirically observable proxies and utility.I conclude that, even if interpersonal comparisons are not empirically meaningful, they are not in principle impossible. (shrink)

If one can get the targets of one's current wants only by acquiring new wants (as in the Prisoner's Dilemma), is it rational to do so? Arguably not. For this could justify adopting unsatisfiable wants, violating the rational duty to maximize one's utility. Further, why cause a want's target if one will not then want it? And people "are" their wants. So if these change, people will not survive to enjoy their wants' targets. I reply that one rationally need not (...) advance one's future wants, only current ones. Furthermore, rational choice seeks not utility (the co-obtaining of a want and its target), but satisfaction (the eventual obtaining of what is now wanted) -- otherwise, it would be irrational to care now about what happens after one dies. Finally, persons survive "rational" changes of values. Thus reflection on the rational revision of values illuminates the conditions on personal identity and the bases and aims of rational choice. (shrink)

It is argued that existing axiomatic theories of utility do not provide the utility principle or the principle of maximising expected utility with a formal justification. It is also argued that these theories only put mild constraints on a decision-maker in a decision-context. Finally, it is argued that the prospects are not particularly bright for finding formal non-circular arguments for the utility principle that do not rely on the law of large numbers.

This article concerns the prescriptive function of decision analysis. Consider an agent who must choose an action yielding welfare that varies with an unknown state of nature. It is often asserted that such an agent should adhere to consistency axioms which imply that behavior can be represented as maximization of expected utility. However, our agent is not concerned the consistency of his behavior across hypothetical choice sets. He only wants to make a reasonable choice from the choice set that he (...) actually faces. Hence, I reason that prescriptions for decision making should respect actuality. That is, they should promote welfare maximization in the choice problem the agent actually faces. Any choice respecting weak and stochastic dominance is rational from the actualist perspective. (shrink)

This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or sure-thing principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of the standard ex post approach. An ex post approach utilizes the decision maker's preferences among risky acts for generating a utility and a probability function, whereas in the ex ante approach a set of preferences among potential outcomes are on the input side (...) of the theory and the decision maker's preferences among risky acts on the output side. (shrink)

In this paper we want to explore an argumentative pattern that provides a normative justification for expected utility functions grounded on empirical evidence, showing how it worked in three different episodes of their development. The argument claims that we should prudentially maximize our expected utility since this is the criterion effectively applied by those who are considered wisest in making risky choices (be it gamblers or businessmen). Yet, to justify the adoption of this rule, it should be proven that this (...) is empirically true: i.e., that a given function allows us to predict the choices of that particular class of agents. We show how expected utility functions were introduced and contested in accordance with this pattern in the 18th century and how it recurred in the 1950s when M. Allais made his case against the neobernoullians. (shrink)

Expected utility theory does not directly deal with the utility of chance. It has been suggested in the literature (Samuelson, 1952, Markowitz, 1959) 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. (shrink)

In an article published in Prolegomena 2006, Christoph Schmidt-Petri has defended his interpretation and attacked mine of Mill’s idea that higher kinds of pleasure are superior in quality to lower kinds, regardless of quantity. Millian qualitative superiorities as I understand them are infinite superiorities. In this paper, I clarify my interpretation and show how Schmidt-Petri has misrepresented it and ignored the obvious textual support for it. As a result, he fails to understand how genuine Millian qualitative superiorities determine the novel (...) structure of Mill’s pluralistic utilitarianism, in which a social code of justice that distributes equal rights and duties takes absolute priority over competing considerations. Schmidt-Petri’s own interpretation is a non-starter, because it does noteven recognize that Mill is talking about different kinds of pleasant feelings, such that the higher kinds are intrinsically more valuable than the lower. I conclude by outlining why my interpretation is free of any metaphysical commitment to the “essence” of pleasure. (shrink)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on the idea of minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unitless numerical measures of how costly or valuable are the various consequences of potential decisions. In this paper, we address directly the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential (...) decisions. The simplest example is to imagine that the loss will be paid in units of some currency. If there are multiple currencies available for paying the loss, one must take explicit account of which currency is used as well as the exchange rates between the various available currencies. (shrink)

An opinionated encyclopedia entry on Hastings Rashdall, in which several worries about his case for ideal utilitarianism are raised.

When a risk is exchanged, the exact value for the minimum price (positive or negative) that the purchaser (investor, or insurer) is willing to pay is given by the certainty equivalent wealth level, which in turn depends on his specific utility function. When this utility function is unknown, then only a sufficient condition on the price can ever be found. This paper provides methods for calculating such a sufficient condition, when only limited information on the utility function is known.

Uncertainty plays an important role in The General Theory, particularly in the theory of interest rates. Keynes did not provide a theory of uncertainty, but he did make some enlightening remarks about the direction he thought such a theory should take. I argue that some modern innovations in the theory of probability allow us to build a theory which captures these Keynesian insights. If this is the right theory, however, uncertainty cannot carry its weight in Keynes’s arguments. This does not (...) mean that the conclusions of these arguments are necessarily mistaken; in their best formulation they may succeed with merely an appeal to risk. (shrink)

Standard principles of rational decision assume that an option’s utility is both comprehensive and accessible. These features constrain interpretations of an option’s utility. This essay presents a way of understanding utility and laws of utility. It explains the relation between an option’s utility and its outcome’s utility and argues that an option’s utility is relative to a specification of the option. Utility’s relativity explains how a decision problem’s framing affects an option’s utility and its rationality even for an agent who (...) is cognitively perfect and lacks only empirical information. The essay rewrites standard laws of utility to accommodate relativization to propositions’ specifications. The new laws are generalizations of the standard laws and yield them as special cases. (shrink)

This paper summarizes and rebuts the three standard objections made by social choice theorists against interpersonal utility. The first objection argues that interpersonal utility is measningless. I show that this objection either focuses on irrelevant kinds of meaning or else uses implausible criteria of meaningfulness. The second objection argues that interpersonal utility has no role to play in social choice theory. I show that on the contrary interpersonal utility is useful in formulating goals for social choice. The third objection argues (...) that interpersonal utility in social choice theory can be replaced by clearer notions. I show that the replacements proposed are unsatisfactory in either interpersonal utility's descriptive or explanatory role. My conclusion is that interpersonal utility has a legitimate place in social choice theory. (shrink)