Preferences in Decision Theory

This paper proposes several concepts of efficient solutions for multicriteria decision problems under uncertainty. We show how alternative notions of efficiency may be grounded on different decision ‘contexts’, depending on what is known about the Decision Maker's (DM) preference structure and probabilistic anticipations. We define efficient sets arising naturally from polar decision contexts. We investigate these sets from the points of view of their relative inclusions and point out some particular subsets which may be especially relevant to some decision situations.

The best justification of time-discounting is roughly that it is rational to care less about your more distant future because there is less of you around to have it. I argue that the standard version of this argument, which treats both psychological continuity and psychological connectedness as reasons to care about your future, can only rationalize an irrational—because exploitable—form of future discounting.

Probably many people have cyclic preferences: they prefer A to B, B to C and C to A for some objects of choice A, B and C. Recent work has resurrected the objection to cyclic preference that agents possessing them are open to exploitation by means of ‘money pumps’. The paper briefly reviews this work and proposes a general approach to problems of sequential choice that makes cyclic preference immune to exploitation by means of these new mechanisms.

Models in decision theory and game theory assume that preferences are determinate: for any pair of possible outcomes, a and b, an agent either prefers a to b, prefers b to a, or is indifferent as between a and b. Preferences are also assumed to be stable: provided the agent is fully informed, trivial situational influences will not shift the order of her preferences. Research by behavioral economists suggests, however, that economic and hedonic preferences are to some degree indeterminate and (...) unstable, which in turn suggests that other sorts of preferences may suffer the same problem. Even fully informed agents do not always determinately prefer a to b, prefer b to a, or feel indifferent as between a and b. Seemingly trivial situational influences rearrange the order of their preferences. One could respond that decision theory and game theory are not meant to describe actual behavior, and that they instead adumbrate an ideal of rationality from which human action diverges in various ways. When the divergences are small and systematic, they help us identify the heuristics that conspire to help people approximate rationality. One such heuristic, dubbed the Wilde heuristic, is explored. However, the divergences documented by behavioral economists threaten to be too large to handle through idealization. The Rum Tum Tugger Model, in which indifference is intransitive, is spelled out as one promising way for decision and game theory to retrench. Preferences may be locally unstable and indeterminate, but when the differences between options are sufficiently large, they approximate stability and determinacy. (shrink)

For (S, Σ) a measurable space, let ${\cal C}_1$ and ${\cal C}_2$ be convex, weak* closed sets of probability measures on Σ. We show that if ${\cal C}_1$ ∪ ${\cal C}_2$ satisfies the Lyapunov property , then there exists a set A ∈ Σ such that minμ1∈ ${\cal C}_1$ μ1(A) > maxμ2 ∈ ${\cal C}_2$ (A). We give applications to Maxmin Expected Utility (MEU) and to the core of a lower probability.

The money-pump argument figures as the staple argument in support of the view that cyclic preferences are irrational. According to a prominent way of understanding the argument, it is grounded in the assumption that it is irrational to make choices that lead one to a dispreferred alternative. My aim in this paper is to motivate diffidence with respect to understanding the money-pump argument in this way by suggesting that if it is so understood, the argument emerges as question-begging and as (...) a complicated distraction in the debate concerning cyclic preferences, and that there is a way of understanding the argument that casts it as grounded in a less controversial starting point. (shrink)

The puzzle of the self-torturer raises intriguing questions concerning rationality, cyclic preferences, and resoluteness. Interestingly, what makes the case puzzling has not been clearly pinpointed. The puzzle, it seems, is that a series of rational choices foreseeably leads the self-torturer to an option that serves his preferences worse than the one with which he started. But this is a very misleading way of casting the puzzle. I pinpoint the real puzzle of the self-torturer and, in the process, reveal a neglected (...) but crucial dimension of instrumental rationality. (shrink)

This paper draws a distinction between two closely related conceptions of 'preference' that is of great significance relative to a set of interrelated debates in rational choice theory. The distinction is particularly illuminating in relation to the idea that there is a rational defect inherent in individuals with intransitive preferences and, relatedly, in democratic collectives. I use the distinction to show that things are more complicated than they seem.

I consider the implications of incommensurability for the assumption, in rational choice theory, that a rational agent’s preferences are complete. I argue that, contrary to appearances, the completeness assumption and the existence of incommensurability are compatible. Indeed, reflection on incommensurability suggests that one’s preferences should be complete over even the incommensurable alternatives one faces.

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.

Sequel to Armendt 1986, ‘A Foundation for Causal Decision Theory.’ The representation theorem for causal decision theory is slightly revised, with the addition of a new restriction on lotteries and a new axiom (A7). The discussion gives some emphasis to the way in which appropriate K-partitions are characterized by relations found among the agent’s conditional preferences. The intended interpretation of conditional preference is one that embodies a sensitivity to the agent’s causal beliefs.

Defenders of sophisticated evidential decision theory (EDT) have argued (1) that its failure to provide correct recommendations in problems where the agent believes himself asymmetrically fallible in executing his choices is no flaw of the theory, and (2) that causal decision theory gives incorrect recommendations in certain examples unless it is supplemented with an additional metatickle or ratifiability deliberation mechanism. In the first part of this paper, I argue that both positions are incorrect. In the second part of the paper, (...) I show how the agent's preferences involved in standard counterexamples to EDT, such as Newcomb's problem, violate the Jeffrey/Bolker preference axioms, specifically the Impartiality axiom. (shrink)

The primary aim of this paper is the presentation of a foundation for causal decision theory. This is worth doing because causal decision theory (CDT) is philosophically the most adequate rational decision theory now available. I will not defend that claim here by elaborate comparison of the theory with all its competitors, but by providing the foundation. This puts the theory on an equal footing with competitors for which foundations have already been given. It turns out that it will also (...) produce a reply to the most serious objections made so far against CDT and against the particular version of CDT I will defend. (shrink)

I comment on Amartya Sen's study of the relations between the analysis of freedom and the theory of social choice. Two of his themes are analysed with regard to their contribution to an analytic understanding of the issues. These are: (1) the multiple interpretations of the concept of ‘preferences’ as a foundation for the formal conceptualizations of social choice and freedom; and (2) some issues in the formalization of freedom as a value to be compared with outcomes. Under (2), I (...) mainly point out some difficulties in the existing analyses and mildly support a ‘flexibility’ interpretation of freedom that I have advanced earlier. I conclude with some observations drawn from history and literature which complicate the value bien-pensant thinkers are prone to place on freedom. (Published Online February 16 2006). (shrink)

This paper considers lexical combinations of choice functions where at least one is interpreted as arising from a norm. It is shown that in for all possibilities in which a norm is present, in general final choice may be consistent with preference optimization, but that it need not be so. It is concluded therefore that a fruitful approach to understanding the effect of norms on choice is to consider particular classes of norms rather than norms in general as in the (...) work by Wulf Gaertner among others. (shrink)

Orthodox decision theory gives no advice to agents who hold two goods to be incommensurate in value because such agents will have incomplete preferences. According to standard treatments, rationality requires complete preferences, so such agents are irrational. Experience shows, however, that incomplete preferences are ubiquitous in ordinary life. In this paper, we aim to do two things: (1) show that there is a good case for revising decision theory so as to allow it to apply non-vacuously to agents with incomplete (...) preferences, and (2) to identify one substantive criterion that any such non-standard decision theory must obey. Our criterion, Competitiveness, is a weaker version of a dominance principle. Despite its modesty, Competitiveness is incompatible with prospectism, a recently developed decision theory for agents with incomplete preferences. We spend the final part of the paper showing why Competitiveness should be retained, and prospectism rejected. (shrink)

Nakata (Theory Decis 71:559–574, 2011) presents a model of acquisition of information where the agent does not know what pieces of information she is missing. In this note, we point out some technical problems in a few of Nakata’s results and show how to correct them.

Various types of continuity for preference relations on a metric space are examined constructively. In particular, necessary and sufficient conditions are given for an order-dense, strongly extensional preference relation on a complete metric space to be continuous. It is also shown, in the spirit of constructive reverse mathematics, that the continuity of sequentially continuous, order-dense preference relations on complete, separable metric spaces is connected to Ishihara's principleBD-ℕ, and therefore is not provable within Bishop-style constructive mathematics alone.

We examine a distinctive kind of problem for decision theory, involving what we call discontinuity at infinity. Roughly, it arises when an infinite sequence of choices, each apparently sanctioned by plausible principles, converges to a ‘limit choice’ whose utility is much lower than the limit approached by the utilities of the choices in the sequence. We give examples of this phenomenon, focusing on Arntzenius et al.’s Satan’s apple, and give a general characterization of it. In these examples, repeated dominance reasoning (...) (a paradigm of rationality) apparently gives rise to a situation closely analogous to having intransitive preferences (a paradigm of irrationality). Indeed, the agents in these examples are vulnerable to a money pump set-up despite having preferences that exhibit no obvious defect of rationality. We explore several putative solutions to such problems, particularly those that appeal to binding and to deliberative dynamics. We consider the prospects for these solutions, concluding that if they fail, the examples show that money pump arguments are invalid. (shrink)

Are risk preferences stable over time? To address this question we elicit risk preferences from the same pool of subjects at two different moments in time. To interpret the results, we use a Fechner stochastic choice model in which the revealed preference of individuals is governed by some underlying preference, together with a random error. We take cumulative prospect theory as the underlying preference model (Kahneman and Tversky, Econometrica 47:263–292, 1979; Tversky and Kahneman, Journal of Risk and Uncertainty 5:297–323, 1992). (...) We observe that the aggregate pattern of preferences is very similar in both sessions, and it matches the results reported in the literature. Most subjects are risk averse for gains, and risk seeking for losses. However, the subjects that jointly agree with the reflection effect of prospect theory are around 50%. The percentage of individuals that change their responses across sessions is quite high, 63%. Estimating the stochastic choice model we find that 72% of the subjects have an underlying preference which agrees with the reflection effect of prospect theory. The remaining 28% are mainly classified as risk averse for both gains and losses. The results reinforce the empirical validity of the reflection effect. Deviations from the reflection effect can be attributed to noise, as well as to the existence of a fraction of risk averse subjects. (shrink)

An individual is said to have a taste for a particular menu, i.e. a subset of available commodities, if he is indifferent between all commodity bundles that contain the same quantity for each commodity which actually is in the menu, whatever the rest of the bundle. Then, a taste is directly defined as a deep property of preferences. As a first result, it is shown that a complete and transitive preference relation over the commodity bundles is equivalent to regular tastes (...) where regularity means that tastes can be derived from a pure qualitative relation between the different commodities. Besides, a preference family based on preference relations corresponding to each particular commodity is said to be rationalizable if there exists a metapreference over commodity bundles which consistently summarizes the preference family and then allows to decide. As a second result, it is shown that if a preference family is rationalizable, then the tastes are organized thanks to a reflexive and transitive qualitative relation between the different commodities. (shrink)

Adapting a definition introduced by Milgrom (1981) we say that a signal about the environment is good news relative to some initial beliefs if the posterior beliefs dominate the initial beliefs in the sense of first-order stochastic dominance (the assumption being that higher values of the parameter representing the environment mean better environments). We give an example where good news leads to the adoption of a more pessimistic course of action (we say that action a, reveals greater pessimism than action (...) a„ if it gives higher payoff in bad environments and lower payoff in good environments). We then give sufficient conditions for a signal not to induce a more pessimistic choice of action. (shrink)

The contributions to the Special Issue on Multiple Belief Change, Iterated Belief Change and Preference Aggregation are divided into three parts. Four contributions are grouped under the heading "multiple belief change" (Part I, with authors M. Falappa, E. Fermé, G. Kern-Isberner, P. Peppas, M. Reis, and G. Simari), five contributions under the heading "iterated belief change" (Part II, with authors G. Bonanno, S.O. Hansson, A. Nayak, M. Orgun, R. Ramachandran, H. Rott, and E. Weydert). These papers do not only pick (...) up the particular questions raised, but also extend and modify the framework of Alchourrón, Gärdenfors and Makinson. Part III deals with preference aggregation and consists of one contribution (by F. Herzberg and D. Eckert). (shrink)

People can reason about the preferences of other agents, and predict their behavior based on these preferences. Surprisingly, the psychology of reasoning has long neglected this fact, and focused instead on disinterested inferences, of which preferences are neither an input nor an output. This exclusive focus is untenable, though, as there is mounting evidence that reasoners take into account the preferences of others, at the expense of logic when logic and preferences point to different conclusions. This article summarizes the most (...) recent account of how reasoners predict the behavior and attitude of other agents based on conditional rules describing actions and their consequences, and reports new experimental data about which assumptions reasoners retract when their predictions based on preferences turn out to be false. (shrink)

I examine the normative status of various wanting-to-believe cases and wanting-to-desire cases.

This article examines Becker's thesis that the hypothesis that choices maximize expected utility relative to fixed and universal tastes provides a general framework for the explanation of behaviour. Three different models of preference revision are presented and their scope evaluated. The first, the classical conditioning model, explains all changes in preferences in terms of changes in the information held by the agent, holding fundamental beliefs and desires fixed. The second, the Jeffrey conditioning model, explains them in terms of changes in (...) both the information held by the agent and changes in her prior beliefs, holding her fundamental desires fixed. The final model, that of generalized conditioning, allows for explanations in terms of changes in the values of all three variables. Key Words: preference change • decision theory • probability • desirability • attitude change. (shrink)

Conditional attitudes are not the attitudes an agent is disposed to acquire in event of learning that a condition holds. Rather they are the components of agent's current attitudes that derive from the consideration they give to the possibility that the condition is true. Jeffrey's decision theory can be extended to include quantitative representation of the strength of these components. A conditional desirability measure for degrees of conditional desire is proposed and shown to imply that an agent's degrees of conditional (...) belief are conditional probabilities. Rational conditional preference is axiomatised and by application of Bolker's representation theorem for rational preferences it is shown that conditional preference rankings determine the existence of probability and desirability measures that agree with them. It is then proven that every conditional desirability function agrees with an agent's conditional preferences and, under certain assumptions, every desirability function agreeing with an agent's conditional preferences is a conditional desirability function agreeing with her unconditional preferences. (shrink)

Risk-weighted expected utility theory permits preferences which violate the Sure-Thing Principle. But preferences that violate the STP can lead to bad decisions in sequential choice problems. In particular, they can lead decision-makers to adopt a strategy that is dominated – i.e. a strategy such that some available alternative leads to a better outcome in every possible state of the world.

In this paper, we analyze an intra-personal game where a decision-maker is summarized by a succession of selves. Selves may (or may not) have conflicting interests, and earlier selves may have imperfect knowledge of the preferences of future selves. At date 1, self-1 chooses a menu, at date 2, the preferences of self-2 realize and self-2 chooses an item from the menu. We show that equilibrium choice is consistent with either a preference for flexibility, a preference for betweenness or a (...) preference for systematic restriction. Overall, the analysis reconciles the decision–theoretic approach of choice over time with the game–theoretic multiple-selves approach. (shrink)

Decision theory explicates norms of rationality for deriving preferences from preferences and beliefs. Empirical studies have found that actual preferences regularly violate these norms, launching a debate on whether this shows that subjects are prone to certain forms of irrationality or that decision theory needs to be revised. It has been claimed that such a revision is necessitated by the fact that normative uses of decision theory must be justified by a reflective equilibrium. The paper discusses three points. First, the (...) debate over the impact of empirical studies on decision theories is only meaningful with respect to a decision theory that includes not only a formal system but also a theory of application. Second, differences in the concepts of reflective equilibrium appealed to are a source of confusion in the debate on rationality. Third, the assumption that normative uses of decision theory are justified by reflective equilibrium is not sufficient ground for arguing that the empirical studies call for a revision of decision theory. Such an argument must rely on substantive claims about rationality, preferences and beliefs. (shrink)

Francis Hauksbee is well known for his double-barrelled air-pump. However, the origin of this pump, and Hauksbee's background, are often described as a mystery. This text seeks to dispel the riddle. It is argued that Hauksbee's competence as an exceptional maker of air-pumps was developed between 1699 and 1703 as a result of his experiences with the construction, manufacturing and sale of cupping-glasses. His cupping utensils embodied a new design, where syringes were used to evacuate the glasses, instead of the (...) traditional way by fire or mouth suction. These syringes, which in fact were small air-pumps, were perfected between 1699 and 1701. A larger syringe, introduced in 1701, served as a transition from the cupping-syringe to his first air-pump for use in natural philosophy. This syringe was described as a ‘combined engine’, which could serve as an air-pump, a condensing engine and a syringe for injecting air, wax or mercury into pathological specimens. Hauksbee's first air-pump was a single-barrelled model introduced in 1702, based on the combined engine. Its various features, such as easy and convenient leak-tightening, exact pressure measurements by an in-built barometer and an air-inlet function for readmission of air into the receiver, are discussed. Finally, it is shown that these activities gave Hauksbee the reputation of being an outstanding instrument-maker, years before the double-barrelled air-pump was in sight. (shrink)

Decision theory has at its core a set of mathematical theorems that connect rational preferences to functions with certain structural properties. The components of these theorems, as well as their bearing on questions surrounding rationality, can be interpreted in a variety of ways. Philosophy’s current interest in decision theory represents a convergence of two very different lines of thought, one concerned with the question of how one ought to act, and the other concerned with the question of what action consists (...) in and what it reveals about the actor’s mental states. As a result, the theory has come to have two different uses in philosophy, which we might call the normative use and the interpretive use. It also has a related use that is largely within the domain of psychology, the descriptive use. This essay examines the historical development of decision theory and its uses; the relationship between the norm of decision theory and the notion of rationality; and the interdependence of the uses of decision theory. (shrink)

Some early phase clinical studies of candidate HIV cure and remission interventions appear to have adverse medical risk–benefit ratios for participants. Why, then, do people participate? And is it ethically permissible to allow them to participate? Recent work in decision theory sheds light on both of these questions, by casting doubt on the idea that rational individuals prefer choices that maximise expected utility, and therefore by casting doubt on the idea that researchers have an ethical obligation not to enrol participants (...) in studies with high risk–benefit ratios. This work supports the view that researchers should instead defer to the considered preferences of the participants themselves. This essay briefly explains this recent work, and then explores its application to these two questions in more detail. (shrink)

I have claimed that risk-weighted expected utility maximizers are rational, and that their preferences cannot be captured by expected utility theory. Richard Pettigrew and Rachael Briggs have recently challenged these claims. Both authors argue that only EU-maximizers are rational. In addition, Pettigrew argues that the preferences of REU-maximizers can indeed be captured by EU theory, and Briggs argues that REU-maximizers lose a valuable tool for simplifying their decision problems. I hold that their arguments do not succeed and that my original (...) claims still stand. However, their arguments do highlight some costs of REU theory. (shrink)