Preferences in Decision Theory

We argue that all gradable expressions in natural language obey a principle that we call Comparability: if x and y are both F to some degree, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns of (...) inference that seem manifestly valid. We reply to some influential arguments against Comparability, raise and reject some new arguments, and draw out some surprising implications of Comparability for debates concerning preference and credence. (shrink)

Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant of (...) Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions. (shrink)

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

Tough anti-terrorism policies are often defended by focusing on a fixed minority of the population who prefer violent outcomes, and arguing that toughness reduces the risk of terrorism from this group. This reasoning implicitly assumes that tough policies do not increase the group of 'potential terrorists', i.e., of people with violent preferences. Preferences and their level of violence are treated as stable, exogenously fixed features. To avoid this unrealis- tic assumption, I formulate a model in which policies can 'brutalise' or (...) 'appease' someone's personality, i.e., his preferences. This follows the endogenous prefer- ences approach, popular elsewhere in political science and economics. I formally decompose the effect of toughness into a (desirable) deterrence effect and an (un- desirable) provocation effect. Whether toughness is overall effi cient depends on which effect overweighs. I show that neglecting provocation typically leads to toughness exaggeration. This suggests that some tough anti-terrorism policies observable in the present and past can be explained by a neglect of provocation. (shrink)

Rational decision change can happen without information change. This is a problem for standard views of decision theory, on which linguistic intervention in rational decision-making is captured in terms of information change. But the standard view gives us no way to model interventions involving expressions that only have an attentional effects on conversational contexts. How are expressions with non-informational content - like epistemic modals - used to intervene in rational decision making? We show how to model rational decision change without (...) information change: replace a standard conception of value (on which the value of a set of worlds reduces to values of individual worlds in the set) with one on which the value of a set of worlds is determined by a selection function that picks out a generic member world. We discuss some upshots of this view for theorizing in philosophy and formal semantics. (shrink)

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.

Decision theorists have attempted to accommodate several violations of decision theory’s axiomatic requirements by modifying how agents’ choice options are individuated and formally represented. In recent years, prominent authors have worried that these modifications threaten to trivialize decision theory, make the theory unfalsifiable, impose overdemanding requirements on decision theorists and hamper decision theory’s internal coherence. In this paper, I draw on leading descriptive and normative works in contemporary decision theory to address these prominent concerns. In doing so, I articulate and (...) assess several different criteria for individuating and formally representing agents’ choice options. (shrink)

This book is divided into 4 chapters. In Chapters 1 and 2, I address (1) how to acquire rational belief attitudes and (2) how to make rational choices. Building on Chapters 1 and 2, I then answer two of the most pressing questions of our time: (3) Should you be skeptical of climate change? (4) Should you invest in life-extension medical research?

We study the representation of attitudes to risk in Jeffrey’s decision-theoretic framework suggested by Stefánsson and Bradley :602–625, 2015; Br J Philos Sci 70:77–102, 2017) and Bradley :231–248, 2016; Decisions theory with a human face, Cambridge University Press, Cambridge, 2017). We show that on this representation, the value of any prospect may be expressed as a sum of two components, the prospect’s instrumental value and the prospect’s intrinsic value. Both components have an expectational form. We also make a distinction between (...) a prospect’s overall intrinsic value and a prospect’s conditional intrinsic value given each one of its possible outcomes and argue that this distinction has great explanatory power. We explore the relation between these two types of intrinsic values and show that they are determined at the level of preferences. Finally, we explore the relation between the intrinsic values of different prospects and point to a strong restriction on this relation that is implicit in Jeffrey’s axioms. We suggest a natural interpretation to this restriction. (shrink)

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This result also (...) generalizes Aizerman and Malishevski's characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. (shrink)

Joe Horton’s all-or-nothing problem concerns a situation in which it is morally permissible to do nothing and to save two people but not to save only one. This description seems to entail that we should do nothing rather than save only one. I object to Horton’s solution and challenge a principle he draws attention to, which is required to generate the problem but which Horton regards as beyond dispute.

In this paper, I investigate the betting behavior of a decision-maker who can influence the likelihood of the events upon which she is betting. In decision theory, this is best known as a situation of moral hazard. Focusing on a particularly simple case, I sketch the first systematic analysis of moral hazard in the canonical Savage framework. From the results of this analysis, I draw two philosophical conclusions. First, from an observational and a descriptive point of view, there need to (...) be no incompatibility between moral hazard and the Savage framework. This qualifies the incompatibility view, that is ubiquitous in decision theory. Second, in general, moral hazard is not sufficient to overcome the challenges posed by state-dependent utility to the behavioral identification of beliefs. This qualifies the sufficiency view, that is influential in decision theory. These two philosophical conclusions are the main contributions of my paper. (shrink)

Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on smaller (...) sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections. (shrink)

Preference relations are intensively studied in Economics, but they are also approached in AI, Knowledge Representation, and Conceptual Modelling, as they provide a key concept in a variety of domains of application. In this paper, we propose an ontological foundation of preference relations to formalise their essential aspects across domains. Firstly, we shall discuss what is the ontological status of the relata of a preference relation. Secondly, we investigate the place of preference relations within a rich taxonomy of relations (e.g. (...) we ask whether they are internal or external, essential or contingent, descriptive or nondescriptive relations). Finally, we provide an ontological modelling of preference relation as a module of a foundational (or upper) ontology (viz. OntoUML). The aim of this paper is to provide a sharable foundational theory of preference relation that foster interoperability across the heterogeneous domains of application of preference relations. (shrink)

In this paper, I examine the decision-theoretic status of risk attitudes. I start by providing evidence showing that the risk attitude concepts do not play a major role in the axiomatic analysis of the classic models of decision-making under risk. This can be interpreted as reflecting the neutrality of these models between the possible risk attitudes. My central claim, however, is that such neutrality needs to be qualified and the axiomatic relevance of risk attitudes needs to be re-evaluated accordingly. Specifically, (...) I highlight the importance of the conditional variation and the strengthening of risk attitudes, and I explain why they establish the axiomatic significance of the risk attitude concepts. I also present several questions for future research regarding the strengthening of risk attitudes. (shrink)

This note considers the conceptual part of Sen’s «Internal Consistency of Choice». Amongst the various claims this paper features, two are singled out. A first, negative, claim is that no formal condition of choice consistency is normatively compelling without exception. A second, positive, claim, is that a formal condition of choice consistency is normatively compelling only under some assumptions involving preference. Here, the puzzling choices Sen puts forward are scrutinized and it is argued that such a scrutiny leads to question (...) the negative claim, but in a subtle way, so that the positive claim is comforted, even strengthened. -/- Cette note examine la partie conceptuelle d’un article de Sen, «Internal Consistency of Choice». Elle isole deux thèses parmi celles que Sen défend. Une première, négative, est qu’aucune condition formelle de cohérence du choix n’est normativement valable sans exception. Une seconde, positive, est qu’une condition formelle de cohérence du choix n’est normativement valable que sous des suppositions faisant intervenir la préférence. Nous procédons à une analyse détaillée des choix énigmatiques dont Sen prend argument et affirmons que cet examen mène à remettre en cause la thèse négative, mais d’une manière subtile qui confirme — même renforce — la thèse positive. (shrink)

Arguments for moral consequentialism often appeal to an alleged structural similarity between consequentialist reasoning in ethics and rational decision-making in everyday life. Ordinary rational decision-making is seen as a paradigmatic case of goal-oriented, teleological decision-making, since it allegedly aims at maximizing the goal of preference satisfaction. This chapter describes and discusses a neglected type of preference change, “predictable preference accommodation.” This phenomenon leads to a number of critical cases in which the rationality of a particular choice does not depend on (...) features of the outcome of the chosen act. On the basis of these cases, it is argued that consequentialists cannot point to everyday decision-making as an uncontroversial example of consequentialist reasoning. On the contrary, it is suggested that an adequate account of rationality in prudential choice may need a Kantian notion of respect. (shrink)

According to the preference-centric approach to understanding partial belief, the connection between partial beliefs and preferences is key to understanding what partial beliefs are and how they’re measured. As Ramsey put it, the ‘degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it’ The Foundations of Mathematics and Other Logical Essays, Routledge, Oxon, pp 156–198, 1931). But this idea is not as popular as (...) it once was. Nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, unpalatably anti-realist, and/or prone to devastating counterexamples. Cases like Eriksson and Hájek’s :183–213, 2007) preferenceless Zen monk and Christensen’s :356–376, 2001) other roles argument have suggested to many that any account of partial belief that ties them too closely to preferences is irretrievably flawed. In this paper I provide a defence of preference-centric accounts of partial belief. (shrink)

I have argued elsewhere that human free action is governed by objective probabilities. This view, I suggested, is strongly supported by our experience of motivated decision-making and by our having emerged from probabilistically-governed physical causes. Leigh Vicens criticizes these arguments. She also argues that an account of human freedom as probabilisticallyunstructured indeterminacy is less vulnerable to challenges to the plausibility of libertarian views of freedom. In this article, I explain why I am not persuaded by Vicens’s arguments.

Human folly, it seems, traces not only to ignorance and impulsiveness but also to the power of wishes that the erring agent acknowledges as unfit to motivate him. The possibility of genuinely perverse preference can be either denied or explained. To explain it, sense must be made of how a person’s understanding of the choices before him could fail to decide his preference—how what convinces could fail to persuade. The question is how the influence a given consideration has over a (...) person’s choice can be other than a function of the beliefs he holds about its merits, so that as between competing considerations the one esteemed best doesn’t win, despite continuing to be esteemed best. (shrink)

A pure time preference is a preference for something to occur at one point in time rather than another, merely because of when it occurs in time. Such preferences are widely regarded as paradigm examples of irrational preferences. However, Rosemary Lowry and Martin Peterson have recently argued that, for instance, a pure time preference to go to the opera tonight rather than next month may be rationally permissible, even if the amounts of intrinsic value realized in both cases are identical. (...) In this reply, we argue that Lowry and Peterson's argument is unsuccessful. (shrink)

I argue that any plausible decision theory for agents with incomplete preferences which obeys the Never Worse Principle will violate Transitivity. The Never Worse Principle says that if one option never does worse than another, you shouldn’t disprefer it. Transitivity says that if you prefer X to Y and you prefer Y to Z, then you should prefer X to Z. Violating Transitivity allows one to be money pumped. Although agents with incomplete preferences are already, in virtue of having incomplete (...) preferences, vulnerable to being money pumped, I argue that the money pump argument for Transitivity is more serious than the one for Completeness. (shrink)

In the context of two recent yet distinct philosophical debates—over choice under conditions of moral uncertainty and over transformative choices—several philosophers have implicitly adopted a thesis about how to evaluate alternatives of uncertain value. The thesis says that the value a rational agent ought to attach to an alternative under the hypothesis that the value of this alternative is x, ought to be x. I argue that while in some contexts this thesis trivially holds, in the context of the two (...) debates in which the thesis has been adopted, it does not. I also discuss several implications of this failure. (shrink)

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

Among the possible solutions to the paradoxes of collective preferences, single-peakedness is significant because it has been associated to a suggestive conceptual interpretation: a single-peaked preference profile entails that, although individuals may disagree on which option is the best, they conceptualize the choice along a shared unique dimension, i.e. they agree on the rationale of the collective decision. In this article, we discuss the relationship between the structural property of singlepeakedness and its suggested interpretation as uni-dimensionality of a social choice. (...) In particular, we offer a formalization of the relationship between single-peakedness and its conceptual counterpart, we discuss their logical relations, and we question whether single-peakedness provides a rationale for collective choices. (shrink)

Public deliberation has been defended as a rational and noncoercive way to overcome paradoxical results from democratic voting, by promoting consensus on the available alternatives on the political agenda. Some critics have argued that full consensus is too demanding and inimical to pluralism and have pointed out that single-peakedness, a much less stringent condition, is sufficient to overcome voting paradoxes. According to these accounts, deliberation can induce single-peakedness through the creation of a ‘meta-agreement’, that is, agreement on the dimension according (...) to which the issues at stake are ‘conceptualized’. We argue here that once all the conditions needed for deliberation to bring about single-peakedness through meta-agreement are unpacked and made explicit, meta-agreement turns out to be a highly demanding condition, and one that is very inhospitable to pluralism. (shrink)

Let’s say that you regard two things as on a par when you don’t prefer one to other and aren’t indifferent between them. What does rationality require of you when choosing between risky options whose outcomes you regard as on a par? According to Prospectism, you are required to choose the option with the best prospects, where an option’s prospects is a probability-distribution over its potential outcomes. In this paper, I argue that Prospectism violates a dominance principle—which I call The (...) Principle of Predominance—because it sometimes requires you to do something that’s no better than the alternatives and might be worse. I argue that this undermines the strongest argument that’s been given in favor of Prospectism. (shrink)

Feminist philosophers have questioned whether liberal theory can account for the phenomenon of adaptive preferences, specifically women’s preferences that are formed under conditions of sexist oppression. In this paper, I examine the argument of one feminist who addresses the problem of women’s “deformed desires” by relying on a liberal framework. Assessing her argument, I conclude that liberalism provides inadequate resources for responding to this issue since it errs in understanding adaptive preferences as exceptional, provides little explanation of how changes in (...) individual preferences are motivated, and often fails to identify the adaptive nature of such preferences. I illustrate my arguments through a brief discussion of women’s choices around motherhood and sexuality, and I conclude by offering several suggestions of how an alternative theory might better address the problems raised by preference adaptation in the context of oppression. (shrink)

According to Wlodek Rabinowicz's (2008) fitting-attitude analysis of value relations, two items are on a par if and only if it is both permissible to strictly prefer one to the other and permissible to have the opposite strict preference. Rabinowicz’s account is subject, however, to one important objection: if strict preferences involve betterness judgements, then his analysis contrasts with the intuitive understanding of parity. In this paper, I examine Rabinowicz’s three responses to this objection and argue that they do not (...) succeed. I then propose an alternative solution. I argue that the objection can be avoided if we ‘relativize’ Rabinowicz’s account and define parity in terms of opposite strict preferences between two items that are only relatively permissible, rather than permissible simpliciter. I argue that this account of parity can be defended if we take seriously the distinction between sufficient and decisive reason for a preference relation. I also show that, on the basis of this distinction, we can arrive at a more extensive taxonomy of value relations than the one proposed by Rabinowicz. (shrink)

According to Wlodek Rabinowicz's fitting-attitude analysis of comparative value, it is possible to analyse both standard and non-standard value relations in terms of the standard preference relations and two levels of normativity. In a recent article, however, Johan Gustafsson has argued that Rabinowicz's analysis violates a principle of value–preference symmetry, according to which for any value relation, there is a corresponding preference relation. Gustafsson has proposed an alternative analysis which respects this principle and which allegedly accounts for the idea that (...) originally motivated Rabinowicz's analysis, namely, that in some cases different preference relations between a pair of items are equally permissible. The goal of my article is to show that the arguments offered by Gustafsson in favour of his account do not succeed. In particular, I argue that Gustafsson faces a dilemma: either he abandons the principle of value–preference symmetry or he cannot make conceptual room for multiple permissible preferences. (shrink)

Taking the philosophical standpoint, this article compares the mathematical theory of individual decision-making with the folk psychology conception of action, desire and belief. It narrows down its topic by carrying the comparison vis-à-vis Savage's system and its technical concept of subjective probability, which is referred to the basic model of betting as in Ramsey. The argument is organized around three philosophical theses: (i) decision theory is nothing but folk psychology stated in formal language (Lewis), (ii) the former substantially improves on (...) the latter, but is unable to overcome its typical limitations, especially its failure to separate desire and belief empirically (Davidson), (iii) the former substantially improves on the latter, and through these innovations, overcomes some of the limitations. The aim of the article is to establish (iii) not only against the all too simple thesis (i), but also against the subtle thesis (ii). (shrink)

This paper (first published under the same title in Journal of Mathematical Economics, 29, 1998, p. 331-361) is a sequel to "Consistent Bayesian Aggregation", Journal of Economic Theory, 66, 1995, p. 313-351, by the same author. Both papers examine mathematically whether the the following assumptions are compatible: the individuals and the group both form their preferences according to Subjective Expected Utility (SEU) theory, and the preferences of the group satisfy the Pareto principle with respect to those of the individuals. While (...) the 1995 paper explored these assumptions in the axiomatic context of Savage's (1954-1972) SEU theory, the present paper explores them in the context of Anscombe and Aumann's (1963) alternative SEU theory. We first show that the problematic assumptions become compatible when the Anscombe-Aumann utility functions are state-dependent and no subjective probabilities are elicited. Then we show that the problematic assumptions become incompatible when the Anscombe-Aumann utility functions are state-dependent, like before, but subjective probabilities are elicited using a relevant technical scheme. This last result reinstates the impossibilities proved by the 1995 paper, and thus shows them to be robust with respect to the choice of the SEU axiomatic framework. The technical scheme used for the elicitation of subjective probabilities is that of Karni, Schmeidler and Vind (1983). (shrink)

According to a familiar (alleged) requirement on practical reason, one must believe a proposition if one is to take it for granted in reasoning about what to do. This paper explores a related requirement, not on thinking but on acting—that one must accept a goal if one is to count as acting for its sake. This is the acceptance requirement. Although it is endorsed by writers as diverse as Christine Korsgaard, Donald Davidson, and Talbot Brewer, I argue that it is (...) vulnerable to counterexamples, in which agents act in light of ends that they do not accept but are still merely considering. For instance, a young professional may keep a job option open not because she definitely wants or intends to take it, but just because she is considering taking it. I try to show that such examples are not easily resisted; that they present challenges specifically for Brewer, Davidson, and especially Korsgaard; and that the examples also raise fresh, non-partisan questions in action theory. What is considering, exactly? How could it fall short of acceptance while still guiding behaviour? How can we act for an end before thinking it through? (shrink)

This paper proposes a new theory of rational choice, Expected Comparative Utility (ECU) Theory. It is first argued that for any decision option, a, and any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility of a in G – that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this principle, it is then argued, roughly (...) speaking, that an agent should rank her decision options (in terms of how choiceworthy they are) according to their expected comparative utility. For any decision option, a, the expected comparative utility of a is the probability-weighted average of the comparative utilities of a across the different states of the world. It is lastly demonstrated that in a number of decision cases, ECU Theory delivers different verdicts from those of standard decision theory. (shrink)

The presented contribution stresses the role of preference ordering and of the logical culture in many spheres of human rational activities, especially in the domains connected with evaluating and decision-making tasks. Since preference relation is conceived as a relation of proposition-like-entities , any construction of preference ordering pre_- supposes the application of comparability principles. Preference expressions can be considered as a special form of propositional attitudes and the concept of preference itsself as an intensional operator.

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)

An explication of preference and equivalence with regard to the evaluation of states of affairs. The logical system developed consists of the ordinary propositional calculus together with connectives standing for the notions above. In the course of this study a number of useful distinctions and definitions can be found. The author indicates that his logic of preference may be of use in connection with utility and decision theory, but does not develop this point.--R. H. T.

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)

In economics, it has often been claimed that testing choice data for violation of certain axioms - particularly if the choice data is observed under laboratory conditions - allows conclusions about the validity of certain preference axioms and the neoclassical maximization hypothesis. In this paper I argue that these conclusions are unfounded. In particular, it is unclear what exactly is tested, and the interpretation of the test results are ambiguous. Further, there are plausible reasons why the postulated choice axioms should (...) not hold. Last, these tests make implicit assumptions about beliefs that further blur the interpretations of the results. The tests therefore say little if anything about the validity of certain preference axioms or the maximization hypothesis. (shrink)