Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated (...) with the St. Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory. (shrink)

Employees face an array of moral issues in their everyday decision making. Environmental concerns, employee and community welfare, and the interests of other companies (competitors, customers, and suppliers) are only a few examples. Yet, businesses do not always address the issue of how employees should assess the moral import of their actions and incorporate these considerations into their decisions. As a result, moral considerations are often ignored, leading to unethical practices which may hurt the long-term interests of the company. In (...) this paper, we present a model to help eliminate this problem. Our model uses expectancy theory, a process theory of motivation, to show that teaching employees to engage in moral reasoning, and creating a corporate culture in which ethical behavior is both encouraged and rewarded, can increase the likelihood that a company's employees will act ethically. (shrink)

:We address the question, in decision theory, of how the value of risky options should be assessed when they have no finite standard expected value, that is, where the sum of the probability-weighted payoffs is infinite or not well defined. We endorse, combine and extend the proposal of Easwaran to evaluate options on the basis of their weak expected value, and the proposal of Colyvan to rank options on the basis of their relative expected value.

This paper is concerned with how we ought to think about legitimate expectations in the non-ideal, ‘real’ world. In one (dominant) strand of contemporary theories of justice, justice requires not that each gets what she deserves, but that each gets that to which she is entitled in accordance with what Rawls calls ‘the public rules that specify the scheme of cooperation’. However, that is true only if those public rules are part of a fully just scheme and it is plausibly (...) the case that no such scheme obtains in the real world. Given that, and given the centrality of legitimate expectations to theories of justice, it is vital to think about the status of such expectations in non-ideal circumstances. Having explained the sense in which legitimate expectations have come to play a role often previously associated with desert, a brief argument in favour of an ‘expectations’ view of punishment is considered to show that the system to public rules that generates expectations must itself be (in some sense) just. This argument is illustrated by appeal to just punishment and the relevance of thinking about punishment and not merely distributive justice is defended. In the absence of justice, one possibility would be simply to declare that there are no legitimate expectations and so theories of justice provide no guidance as to who should get what in non-ideal conditions. However, this would be to render such theories more-or-less useless in practice. Through discussion of a series of vignettes, the paper offers an account of how we might think about the demands such expectations place on the systems that give rise to them even in cases where the system is unjust. (shrink)

Ethics theory is highly valued to the point that some commentators have claimed that it has taken on a life of its own, with too much focus on the justification of moral judgment and not enough on the needs of users of such theory. Building from various personal experiences of interdisciplinary ethics collaborative developments and empirical research projects, the wisdom gleaned by others, as well as insights from pragmatist theory, this article offers five (non-exhaustive) expectations for ethics (...) theory from the standpoint of a user. The article is intended to prompt broad reflection on expectations toward ethics theory and why user perspectives should be considered early in the development of ethics scholarship. (shrink)

The law persists because people have reasons to comply with its rules. What characterizes those reasons is their interdependence: each of us only has a reason to comply because he or she expects the others to comply for the same reasons. The rules may help us to solve coordination problems, but the interaction patterns regulated by them also include Prisoner's Dilemma games, Division problems and Assurance problems. In these "games" the rules can only persist if people can be expected to (...) be moved by considerations of fidelity and fairness, not only of prudence.This book takes a fresh look at the perennial problems of legal philosophy - the source of obligation to obey the law, the nature of authority, the relationship between law and morality, and the nature of legal argument - from the perspective of this conventionalist understanding of social rules. It argues that, since the resilience of such rules depends on cooperative dispositions, conventionalism, properly understood, does not imply positivism. (shrink)

In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.

This note is a generalization and improved interpretation of the main result of Karni and Schmeidler. A decision-maker is supposed to possess a preference relation on acts and another preference relation on state-prize lotteries, both of which are assumed to satisfy the von Neumann–Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with state-dependent (...) utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable. (shrink)

The paper summarizes expected utility theory, both in its original von Neumann-Morgenstern version and its later developments, and discusses the normative claims to rationality made by this theory.

Expected-utility theory has been a popular and influential theory in philosophy, law, and the social sciences. While its original developers, von Neumann and Morgenstern, presented it as a purely predictive theory useful to the practitioners of economic science, many subsequent theorists, particularly those outside of economics, have come to endorse EU theory as providing us with a representation of reason. But precisely in what sense does EU theory portray reason? And does it do so successfully? (...) There are two strikingly different answers to these questions in the literature. On the one hand, there is the view of people such as David Gauthier that EU theory is an implementation of the idea that reason's only role is instrumental. On the other hand, there is the view suggested by Leonard Savage that the theory is a “formal” and noninstrumental characterization of our reasoning process. (shrink)

We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Γ-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probability in a (closed) convex set. If the convex set is a singleton, then each rule agrees with maximizing expected utility. We show that, even when the option set (...) is convex, this pairwise comparison between acts may fail to identify those acts which are Bayes for some probability in a convex set that is not closed. This limitation affects two of the decision rules but not E-admissibility, which is not a pairwise decision rule. E-admissibility can be used to distinguish between two convex sets of probabilities that intersect all the same supporting hyperplanes. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty (...) about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg (...) paradoxes, a strategy that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested. (shrink)

Largely a response to Lee Basham’s essay “Malevolent Global Conspiracy.” After presenting an update on the status of conspiracy theories surrounding the 1995 Oklahoma City bombing, I agree with Basham that falsification and paranoia are not effective ways to criticize conspiratorial thinking. However, I am not convinced with the case Basham presents against worries that conspiracy theories often falter by overestimating the ability of large, public institutions to be secretly and effectively controlled. His appeal to the historical record can be (...) read as suggesting that malevolent global action can be effectively carried out in full public view, obviating recourse to conspiracy. (shrink)

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)

There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s risk-weighted expected utility (...) class='Hi'>theory. I will show that the orthodoxy can be made to accommodate all of the preferences that Buchak’s theory can accommodate. (shrink)

In this paper, I argue for a new normative theory of rational choice under risk, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility (CU) 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, I then argue that for any agent, S, faced with any decision under risk, S should rank his or her decision options (in terms of how choiceworthy they are) according to their comparative expected comparative utility (CECU) and should choose whichever option carries the greatest CECU. For any option, a, a’s CECU is the difference between its ECU and that of whichever alternative to a carries the greatest ECU, where a’s ECU is a probability‐weighted sum of a’s CUs across the various possible states of the world. I lastly demonstrate that in some ordinary decisions under risk, ECU theory delivers different verdicts from those of standard decision theory. (shrink)

Cerreia-Vioglio et al. :341–375, 2011) have proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences—and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory, is employed.

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)

This essay considers the relationship between ideal theory and non-ideal theory. It begins with Rawls’s conception of ideal theory and A. John Simmons’s articulation of non-ideal theory. Both defend the priority of ideal theory over non-ideal theory. The essay then considers three different conceptions of the social barriers standing in the way of an ideal society, taken broadly from Mill, Marx, and Foucault. Each conception of power suggests a divergent strategy for pursuing non-ideal (...) class='Hi'>theory. The Foucauldian conception also suggests reasons to mistrust our own political and moral judgments. The essay advocates a more limited view of the relationship between ideal and non-ideal theory than is commonly described, in which ideal theory retains its logical priority but not its temporal priority. In other words, the essay argues that we will fare best when we focus first on reducing specific injustices while setting aside further speculation about the character of an ideal society. (shrink)

One of the most problematic aspects of the ‘Harvard School’ of liberal international theory is its failure to fulfil its own methodological ideals. Although Harvard School liberals subscribe to a nomothetic model of explanation, in practice they employ their theories as heuristic resources. Given this practice, we should expect them neither to develop candidate causal generalizations nor to be value-neutral: their explanatory insights are underpinned by value-laden choices about which questions to address and what concepts to employ. A key (...) question for liberal theorists, therefore, is how a theory may be simultaneously explanatory and value-oriented. The difficulties inherent in resolving this problem are manifested in Ikenberry's writing: whilst his work on constitutionalism in international politics partially fulfils the requirements of a more satisfactory liberal explanatory theory, his recent attempts to develop prescriptions for US foreign policy reproduce, in a new form, key failings of Harvard School realism. (shrink)

It is an unfortunate but unavoidable feature of even well-ordered democratic societies that governmental administrative agencies often create legitimate expectations (procedural or substantive) on the part of non-governmental agents (individual citizens, groups, businesses, organizations, institutions, and instrumentalities) but find themselves unable to fulfil those expectations for reasons of justice, the public interest, severe financial constraints, and sometimes harsh political realities. How governmental administrative agencies, operating on behalf of society, handle the creation and frustration of legitimate expectations implicates a whole host (...) of values that we have reason to care about, including under non-ideal conditions-not least justice, fairness, autonomy, the rule of law, responsible uses of power, credible commitments, reliance interests, security of expectations, stability, democracy, parliamentary supremacy, and legitimate authority. -/- This book develops a new theory of legitimate expectations for public administration drawing on normative arguments from political and legal theory. Brown begins by offering a new account of the legitimacy of legitimate expectations. He argues that it is the very responsibility of governmental administrative agencies for creating expectations that ought to ground legitimacy, as opposed to the justice or the legitimate authority of those agencies and expectations. He also clarifies some of the main ways in which agencies can be responsible for creating expectations. Moreover, he argues that governmental administrative agencies should be held liable for losses they directly cause by creating and then frustrating legitimate expectations on the part of non-governmental agents and, if liable, have an obligation to make adequate compensation payments in respect of those losses. (shrink)

The central ideas coming out of the so-called pragmatic turn in philosophy have set in motion what may be described as a pragmatic turn in normative political theory. It has become commonplace among political theorists to draw on theories of language and meaning in theorising democracy, pluralism, justice, etc. The aim of this paper is to explore attempts by political theorists to use theories of language and meaning for such normative purposes. Focusing on Wittgenstein's account, it is argued that (...) these attempts are unsuccessful. It is shown that pragmatically influenced political theorists draw faulty epistemological, ontological and semantic conclusions from Wittgenstein's view in their normative theorising, and it is argued that pragmatically influenced theories of language and meaning, however full of insight, cannot be put to substantial normative use in political theory. The general scope of the thesis is motivated by pointing to the general form of the argument and by moving beyond Wittgenstein to other philosophers of mind and language, illustrating how similar overextensions are made with regard to Robert Brandom's theory of language and meaning. (shrink)

According to the axiologist the value concepts are basic and the deontic concepts are derivative. This paper addresses two fundamental problems that arise for the axiologist. Firstly, what ought the axiologist o understand by the value of an act? Second, what are the prospects in principle for an axiological representation of moral theories. Can the deontic concepts of any coherent moral theory be represented by an agent-netural axiology: (1) whatever structure those concepts have and (2) whatever the causal structure (...) of the world happens to be. We show that the answer is "almost always". The only substantive constraint is that autonomous moral agents cannot have the power to simultaneously block the options open to other autonomous moral agents. But this seems to be part and parcel of the notion of an autonomous moral agent. (shrink)

A common objection to the precautionary principle is that it is irrational. I argue that this objection goes beyond the often-discussed claim that the principle is incoherent. Instead, I argue, exp...

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture space (...) is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result. (shrink)

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture space (...) is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result. (shrink)

This monographic chapter explains how expected utility (EU) theory arose in von Neumann and Morgenstern, how it was called into question by Allais and others, and how it gave way to non-EU theories, at least among the specialized quarters of decion theory. I organize the narrative around the idea that the successive theoretical moves amounted to resolving Duhem-Quine underdetermination problems, so they can be assessed in terms of the philosophical recommendations made to overcome these problems. I actually follow (...) Duhem's recommendation, which was essentially to rely on the passing of time to make many experiments and arguments available, and evebntually strike a balance between competing theories on the basis of this improved knowledge. Although Duhem's solution seems disappointingly vague, relying as it does on "bon sens" to bring an end to the temporal process, I do not think there is any better one in the philosophical literature, and I apply it here for what it is worth. In this perspective, EU theorists were justified in resisting the first attempts at refuting their theory, including Allais's in the 50s, but they would have lacked "bon sens" in not acknowledging their defeat in the 80s, after the long process of pros and cons had sufficiently matured. This primary Duhemian theme is actually combined with a secondary theme - normativity. I suggest that EU theory was normative at its very beginning and has remained so all along, and I express dissatisfaction with the orthodox view that it could be treated as a straightforward descriptive theory for purposes of prediction and scientific test. This view is usually accompanied with a faulty historical reconstruction, according to which EU theorists initially formulated the VNM axioms descriptively and retreated to a normative construal once they fell threatened by empirical refutation. From my historical study, things did not evolve in this way, and the theory was both proposed and rebutted on the basis of normative arguments already in the 1950s. The ensuing, major problem was to make choice experiments compatible with this inherently normative feature of theory. Compability was obtained in some experiments, but implicitly and somewhat confusingly, for instance by excluding overtly incoherent subjects or by creating strong incentives for the subjects to reflect on the questions and provide answers they would be able to defend. I also claim that Allais had an intuition of how to combine testability and normativity, unlike most later experimenters, and that it would have been more fruitful to work from his intuition than to make choice experiments of the naively empirical style that flourished after him. In sum, it can be said that the underdetermination process accompanying EUT was resolved in a Duhemian way, but this was not without major inefficiencies. To embody explicit rationality considerations into experimental schemes right from the beginning would have limited the scope of empirical research, avoided wasting resources to get only minor findings, and speeded up the Duhemian process of groping towards a choice among competing theories. (shrink)

We discuss recent work on bounded rationality and learning in relation to Soros' principle of reflexivity and stress the empirical importance of non-rational, almost self-fulfilling equilibria in positive feedback systems. As an empirical example, we discuss a behavioral asset pricing model with heterogeneous expectations. Bubble and crash dynamics is triggered by shocks to fundamentals and amplified by agents switching endogenously between a mean-reverting fundamental rule and a trend-following rule, based upon their relative performance. We also discuss learning-to-forecast laboratory experiments, showing (...) that in positive feedback systems individuals coordinate expectations on non-rational, almost self-fulfilling equilibria with persistent price fluctuations very different from rational equilibria. Economic policy analysis may benefit enormously by focusing on efficiency and welfare gains in correcting mispricing along almost self-fulfilling equilibria. (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)

This paper presents a personal view of the interaction between the analysis of choice under uncertainty and the analysis of production under uncertainty. Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under uncertainty. This interest led to the development of generalized models including rank-dependent expected utility theory. In turn, the development of generalized expected utility models raised the question of (...) whether such models could be used in the analysis of applied problems such as those involving production under uncertainty. Finally, the revival of the state-contingent approach led to the recognition of a fundamental duality between choice problems and production problems. (shrink)