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)

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)

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)

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.

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.

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)

Maximize Expected Choiceworthiness (MEC) is a theory of decision-making under moral uncertainty. It says that we ought to handle moral uncertainty in the way that Expected Value Theory (EVT) handles descriptive uncertainty. MEC inherits from EVT the problem of fanaticism. Roughly, a decision theory is fanatical when it requires our decision-making to be dominated by low-probability, high-payoff options. Proponents of MEC have offered two main lines of response. The first is that MEC should simply import whatever are (...) the best solutions to fanaticism on offer in decision theory. The second is to propose statistical normalization as a novel solution on behalf of MEC. This paper argues that the first response is open to serious doubt and that the second response fails. As a result, MEC appears significantly less plausible when compared to competing accounts of decision-making under moral uncertainty, which are not fanatical. (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.

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.

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)

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)

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)

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 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)

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)

The Desire-as-Belief thesis (DAB) states that any rational person desires a proposition exactly to the degree that she believes or expects the proposition to be good. Many people take David Lewis to have shown the thesis to be inconsistent with Bayesian decision theory. However, as we show, Lewis's argument was based on an Invariance condition that itself is inconsistent with the (standard formulation of the) version of Bayesian decision theory that he assumed in his arguments against DAB. The (...) aim of this paper is to explore what impact the rejection of Invariance has on the DAB thesis. Without assuming Invariance, we first refute all versions of DAB that entail that there are only two levels of goodness. We next consider two theses according to which rational desires are intimately connected to expectations of (multi-levelled) goodness, and show that these are consistent with Bayesian decision theory as long as we assume that the contents of 'value propositions' are not fixed. We explain why this conclusion is independently plausible, and show how to construct such propositions. (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)

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)

Within the domain of philosophy, it is not unusual to hear the claim that most questions about the nature of consciousness are essentially and absolutely beyond the scope of science, no matter how science may develop in the twenty-first century. Some things, it is pointed out, we shall never _ever_ understand, and consciousness is one of them (Vendler 1994, Swinburne 1994, McGinn 1989, Nagel 1994, Warner 1994). One line of reasoning assumes that consciousness is the manifestation of a distinctly nonphysical (...) thing, and hence has no physical properties that might be explored by techniques suitable to physical things. Dualism, as this view is known, is still to be found among those within the tradition of Kant and Hegel, as well as among some with religious convictions. Surprisingly, however, strenuous foot-dragging is evident even among philosophers of a materialist conviction. Indeed, one might say that it is the philosophical fashion of the 90's to pronounce consciousness unexplainable, and to find the explanatory aspirations of neurobiology to be faintly comic if not rather pitiful. The very word, "reductionism" has come to be used more or less synonymously with "benighted-scientism-run-amok", where scientistm apparently means "applying scientific techniques to domains where they are inapplicable." McGinn, perhaps the most unblushing of the naysayers, insists that we cannot expect even to make any headway on the problem. (p. 114) Ironically perhaps, here we are at a conference in honor of Dr. Herbert Jasper who was a great pioneer in moving neuroscience forward on this problem, and where results will be presented allegedly _showing_ additional progress on the problem. Because I am quite optimistic about future scientific progress on the nature of consciousness, my aim here, as a philosopher, is to address the most popular and influential of the skeptical arguments, and to explain why I find them unconvincing. Thus the overall form of the paper is negative, in the sense that I want to show why a set of naysaying arguments fail. (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)

This article analyses how normative decision theory is understood by economists. The paradigmatic example of normative decision theory, discussed in the article, is the expected utility theory. It...

This book studies the philosophies of Paul Tillich. Its focus is on justice, covering two dimensions of justice. The first is the social dimension, manifested in human relationships. The second dimension is at the individual level, seen in each person's struggle to feel a secure sense of selfhood.

Pascal’s Wager involves expected utilities. In this chapter, we examine the Wager in light of two main features of expected utility theory: utilities and probabilities. We discuss infinite and finite utilities, and zero, infinitesimal, extremely low, imprecise, and undefined probabilities. These have all come up in recent literature regarding Pascal’s Wager. We consider the problems each creates and suggest prospects for the Wager in light of these problems.

A simple argument suggests that we can fruitfully model advanced AI systems using expected utility theory. According to this argument, an agent will need to act as if maximising expected utility if they’re to avoid exploitation. Insofar as we should expect advanced AI to avoid exploitation, it follows that we should expected advanced AI to act as if maximising expected utility. I spell out this argument more carefully and demonstrate that it fails, but show that the manner of its (...) failure is instructive: in exploring the argument, we gain insight into how to model advanced AI systems. (shrink)