Al-Najjar and Weinstein argue that the extant literature on ambiguity aversion is not successful in accounting for Ellsberg choices as rational responses to ambiguity. We concur, and propose that rational choice under ambiguity aims at robustness rather than avoidance of ambiguity. A central argument explains why robust choice is intrinsically context-dependent and legitimately violates standard choice consistency conditions. If choice consistency is forced, however, ambiguity-aversion emerges as a semi-rational response to ambiguity.

John Rawls famously argued that the Difference Principle would be chosen by any rational agent in the original position. Derek Parfit and Philippe Van Parijs have claimed, contra Rawls, that it is not the Difference Principle which is implied by Rawls’ original position argument, but rather the more refined Lexical Difference Principle. In this paper, we study both principles in the context of social choice under ignorance. First, we present a general format for evaluating original position arguments in this context. (...) We argue that in this format, the Difference Principle can be specified in three conceptually distinct ways. We show that these three specifications give the same choice recommendations, and can be grounded in an original position argument in combination with the well-known maximin rule. Analogously, we argue that one can give at least four plausible specifications of the Lexical Difference Principle, which however turn out to give different recommendations in concrete choice scenarios. We prove that only one of these four specifications can be grounded in an original position argument. Moreover, this one specification seems the least appealing from the viewpoint of distributive justice. This insight points towards a general weakness of original position arguments. (shrink)

Contemporary decision theory places crucial emphasis on a family of mathematical results called representation theorems, which relate criteria for evaluating the available options to axioms pertaining to the decision-maker’s preferences. Various claims have been made concerning the reasons for the importance of these results. The goal of this article is to assess their semantic role: representation theorems are purported to provide definitions of the decision-theoretic concepts involved in the evaluation criteria. In particular, this claim shall be examined from the perspective (...) of philosophical theories of the meaning of theoretical terms. (shrink)

In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287–316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and Weak Separability. (...) In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule. (shrink)

Savage denied that Bayesian decision theory applies in large worlds. This paper proposes a minimal extension of Bayesian decision theory to a large-world context that evaluates an event E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} by assigning it a number π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} that reduces to an orthodox probability for a class of measurable events. The Hurwicz criterion evaluates π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} (...) as a weighted arithmetic mean of its upper and lower probabilities, which we derive from the measurable supersets and subsets of E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document}. The ambiguity aversion reported in experiments on the Ellsberg paradox is then explained by assigning a larger weight to the lower probability of winning than to the upper probability. However, arguments are given here that would make anything but equal weights irrational when using the Hurwicz criterion. The paper continues by embedding the Hurwicz criterion in an extension of expected utility theory that we call expectant utility. (shrink)

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms or (...) conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity. To give the strategy more structure, philosophers have developed “principles of individuation”; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion. We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory. (shrink)

In situations where we ignore everything but the space of possibilities, we ought to suspend judgment—that is, remain agnostic—about which of these possibilities is the case. This means that we cannot sum our degrees of belief in different possibilities, something that has been formalized as an axiom of non-additivity. Consistent with this way of representing our ignorance, I defend a doxastic norm that recommends that we should nevertheless follow a certain additivity of possibilities: even if we cannot sum degrees of (...) belief in different possibilities, we should be more confident in larger groups of possibilities. It is thus shown that, in the type of situation considered (in so-called ‘classical ignorance’, i.e. “behind a thin veil of ignorance”), it is epistemically rational for advocates of suspending judgment to endorse this comparative confidence; while on the other hand it is shown that, even in classical ignorance, no stronger belief—such as a precise uniform probability distribution—is warranted. (shrink)

Suppose that you prefer A to B, B to C, and C to A. Your preferences violate Expected Utility Theory by being cyclic. Money-pump arguments offer a way to show that such violations are irrational. Suppose that you start with A. Then you should be willing to trade A for C and then C for B. But then, once you have B, you are offered a trade back to A for a small cost. Since you prefer A to B, you (...) pay the small sum to trade from B to A. But now you have been turned into a money pump. You are back to the alternative you started with but with less money. This Element shows how each of the axioms of Expected Utility Theory can be defended by money-pump arguments of this kind. The Element also defends money-pump arguments from the standard objections to this kind of approach. This title is also available as Open Access on Cambridge Core. (shrink)

Since the middle of this century, the dominant prescriptive approach to decision theory has been a deductive viewpoint which is concerned with axioms of rational preference and their consequences. After summarizing important problems with the preference primitive, this paper argues for a constructive approach in which information is the foundation for decision-making. This approach poses comparability of uncertain acts as a question rather than an assumption. It is argued that, in general, neither preference nor subjective probability can be assumed given, (...) and that these need to be generated by using the relevant information available to the decision-agent in a given situation. A specific constructive model is discussed and illustrated with a real example from this viewpoint. (shrink)

It is natural for humans to judge the outcome of a decision under uncertainty as a percentage of an ex-post optimal performance. We propose a robust decision-making framework based on a relative performance index. It is shown that if the decision maker’s preferences satisfy quasisupermodularity, single-crossing, and a nondecreasing log-differences property, the worst-case relative performance index can be represented as the lower envelope of two extremal performance ratios. The latter is used to characterize the agent’s optimal robust decision, which has (...) implications both computationally and for obtaining closed-form solutions. We illustrate our results in an application which compares the performance of relative robustness to solutions that optimize worst-case payoffs, maximum absolute regret, and expected payoffs under a Laplacian prior. (shrink)

This paper discusses Jean-Yves Jaffray’s ideas on ambiguity and the views underlying his ideas. His models, developed 20 years ago, provide the most tractable separation of risk attitudes, ambiguity attitudes, and ambiguity beliefs available in the literature today.

The current paper is the first to report an experimental study of “Min- and Max-induced rankings” (MMIR), i.e., a family of set rankings that require preferences over sets to be induced from comparison of the best and/or worst elements within those sets. These MMIR do not perform well in predicting preferences over simple sets of monetary outcomes. In this paper, we investigate the axiomatic underpinnings of these models by means of pairwise choice experiments. From this investigation, some important conclusions can (...) be drawn: Axioms that prevent rankings to be based on total-goodness, as well as monotonicity conditions (ensuring that replacing a set element with a better one results in a better set) cannot be refuted. Axioms that rule out any utilization of the relative difference in the values of the outcomes and axioms that prevent rankings to be based on average-goodness are all systematically violated. The Uniform Expected Utility (UEU) criterion seems to meet the apparent shortcomings of the MMIR. Some frequently occurring preference patterns, however, suggest that a significant portion of the participants uses neither a Min- or Max-induced ranking, nor UEU, but some other unspecified decision rule, possibly characterized by the tendency to prefer a diversification of uncertainty. (shrink)

Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of (...) insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon. (shrink)

This article provides unified axiomatic foundations for the most common optimality criteria in statistical decision theory. It considers a decision maker who faces a number of possible models of the world (possibly corresponding to true parameter values). Every model generates objective probabilities, and von Neumann–Morgenstern expected utility applies where these obtain, but no probabilities of models are given. This is the classic problem captured by Wald’s (Statistical decision functions, 1950) device of risk functions. In an Anscombe–Aumann environment, I characterize Bayesianism (...) (as a backdrop), the statistical minimax principle, the Hurwicz criterion, minimax regret, and the “Pareto” preference ordering that rationalizes admissibility. Two interesting findings are that c-independence is not crucial in characterizing the minimax principle and that the axiom which picks minimax regret over maximin utility is von Neumann–Morgenstern independence. (shrink)

The examples and concepts that Shoemaker cites are rather heterogeneous. Some distinctions need to be drawn. An optimality thesis involves not just an ordering of options, but a value judgment about them. So let us begin by distinguishing minimality from optimality. And the concept of minimality can play a variety of roles, among which I distinguish between extremum descriptions, statements hypothesizing an optimizing process, and methodological recommendations. Finally, I consider how the three categories relate to Shoemaker’s question that “Who is (...) optimizing: the scientist or nature?” . (shrink)

This paper examines the strengths and weaknesses of one of science's most pervasive and flexible metaprinciples;optimalityis used to explain utility maximization in economics, least effort principles in physics, entropy in chemistry, and survival of the fittest in biology. Fermat's principle of least time involves both teleological and causal considerations, two distinct modes of explanation resting on poorly understood psychological primitives. The rationality heuristic in economics provides an example from social science of the potential biases arising from the extreme flexibility of (...) optimality considerations, including selective search for confirming vidence, ex post rationalization, and the confusion of prediction with explanation. Commentators are asked to reflect on the extent to which optimality is an organizing principle of nature, a set of relatively unconnected techniques of science, a normative principle for rational choice and social organization, a metaphysical way of looking at the world, or something else still. (shrink)

One central objection to the maximin payoff criterion is that it focuses on the state that yields the lowest payoffs regardless of how low these are. We allow different states to have different sets of possible outcomes and show that the original axioms of Milnor (1954) continue to characterize the maximin payoff criterion, provided that the sets of payoffs achievable across states overlap. If instead payoffs in some states are always lower than in all others then ignoring the “bad” states (...) is no longer inconsistent with these axioms. Similar dependence on overlap of outcome spaces across states holds for the minimax regret and maximin joy criteria. (shrink)

The context-free weak ordering principle is viewed by many as a cornerstone of rational choice theory. McClennen, for example, claims that this principle is one of a pair on which '[t]he theory of rational choice and preference, as it has been developed in the past few decades by economists and decision theorists, rests', and Sen characterizes a version of context freedom as ‘a very basic requirement of rational choice’. But this principle is certainly not uncontroversial: there are examples of principle (...) is certainly not apper irrational. (shrink)

This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called `Simultaneous (...) Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons. (shrink)

A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.

A transformative decision rule transforms a given decision probleminto another by altering the structure of the initial problem,either by changing the framing or by modifying the probability orvalue assignments. Examples of decision rules belonging to thisclass are the principle of insufficient reason, Isaac Levi'scondition of E-admissibility, the de minimis rule, andthe precautionary principle. In this paper some foundationalissues concerning transformative decision rules are investigated,and a couple of formal properties of this class of rules areproved.