The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and (...) P3 is equivalent to a dominance condition; that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (shrink)

Orthodox causal decision theory is unstable. Its advice changes as you make up your mind about what you will do. Several have objected to this kind of instability and explored stable alternatives. Here, I'll show that explorers in search of stability must part with a vestige of their homeland. There is no plausible stable decision theory which satisfies Savage's Sure Thing Principle. So those in search of stability must learn to live without it.

This paper offers a fine analysis of different versions of the well known sure-thing principle. We show that Savage's formal formulation of the principle, i.e., his second postulate (P2), is strictly stronger than what is intended originally.

This paper examines the relationship between Savage's sure thing principle and the value of information. We present two classes of results. First, we show that, under a consequentialist axiom, the sure-thing principle is neither sufficient nor necessary for perfect information to be always desirable: specifically, under consequentialism, the sure thing principle is not implied by the condition that perfect information is always valuable; moreover, the joint imposition of the sure (...) class='Hi'>thing principle, consequentialism and either one of two state independence axioms does not imply that perfect information is always desirable. Second, we demonstrate that, under consequentialism, the sure thing principle is necessary for a nonnegative value of possibly imperfect information (though of course the principle is still not sufficient). One implication of these results is that the sure thing principle, under consequentialism, plays a somewhat different role in ensuring dynamic consistency in decision making under uncertainty than does the independence axiom in decision making under risk. (shrink)

The Sure Thing Principle (1), Dominance Principle (2), and Strong Independence Axiom (3) have been attacked and defended in various ways over the past 30 years. In the course of a survey of some of that literature, it is argued that these principles are acceptable iff suitably qualified.

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

In evolutionary biology changes in population structure are explained by citing trait fitness distribution. I distinguish three interpretations of fitness explanations—the Two‐Factor Model, the Single‐Factor Model, and the Statistical Interpretation—and argue for the last of these. These interpretations differ in their degrees of causal commitment. The first two hold that trait fitness distribution causes population change. Trait fitness explanations, according to these interpretations, are causal explanations. The last maintains that trait fitness distribution correlates with population change but does not cause (...) it. My defense of the Statistical Interpretation relies on a distinctive feature of causation. Causes conform to the Sure Thing Principle. Trait fitness distributions, I argue, do not. *Received July 2009; revised October 2009. †To contact the author, please write to: Department of Philosophy/Institute for the History, Philosophy of Science and Technology, University of Toronto, Victoria College, 91 Charles Street West, Toronto, ON M5S 1K7, Canada; e‐mail: [email protected]. (shrink)

The main result of this paper is a formal argument for the principle of maximizing expected utility that does not rely on the law of large numbers. Unlike the well-known arguments by Savage and von Neumann & Morgenstern, this argument does not presuppose the sure-thing principle or the independence axiom. The principal idea is to use the concept of transformative decision rules for decomposing the principle of maximizing expected utility into a sequence of normatively reasonable (...) subrules. It is shown that this procedure provides a resolution of Allais's paradox that cannot be obtained by Savage-style or von Neumann & Morgenstern-style arguments. (shrink)

We postulate the Testing Principle : that individuals ''act like statisticians'' when they face uncertainty in a decision problem, ranking alternatives to the extent that available evidence allows. The Testing Principle implies that completeness of preferences, rather than the sure-thing principle , is violated in the Ellsberg Paradox. In the experiment, subjects chose between risky and uncertain acts in modified Ellsberg-type urn problems, with sample information about the uncertain urn. Our results show, consistent with the (...) Testing Principle, that the uncertain urn is chosen more often when the sample size is larger, holding constant a measure of ambiguity (proportion of balls of unknown colour in the urn). The Testing Principle rationalises the Ellsberg Paradox. Behaviour consistent with the principle leads to a reduction in Ellsberg-type violations as the statistical quality of sample information is improved, holding ambiguity constant. The Testing Principle also provides a normative rationale for the Ellsberg paradox that is consistent with procedural rationality. (shrink)

I can be wrong about things I seem to perceive; the conditions might lead me to be mistaken about them. Since I can't rule out the possibility that the conditions are misleading, I can't be sure that I am perceiving this thing in my hand correctly. But suppose that I am able to examine it actively—handling it, looking closer, shining a light on it, and so on. Then, my level of uncertainty goes down; in the limit it is (...) eliminated entirely. Of course, I might be mistaken because I am a brain in a vat, or because some other sceptical scenario obtains. But sceptical scenarios apply not just to this thing in my hand, but to everything all at once. Define "empirical certainty" as the absence of the kind of doubt that spreads to all empirical states of affairs. Sensory exploration, or active examination, can in principle lead to empirical certainty. (shrink)

This chapter concerns with rational preferences in the face of uncertainty. The goodness of uncertain prospects is best understood in terms of rational preferences. The chapter discusses some necessary spadework. Its particular purpose is to defend some parts of expected utility theory as an account of rational preferences. It explains the general idea of expected utility theory, and particularly how it is founded on axioms. The principal axiom is also explained. It is often called the 'sure‐thing principle', (...) and it amounts to an assumption of strong separability. The chapter further aims to develop an argument about individuation in the context of a simpler axiom, namely transitivity. It extends the argument to the sure‐thing principle and then discusses a threat to another of the axioms of expected utility theory, which is raised by author's defence of the sure‐thing principle. (shrink)

This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or sure-thing principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of the standard ex post approach. An ex post approach utilizes the decision maker's preferences among risky acts for generating a utility and a probability function, whereas in the ex ante approach a set of preferences among potential outcomes are (...) on the input side of the theory and the decision maker's preferences among risky acts on the output side. (shrink)

“[T]he Precautionary Principle still has neither a commonly accepted definition nor a set of criteria to guide its implementation. “There is”, Freestone … cogently observes, “a certain paradox in the widespread and rapid adoption of the Precautionary Principle”: While it is applauded as a “good thing”, no one is quite sure about what it really means or how it might be..

I have been supposing that for the theory of reasoning, explicit belief is an all-or-nothing matter, I have assumed that, as far as principles of reasoning are concerned, one either believes something explicitly or one does not; in other words an appropriate "representation" is either in one's "memory" or not. The principles of reasoning are principles for modifying such all-or-nothing representations. This is not to deny that in some ways belief is a matter of degree. For one thing implicit (...) belief is certainly a matter of degree, since it is a matter of how easily and automatically one can infer something from what one believes explicitly. Furthermore, explicit belief is a matter of degree in the sense that one believes some things more strongly than others. Sometimes one is only somewhat inclined to believe something, sometimes one is not sure what to believe, sometimes one is inclined to disbelieve something, sometimes one is quite confident something is not so, and so forth. (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)

The disjunction effect (Tversky & Shafir, 1992) occurs when decision makers prefer option x (versus y) when knowing that event A occurs and also when knowing that event A does not occur, but they refuse x (or prefer y) when not knowing whether or not A occurs. This form of incoherence violates Savage's (1954) sure-thing principle, one of the basic axioms of the rational theory of decision making. The phenomenon was attributed to a lack of clear reasons (...) for accepting an option (x) when subjects are under uncertainty. Through a pragmatic analysis of the task and a consequent reformulation of it, we show that the effect does not depend on the presence of uncertainty, but on the introduction of non-relevant goals into the text problem, in both the well-known Gamble problem and the Hawaii problem. (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)

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing (...) principle, known as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

Behaviour norms are considered for decision trees which allow both objective probabilities and uncertain states of the world with unknown probabilities. Terminal nodes have consequences in a given domain. Behaviour is required to be consistent in subtrees. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree. It implies that behaviour reveals a revealed preference ordering satisfying both the independence axiom and a novel form of sure-thing principle. Continuous consequentialist behaviour (...) must be expected utility maximizing. Other plausible assumptions then imply additive utilities, subjective probabilities, and Bayes' rule. (shrink)

Hierarchical Bayesian models provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘paradigms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher-level theory change may be driven by the impact of evidence on lower levels. HBMs capture features described in the Kuhnian tradition, particularly the idea that higher-level (...) theories guide learning at lower levels. In addition, they help resolve certain issues for Bayesians, such as scientific preference for simplicity and the problem of new theories. (shrink)

We critically examine Denis Walsh’s latest attack on the causalist view of fitness. Relying on Judea Pearl’s Sure-Thing Principle and geneticist John Gillespie’s model for fitness, Walsh has argued that the causal interpretation of fitness results in a reductio. We show that his conclusion only follows from misuse of the models, that is, (1) the disregard of the real biological bearing of the population-size parameter in Gillespie’s model and (2) the confusion of the distinction between ordinary probability (...) and Pearl’s causal probability. Properly understood, the models used by Walsh do not threaten the causalist view of fitness. (shrink)

Sometimes a proposition is ‘opaque’ to an agent: he doesn't know it, but he does know something about how coming to know it should affect his or her credence function. It is tempting to assume that a rational agent's credence function coheres in a certain way with his or her knowledge of these opaque propositions, and I call this the ‘Opaque Proposition Principle’. The principle is compelling but demonstrably false. I explain this incongruity by showing that the (...) class='Hi'>principle is ambiguous: the term ‘know’ as it appears in the principle can be interpreted in two different ways, as either basic-know or super-know. I use this distinction to construct a plausible version of the principle, and then to similarly construct plausible versions of the Reflection Principle and the Sure-Thing Principle. (shrink)

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

We provide a critical assessment of the ambiguity aversion literature, which we characterize in terms of the view that Ellsberg choices are rational responses to ambiguity, to be explained by relaxing Savage's Sure-Thing principle and adding an ambiguity-aversion postulate. First, admitting Ellsberg choices as rational leads to behaviour, such as sensitivity to irrelevant sunk cost, or aversion to information, which most economists would consider absurd or irrational. Second, we argue that the mathematical objects referred to as “beliefs” (...) in the ambiguity aversion literature have little to do with how an economist or game theorist understands and uses the concept. This is because of the lack of a useful notion of updating. Third, the anomaly of the Ellsberg choices can be explained simply and without tampering with the foundations of choice theory. These choices can arise when decision makers form heuristics that serve them well in real-life situations where odds are manipulable, and misapply them to experimental settings. (shrink)

I re-examine Coherence Arguments (Dutch Book Arguments, No Arbitrage Arguments) for diachronic constraints on Bayesian reasoning. I suggest to replace the usual game–theoretic coherence condition with a new decision–theoretic condition ('Diachronic Sure Thing Principle'). The new condition meets a large part of the standard objections against the Coherence Argument and frees it, in particular, from a commitment to additive utilities. It also facilitates the proof of the Converse Dutch Book Theorem. I first apply the improved Coherence Argument (...) to van Fraassen's (1984) Reflection principle. I then point out the failure of a Coherence Argument that is intended to support Conditionalization as a naive, universal, update rule. I also point out that Reflection is incompatible with the universal use of Conditionalization thus interpreted. The Coherence Argument therefore defeats the naive view on Bayesian learning that it was originally designed to justify. (shrink)

This article examines Simpson's paradox as applied to the theory of probabilites and percentages. The author discusses possible flaws in the paradox and compares it to the Sure Thing Principle, statistical inference, causal inference and probabilistic analyses of causation.

The paradigm for modelling decision-making under uncertainty has undoubtedly been the theory of Expected Utility, which was first developed by von Neumann and Morgenstern (1944) and later extended by Savage (1954) to the case of subjective uncertainty. The inadequacy of the theory of Subjective Expected Utility (SEU) as a descriptive theory was soon pointed out in experiments, most famously by Allais (1953) and Ellsberg (1961). The observed departures from SEU noticed by Allais and Ellsberg became known as “paradoxes”. The Ellsberg (...) paradox gave rise, several years later, to a new literature on decision-making under ambiguity. The theoretical side of this literature was pioneered by Schmeidler (1989). This literature views the departures from SEU in situations similar to those discussed by Ellsberg as rational responses to ambiguity. The rationality is “recovered” by relaxing Savage's Sure-Thing principle and adding an ambiguity-aversion postulate. Thus the ambiguity-aversion literature takes a normative point of view and does consider Ellsberg-type choices as behavioural “anomalies”. (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)

Simpson's Paradox is introduced and analysed via the mishaps of a researcher who at first falls afoul of the traps Simpson-reversals can set, and then he learns to exploit those traps to advantage. (Note: An error in the treatment of the Sure Thing Principle is corrected in "Simpson's Paradox: A Logically Benign, Empirically Treacherous Hydra").

The disjunction effect (Tversky and Shafir in Psychol Sci 3:305–309, 1992) occurs when decision makers prefer option x (versus y) when knowing that event A occurs and also when knowing that event A does not occur, but they refuse x (or prefer y) when not knowing whether or not A occurs. This form of incoherence violates Savage’s (Cognition 57:31–95, 1954) sure-thing principle, one of the basic axioms of the rational theory of decision-making. The phenomenon was attributed to (...) a lack of clear reasons for accepting an option (x) when the subjects are under uncertainty. Through a pragmatic analysis of the task and a consequent reformulation of it, we show that the effect does not depend on the presence of uncertainty, but on the introduction into the text-problem of a non-relevant goal. (shrink)

This paper studies decisions under ambiguity when attention is paid to extreme outcomes. In a purely subjective framework, we propose an axiomatic characterization of affine capacities, which are Choquet capacities consisting in an affine transformation of a subjective probability. Our main axiom restricts the well-known Savage’s Sure-Thing Principle to a change in a common intermediate outcome. The representation result is then an affine combination of the expected utility of the valued act and its maximal and minimal utilities.

We report the results of an experimental test of whether preaching the normative appeal of the sure-thing principle leads decision-makers to make choices that satisfy it. We use Allais-type decision problems to observe the incentive-compatible choices of 147 subjects, which either violate the sure-thing principle or adhere to it. Subjects are presented with normative arguments that support the counterfactual behaviour and then repeat their decisions. We observe violations of the sure-thing principle (...) are robust to its normative justification. This result replicates a famous small-sample observation using hypothetical tasks that was published by Paul Slovic and Amos Tversky almost half a century ago. We argue that this finding is as relevant now as it was then and that their design can be usefully applied to address contemporary issues in behavioural economics. (shrink)

The notion of comparative probability defined in Bayesian subjectivist theory stems from an intuitive idea that, for a given pair of events, one event may be considered “more probable” than the other. Yet it is conceivable that there are cases where it is indeterminate as to which event is more probable, due to, e.g., lack of robust statistical information. We take that these cases involve indeterminate comparative probabilities. This paper provides a Savage-style decision-theoretic foundation for indeterminate comparative probabilities.

Simon Blackburn has claimed that on a theory of revealed preference it is tautological that any eligible player - one whose preferences are consistent - plays hawk, chooses a strategy of non-cooperation with the other prisoner. This claim is examined and rejected. A prisoner in the appropriate sense is defined not by preferences over actions (playing hawk or playing dove) but by preferences over the four possible outcomes which result from the players' actions jointly (both playing hawk, both playing dove, (...) the first playing hawk and the second dove, and vice versa). It is not inconsistent to suppose that a prisoner has the appropriate preferences over outcomes but nevertheless chooses to play dove. This can happen either if the prisoner believes for some reason that the full range of outcomes is not available, or if the prisoner is simply a bad strategic thinker. It is perhaps tautological that a player with the appropriate preferences over outcome and with suitable beliefs will if rational choose to play hawk. However, rationality would then involve an appeal to a further principle, the sure-thing principle: if a prisoner would choose hawk knowing that the other will choose hawk, and would also choose hawk knowing that the other will choose dove, then hawk should be chosen when it is uncertain what the other will choose. (shrink)

In a recent article, Machina (Am Econ Rev forthcoming, 2008) suggested choice problems in the spirit of Ellsberg (Q J Econ 75:643–669, 1961), which challenge tail-separability, an implication of Choquet expected utility (CEU), to a similar extent as the Ellsberg paradox challenged the sure-thing principle implied by subjective expected utility (SEU). We have tested choice behavior for bets on one of Machina’s choice problems, the reflection example. Our results indicate that tail-separability is violated by a large majority (...) of subjects (over 70% of the sample). These empirical findings complement the theoretical analysis of Machina (Am Econ Rev forthcoming, 2008) and, together, they confirm the need for new approaches in the analysis of ambiguity for decision making. (shrink)

This paper uses a two-dimensional version of a standard common consequence experiment to test the intransitivity explanation of Allais-paradox-type violations of expected utility theory. We compare the common consequence effect of two choice problems differing only with respect to whether alternatives are statistically correlated or independent. We framed the experiment so that intransitive preferences could explain violating behavior when alternatives are independent, but not when they are correlated. We found the same pattern of violation in the two cases. This is (...) evidence against intransitivity as an explanation of the Allais Paradox. The question whether violations of expected utility are mainly due to intransitivity or to violation of independence is important since it is exactly on this issue the main new decision theories differ. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must (...) be better than C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

In science it is obvious that we are certain about many things, but among philosophers there is little agreement as to why we know these things. In Knowing Things for Sure physicist and realist philosopher, Mariano Artigas traces the confusion to non-realist philosophies and argues that practitioners of experimental science do reach logical truths about reality.

An argument is advanced to show why E-admissibility should be preferred over maximality as a principle of rational choice where rationality is understood as minimal rationality. Consideration is given to the distinction between second best and second worst options in three way choice that is ignored according to maximality. It is shown why the behavior exhibited in addressing the problems posed by Allais (Econometrica 21:503–546, 1952) and by Ellsberg (Q Econ 75:643–669, 1961) do not violate the independence postulate according (...) to minimal rationality. (shrink)

In science it is obvious that we are certain about many things, but among philosophers there is little agreement as to why we know these things. In Knowing Things for Sure physicist and realist philosopher, Mariano Artigas traces the confusion to non-realist philosophies and argues that practitioners of experimental science do reach logical truths about reality.

An Inquiry into the first principles of morals and justice: This book restores to us an understanding that was once settled in the 'moral sciences': that there are propositions, in morals and law, which are not only true but which cannot be ...

Advancement of modern agricultural biotechnology has brought various potential benefits to humankind, but at the same time ethical concerns regarding some applications such as genetically modified foods have been raised among the public. Several questions are being posed; should they utilize such applications to improve quality of their life, or should they refrain in order to save themselves from any associated risk? What are the ethical principles that can be applied to assess these applications? By using GMF as a case (...) study, this paper discusses possible answers to these questions from Islamic perspective. Such answers are based on the understanding of the Islamic concept of maslahah and mafsadah as well as the Islamic principles of priority. There is no specific GMF that has been declared as unlawful by Muslim scholars thus far. Nevertheless, they generally state that any GMF that contains unlawful substance is prohibited in Islam. Such statement can be understood since Islam puts highest priority to preserve shari’ah which prescribes the lawful and unlawful things in human life. Priorities have also been given to preserve human health and environment therefore any GMF that may inflict harm on both entities is also considered as unlawful. (shrink)