Psychological studies have long demonstrated effects of expectations on judgment, whereby the provision of information, either implicitly or explicitly, prior to an experience or decision can exert a substantial influence on the observed behavior. This study extended these expectation effects to the domain of interactive economic decision-making. Prior to playing a commonly-used bargaining task, the Ultimatum Game, participants were primed to expect offers that would be either relatively fair or unfair. A third group played the Game without receiving any prior (...) information about expected offers. As predicted, these expectations had a large effect on decisions made by participants in the Ultimatum Game, with those with expectations of fairness rejecting significantly more unfair offers than those participants who expected low offers. Implications for models of fairness and equity are discussed. (shrink)

We propose a model of an agent’s probability and utility that is a compromise between Savage (The foundations of statistics, Wiley, 1954) and Jeffrey (The Logic of Decision, McGraw Hill, 1965). In Savage’s model the probability–utility pair is associated with preferences over acts which are assignments of consequences to states. The probability is defined on the state space, and the utility function on consequences. Jeffrey’s model has no consequences, and both probability and utility are defined on the same set of (...) propositions. The probability–utility pair is associated with a desirability relation on propositions. Like Savage we assume a set of consequences and a state space. However, we assume that states are comprehensive, that is, each state describes a consequence, as in Aumann (Econometrica 55:1–18, 1987). Like Jeffrey, we assume that the agent has a preference relation, which we call desirability, over events, which by definition involves uncertainty about consequences. For a given probability and utility of consequences, the desirability relation is presented by conditional expected utility, given an event. We axiomatically characterize desirability relations that are represented by a probability–utility pair. We characterize the family of all the probability–utility pairs that represent a given desirability relation. (shrink)

In this paper I study intentions of the form, that is, intentions with a we-content, and their role in interpersonal coordination. I focus on the notion of epistemic support for such intentions. Using tools from epistemic game theory and epistemic logic, I cast doubt on whether such support guarantees the other agents' conditional mediation in the achievement of such intentions, something that appears important if intentions with a we-content are to count as genuine intentions. I then formulate a stronger version (...) of epistemic support, one that does indeed ensure the required mediation, but I then argue that it rests on excessively strong informational conditions. In view of this I provide an alternative set of conditions that are jointly sufficient for coordination in games, and I argue that these conditions constitute a plausible alternative to the proposed notion of epistemic support. (shrink)

According to the orthodox view, it is impossible to know how different people's preferences compare in terms of strength and whether they are interpersonally comparable at all. Against the orthodox view, Donald Davidson (1986, 2004) argues that the interpersonal comparability of preferences is a necessary condition for the correct interpretation of other people's behaviour. In this paper I claim that, as originally stated, Davidson's argument does not succeed because it is vulnerable to several objections, including Barry Stroud's (1968) objection against (...) all transcendental arguments of a 'strong' kind. However, I argue that Davidson's strategy can still achieve results of anti-sceptical significance. If we reformulate Davidson's argument as a 'modest' transcendental argument and if we embrace an 'internal' account of epistemic justification, it is in fact possible to have at least justified beliefs about how different people's preferences compare in terms of strength and about their interpersonal comparability. (shrink)

According to a popular strategy amongst economists and philosophers, in order to solve the problem of interpersonal utility comparisons, we have to look at how ordinary people make such comparisons in everyday life. The most recent attempt to develop this strategy has been put forward by Goldman in his “Simulation and Interpersonal Utility” (Ethics 4:709–726, 1995). Goldman claims, first, that ordinary people make interpersonal comparisons by simulation and, second, that simulation is reliable for making interpersonal comparisons. In this paper, I (...) focus on Goldman’s latter claim. After updating Goldman’s account of how ordinary people make interpersonal comparisons in the light of Goldman’s newest formulation of his simulation theory of mental ascription (Goldman, Simulating Minds. Oxford University Press, Oxford, 2006), I develop and assess Goldman’s arguments in favour of the reliability of simulation for interpersonal comparisons. I argue that, under certain conditions, there may be room for a scientifically acceptable solution to the problem of interpersonal utility comparisons. (shrink)

That the rationality of individual people is ‘bounded’ – that is, finite in scope and representational reach, and constrained by the opportunity cost of time – cannot reasonably be controversial as an empirical matter. In this context, the paper addresses the question as to why, if economics is an empirical science, economists introduce bounds on the rationality of agents in their models only grudgingly and partially. The answer defended in the paper is that most economists are interested primarily in markets (...) and only secondarily in the dynamics of individual decisions – specifically, they are interested in these dynamics mainly insofar as they might systematically influence the most useful approaches to modeling interesting markets. In market contexts, bounds on rationality are typically generated by institutional and informational properties specific to the market in question, which arise and are sustained by structural dynamics that do not originate in or reduce to individuals' decisions or psychologic.. (shrink)

The rise of behavioral economics since the 1980s led to richer mutual influence between economic and psychological theory and experimentation. However, as behavioral economics has become increasingly integrated into the main stream in economics, and as psychology has remained damagingly methodologically conservative, this convergence has recently gone into reverse. At the same time, growing appreciation among economists of the limitations of atomistic individualism, along with advantages in econometric modeling flexibility by comparison with psychometrics, is leading economists to become more pluralistic (...) than psychologists about the ontology of behavioral causation and structures. This, combined with economists’ growing interest in network models, is drawing economists closer in theory and practice to sociologists who use quantitative or mixed methods. (shrink)

Abstract:This paper develops a framework for examining decision making about ethical issues and tests the applicability of a social contract perspective. Using two separate samples of students and salespeople, we determine that community members (salespeople) tend to judge a potentially unethical act to constitute a violation of an implicit social contract and non-community members (students) do not. Also, consistent with the emphasis on context specificity of integrative social contracts theory, situational variables influence perceptions of ethicality for the community members, but (...) do not affect the perceptions of individuals outside the community. The study finds considerable support for the use of a social contractarian perspective in the study of decision-making processes about ethical issues. (shrink)

We conduct a standardized survey on risk preferences in 53 countries worldwide and estimate cumulative prospect theory parameters from the data. The parameter estimates show that significant differences on the cross-country level are to some extent robust and related to economic and cultural differences. In particular, a closer look on probability weighting underlines gender differences, economic effects, and cultural impact on probability weighting. The data set is a useful starting point for future research that investigates the impact of risk preferences (...) on the market level. (shrink)

Knowledge-first epistemology includes a knowledge norm of action: roughly, act only on what you know. This norm has been criticized, especially from the perspective of so-called standard decision theory. Mueller and Ross provide example decision problems which seem to show that acting properly cannot require knowledge. I argue that this conclusion depends on applying a particular decision theory which is ill-motivated in this context. Agents’ knowledge is often most plausibly formalized as an ambiguous epistemic state, and the theory of decision (...) under ambiguity is then the appropriate modeling tool. I show how to model agents as acting rationally on the basis of their knowledge according to such a theory. I conclude that the tension between the knowledge norm of action and formal decision theory is illusory; the knowledge-first paradigm should be used to actively select the decision-theoretical tools that can best capture the knowledge-based decisions in any given situation. (shrink)

There are two prominent viewpoints regarding the nature of rationality and how it should be evaluated in situations of interest: the traditional axiomatic approach and the newer ecological rationality. An obstacle to comparing and evaluating these seemingly opposite approaches is that they employ different language and formalisms, ask different questions, and are at different stages of development. I adapt a formal framework known as SCOP to address this problem by providing a comprehensive common framework in which both approaches may be (...) defined and compared. The main result is that the axiomatic and ecological approaches are in far greater agreement on fundamental issues than has been appreciated; this is supported by a pair of theorems to the effect that they will make accordant rationality judgements when forced to evaluate the same situation. I conclude that ecological rationality has some subtle advantages, but that we should move past the issues currently dominating the discussion of rationality. (shrink)

With concerns regarding climate change rising, companies and policy makers seek to understand the precursors to environmentally-friendly consumer choice. Decision modes are the qualitatively different psychological processes employed to arrive at decisions. Across six studies, the present project establishes (a) which decision modes are employed by consumers to decide between electricity plans that differ in environmental impact, and (b) how employed decision modes affect those choices. We demonstrate that consumers are most likely to use Calculation Modes when facing such choices. (...) Importantly, we find that Affect or Role Modes promote more environmentally-friendly choices, while Calculation Modes decrease environmentally-friendly choices. Experimentally promoting use of a Role Mode over a Calculation Mode increases selection of environmentally-friendly alternatives, and the relative degree of employing the Role Mode mediates this effect. Our findings provide insight into how decision mode usage can alter environmental decisions, and suggest mechanisms and tools for marketers and policy makers to influence consumer choice. (shrink)

Homo sociologicus and homo oeconomicus are, for different reasons, unsatisfactory models for the social sciences. A third model, called “rational model in the broad sense”, seems better endowed to cope with the many different expressions of rationality of the social agent. Some contributions by Weber, Durkheim and Marx are early examples of the application of this model of social explanation based on good subjective reasons. According to this model and to the evidence of cognitive anthropology, it is possible to reconcile (...) primitive thinking with the inferential principles of Western people. Lastly, cognitive psychology can contribute to the discovery of generalizations of reason-based choices that can strengthen the explanatory power of “rational model in the broad sense”. (shrink)

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. 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.

Consider a simple game with n players. Let ψi be the Shapley–Shubik power index for player i. Then 1-ψi measures his powerlessness. We break down this powerlessness into two components – a `quixote index' Q i (which measures how much of a `quixote' i is), and a `follower index' F i (which measures how much of a `follower' he is). Formulae, properties, and axiomatizations for Q and F are given. Examples are also supplied.

Topics in Cognitive Science, Volume 14, Issue 3, Page 528-549, July 2022.

Topics in Cognitive Science, Volume 14, Issue 3, Page 451-466, July 2022.

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...) fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. (shrink)

The noema is one of the most daring and controversial concept of the Husserlian theory of intentionality. It was first introduced by Husserl in 1912, within some research manuscripts, but was only fully developed in Ideen. In this paper I claim that the noema is an ambiguous notion, the result of a theoretical operation, the epoché, whose aim is contradictory. In an effort to keep open the epoché, and therefore maintain distance with respect to every transcendent object, Husserl is forced (...) to multiply intentional objects and complicate the notions of sense and noema. Given that, I propose to overcome the paradoxes of noema through the language of game theory. Game theory offers a very fruitful descriptive model that allows us to save the original Husserlian approach without the contradictions of the epoché. For this reason, I propose to re-interpret intentionality as social game, and the noema as Nash equilibrium. By replying to possible objections, I will show that this approach gives us many theoretical advantages. The general aim of the paper is a global reformulation of the phenomenalogical method. (shrink)

We study political influence in institutions where each member chooses a level of support for a collective goal. These individual choices determine the degree to which the goal is reached. Influence is assessed by newly defined binary relations, each of which ranks members on the basis of their relative performance at a corresponding level of participation. For institutions with three options (e.g., voting games in which each voter may vote “yes”, “abstain”, or vote “no”), we obtain three influence relations, and (...) show that their strict components may be cyclic. This latter property describes a “paradox of power” which contrasts with the transitivity of the unique influence relation of binary voting games. Weak conditions of anonymity suffice for each of these relations to be transitive. We also obtain a necessary and sufficient condition for each of these relations to be complete. Further, we characterize institutions in which the rankings induced by these relations, and the Banzhaf–Coleman and Shapley–Shubik power indices coincide. We argue that extending the influence relations to firms would be useful in efficiently assigning workers to different units of production. Finally, we provide applications to various forms of political and economic organizations. (shrink)

In this paper I analyse different justifications for the claim that the minor premise of the libertarian argument is true, namely, intuition, van Inwagen’s argument from moral responsibility and an argument from rationality. I claim none of these is satisfactory. I conclude by suggesting a possible way of interpreting the meaning of the free will intuition libertarians claim we have.

Counterexamples are constructed for the theory of rational choice that results from a direct application of classical decision theory to ordinary actions. These counterexamples turn on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. An alternative theory of rational choice is proposed that evaluates actions using a more complex measure, and then it is shown that this is equivalent to applying classical decision theory to "conditional (...) policies" rather than ordinary actions. (shrink)

A theory of rational choice is a theory of how an agent should, rationally, go about deciding what actions to perform at any given time. For example, I may want to decide whether to go to a movie this evening or stay home and read a book. The actions between which we want to choose are perfectly ordinary actions, and the presumption is that to make such a decision we should attend to the likely consequences of our decision. It is (...) assumed that these decisions must be made in the face of uncertainty regarding both the agent’s initial situation and the consequences of his actions. (shrink)

Affective forecasting refers to the ability to predict future emotions, a skill that is essential to making decisions on a daily basis. Studies of the concept have determined that individuals are often inaccurate in making such affective forecasts. However, the mechanisms of these errors are not yet clear. In order to better understand why affective forecasting errors occur, this article seeks to trace the theoretical roots of this theory with a focus on its multidisciplinary history. The roots of affective forecasting (...) lie mainly in economics, with early claims positing that utility played a role in decision-making. Furthermore, the philosopher Jeremy Bentham’s descriptions of utilitarianism played a major role in our understanding of whether to define utility as a hedonic quality. The birth of behavioural economics resulted in a paradigm shift, introducing the concept of cognitive biases as influences on the accuracy of predicted utility. Daniel Gilbert and Timothy Wilson, the earliest researchers of affective forecasting errors, have proceeded with the concept of the accuracy of predicted affective utility to conduct experiments that seek to determine why our predictions of future affect are inaccurate and how such errors play a role in our decision-making. (shrink)

We don't yet have adequate theories of what the human mind is representing when it represents a social group. Worse still, many people think we do. This mistaken belief is a consequence of the state of play: Until now, researchers have relied on their own intuitions to link up the concept social group on the one hand and the results of particular studies or models on the other. While necessary, this reliance on intuition has been purchased at a considerable cost. (...) When looked at soberly, existing theories of social groups are either literal, but not remotely adequate, or simply metaphorical. Intuition is filling in the gaps of an explicit theory. This paper presents a computational theory of what, literally, a group representation is in the context of conflict: It is the assignment of agents to specific roles within a small number of triadic interaction types. This “mental definition” of a group paves the way for a computational theory of social groups – in that it provides a theory of what exactly the information-processing problem of representing and reasoning about a group is. For psychologists, this paper offers a different way to conceptualize and study groups, and suggests that a non-tautological definition of a social group is possible. For cognitive scientists, this paper provides a computational benchmark against which natural and artificial intelligences can be held. (shrink)

The Second World War was a watershed in history in many ways. I focus on the World War II discontinuity as it relates to the intersection of scientific and military enterprise. I am interested in how we should conceptualize that intersection and in offering a preliminary tracing of the “World War II regime” that has grown out of it—a regime that includes new forms of scientific and military practice but that has invaded and transformed many other cultural spaces, including—my primary (...) example here—the industrial workplace. I exploit the figure of the cyborg to thematize the social, material, and conceptual heterogeneity of the developments at issue; specify a distinct range of cyborg objects and sciences that emerged from the World War II matrix; and exemplify a historiographical approach that escapes the traditional master-narrative structures of science studies. (shrink)

The authors present an approach to conceptualising and predicting environmental conflicts in which conflicts are analysed as a continuum of disagreement over values and options. They also operationalise this approach using an online values-centred survey tool, the ‘public-to-public decision support system’ (P2P-DSS). The authors put values and conflict in environmental management into perspective. Next, they review how values are defined in scholarship and operationalised for decision support. The relevance of values research to con-flict management is presented. With reference to a (...) real-world aggregate-mining conflict, the authors demonstrate how P2P-DSS can be used to collect data and categorise conflicts to enhance environmental management decision-making. The authors argue that P2P-DSS has potential to support values-sensitive thinking for environmental conflict management. They then set out research priorities to investigate the theoretical and practical implications of this approach. This work contributes to advancing values research in environmental conflict management and expanding values-based decision-making. (shrink)

Hume is rightly credited with giving a brilliant, and perhaps the best, account of justice as convention. Hume's importance as a forerunner of modern economics has also long been recognized. However, most of Hume's readers have not fully appreciated how closely Hume's analysis of convention foreshadows a particular branch of economic theory, namely, game theory. Starting with the work of Barry, Runciman and Sen and Lewis, there has been a flowering of literature on the informal game-theoretic insights to be found (...) in classics of political philosophy such as Hobbes, Locke, Hume and Rousseau. A number of authors in this tradition, including Lewis, Gauthier, Mackie, and Postema, have identified passages in Hume which they interpret as giving informal examples of specific games. Yet, unlike his predecessors, Hobbes and Locke, Hume does much more than present examples which have a game-theoretic structure. In his account of convention, Hume gives general conditions which characterize the resolution of social interaction problems, and in the examples he uses to illustrate this account, Hume outlines several different methods by which agents can arrive at such a resolution. Hume's general account of convention and his explanations of the origins of particular conventions together constitute a theory of strategic interaction, which is precisely what game theory aspires to be. (shrink)

There is a very plausible principle of the transitivity of justifying reasons. It says that if "p" is better justified than "q" (all things considered) and "q" better than "r", then "p" is better justified than "r" (all things considered). There is a corresponding principle of rational theory choice. Call one theory "a better theory than" another theory if all criteria of theory choice considered (explanatory power, simplicity, empirical adequacy, etc.), the first theory meets the criteria better than the second (...) theory. The corresponding transitivity principle says that if theory A is a better theory than theory B and if theory B is a better theory than theory C, then A is a better theory than theory C. I argue against this principle. It turns out that whenever there are 2 or more relevant and independent criteria of theory evaluation, and whenever at least of one the criteria is "non-linear" in a certain sense, there may be violations of transitivity which do not violate any standards of rationality (of theory choice). This shows, again, that theory choice cannot be seen as merely the application of given rules of rational theory choice. (shrink)

We call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in their support. A two-person bargaining solution is called invariant under risk aversion for losses if the assigned outcome does not change after correcting for risk aversion for losses with this outcome as pair of reference levels, provided that the disagreement point only changes proportionally. We present an axiomatic characterization of the Nash bargaining (...) solution based on this condition, and we also provide a decision-theoretic characterization of the concept of risk aversion for losses. (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)

To consequentialise a moral theory means to account for moral phenomena usually described in nonconsequentialist terms, such as rights, duties, and virtues, in a consequentialist framework. This paper seeks to show that all moral theories can be consequentialised. The paper distinguishes between different interpretations of the consequentialiser’s thesis, and emphasises the need for a cardinal ranking of acts. The paper also offers a new answer as to why consequentialising moral theories is important: This yields crucial methodological insights about how to (...) pursue ethical inquires. (shrink)

In classical game theory the idea that players randomize between their actions according to a particular optimal probability distribution has always been viewed as puzzling. In this paper, we establish a fundamental connection between n-person normal form games and quantum mechanics, which eliminates the conceptual problems of these random strategies. While the two theories have been regarded as distinct, our main theorem proves that if we do not give any other piece of information to a player in a game, than (...) the payoff matrix—the axiom of “no-supplementary data” holds—then the state of mind of a rational player is algebraically isomorphic to a pure quantum state. The “no supplementary data” axiom is captured in a Lukasiewicz’s three-valued Kripke semantics wherein statements about whether a strategy or a belief of a player is rational are initially indeterminate i.e. neither true, nor false. As a corollary, we show that in a mixed Nash equilibrium, the knowledge structure of a player implies that probabilities must verify the standard “Born rule” postulate of QM. The puzzling “indifference condition” wherein each player must be rationally indifferent between all the pure actions of the support of his equilibrium strategy is resolved by his state of mind being described by a “quantum superposition” prior a player is asked to make a definite choice in a “measurement”. Finally, these results demonstrate that there is an intrinsic limitation to the predictions of game theory, on a par with the “irreducible randomness” of quantum physics. (shrink)

Zeckhauser’s paradox has puzzled and entertained many rationality enthusiasts for almost half a century. You are forced to play a Russian Roulette with a 6-chamber revolver containing either two bullets, or four bullets. Would you pay more to remove the two bullets in than you would to remove one in? Most would say yes, but rational considerations based on the classical utility theory suggest you should not. We discuss a possible solution within the classical framework, by explicitly stating and accounting (...) for more detailed preferences in terms of fewer bullets and smaller debt. To a large extent, the paradox arises due to a surreptitious trespassing of Savage’s Small-World utilities implied by a limited set of preferences to govern a larger world containing potentially conflicting preferences. To avoid logical issues associated with death in the roulette, we also describe a non-fatal game-show version, where you choose one box out of six that could be either empty or contain prize money. Here, the paradox arises when you pay from the prize money, but not when you pay from your own money. In summary, the paradox provides a useful lesson about the normative role of the utility function as a rational guide for our decisions and preferences. (shrink)

This paper analyses the principles of stable cooperation for stochastic games. Starting from the non-cooperative version of a discounted, non zero-sum stochastic game, we build its cooperative form and find the cooperative solution. We then analyse the conditions under which this solution is stable. Principles of stability include subgame consistency, strategic stability and irrational behaviour proof of the cooperative solution. We finally discuss the existence of a stable cooperative solution, and consider a type of stochastic games for which the cooperative (...) solution is found and the principles of stable cooperation are checked. (shrink)

This paper starts out from the proposition that case-based decision theory is an appropriate tool to explain human decision behavior in situations of structural ignorance. Although the developers of CBDT suggest its reality adequacy, CBDT has not yet been tested empirically very often, especially not in repetitive decision situations. Therefore, our main objective is to analyse the decision behavior of subjects in a repeated-choice experiment by comparing the explanation power of CBDT to reinforcement learning and to classical decision criteria under (...) uncertainty namely maximin, maximax, and pessimism-optimism. Our findings substantiate a predominant significantly higher validity of CBDT compared to the classical criteria and to reinforcement learning. For this reason, the experimental results confirm the suggested reality adequacy of CBDT in repetitive decision situations of structural ignorance. (shrink)

The problem of how to make optimal choices in the face of risk arises in both economics/decision theory and also evolutionary biology; in the former, ‘optimal’ means utility maximizing, while in the latter it means fitness maximizing. This article explores the links, thematic and formal, between the economic and evolutionary theories of optimal choice in risky situations, with particular reference to the relationship between utility and fitness. It is argued that the link is strongest between evolution and ‘nonexpected’ utility theory, (...) rather than traditional expected utility theory. (shrink)

:This paper explores the contrast between mentalistic and behaviouristic interpretations of decision theory. The former regards credences and utilities as psychologically real, while the latter regards them as mere representations of an agent's preferences. Philosophers typically adopt the former interpretation, economists the latter. It is argued that the mentalistic interpretation is preferable if our aim is to use decision theory for descriptive purposes, but if our aim is normative then the behaviouristic interpretation cannot be dispensed with.

I discuss the trilemma that consists of the following three principles being inconsistent: 1. The Common Principle: if one distribution, A, necessarily brings a higher total sum of personal value that is distributed in a more egalitarian way than another distribution, B, A is more valuable than B. 2. (Weak) ex-ante Pareto: if one uncertain distribution, A, is more valuable than another uncertain distribution, B, for each patient, A is more valuable than B. 3. Pluralism about attitudes to risk (Pluralism): (...) the personal value of a prospect is a weighted sum of the values of the prospect’s outcomes, but the weight each outcome gets might be different from the probability the prospect assigns to the outcome. (shrink)