Luce and Narens (Journal of Mathematical Psychology, 29:1–72, 1985) showed that rank-dependent utility (RDU) is the most general interval scale utility model for binary lotteries. It can be easily established that this result cannot be generalized to lotteries with more than two outcomes. This article suggests several additional conditions to ensure RDU as the only utility model with the desired property of interval scalability in the general case. The related axiomatizations of some special cases of (...) RDU of independent interest (the quantile utility, expected utility, and Yaari’s dual expected utility) are also given. (shrink)

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of whatcounts as a constant outcome. Although it is sometimes clear what should be considered constant, in many cases there are several (...) possible choices. Each choice can lead to a different "unique" probability and utility. By focusing attention on statedependent utilities, we determine conditions under which a truly unique probability and utility can be determined from an agent's expressed preferences among acts. Suppose that an agent's preference can be represented in terms of a probability P and a utility U.That is, the agent prefers one act to another iff the expected utility of that act is higher than that of the other. There are many other equivalent representations in terms of probabilities Q, which are mutually absolutely continuous with P, and state-dependent utilities V, which differ from U by possibly different positive affine transformations in each state of nature. We describe an example in which there are two different but equivalent state-independent utility representations for the same preference structure. They differ in which acts count as constants. The acts involve receiving different amounts of one or the other of two currencies, and the states are different exchange rates between the currencies. It is easy to see how it would not be possible for constant amounts of both currencies to have simultaneously constant values across the differentstates. Savage (1954, sec. 5.5) discovered a situation in which two seemingly equivalent preference structures are represented by different pairs of probability and utility. He attributed the phenomenon to the construction of a "small world." We show that the small world problem is just another example of two different, but equivalent, representations treating different actsas constants. Finally, we prove a theorem (similar to one of Karni 1985) that shows how to elicit a unique state-dependent utility and does not assume that there are prizes with constant value. To do this, we define a new hypothetical kind of act in which both the prize to be awarded and the state of nature are determined by an auxiliary experiment. (shrink)

We develop a model of Disappointment in which disappointment and elation arise from comparing the outcome received, not with an expected value as in previous models, but rather with the other individual outcomes of the lottery. This approach may better reflect the way individuals are liable to experience disappointment. The model obtained accounts for classic behavioral deviations from the normative theory, offers a richer structure than previous disappointment models, and leads to a Rank-Dependent Utility formulation in a (...) transparent way. Thus, our disappointment model may provide a clear psychological rationale for the subjective transformation of probabilities. (shrink)

Empirical evidence from both utility and psychophysical experiments suggests that people respond quite differently—perhaps discontinuously—to stimulus pairs when one consequence or signal is set to `zero.' Such stimuli are called unitary. The author's earlier theories assumed otherwise. In particular, the key property of segregation relating gambles and joint receipts (or presentations) involves unitary stimuli. Also, the representation of unitary stimuli was assumed to be separable (i.e., multiplicative). The theories developed here do not invoke separability. Four general cases based on (...) two distinctions are explored. The first distinction is between commutative joint receipts, which are relevant to utility, and the non-commutative ones, which are relevant to psychophysics. The second distinction concerns how stimuli of the form (x, C; y) and the operation of joint receipt are linked: by segregation, which mixes stimuli and unitary ones, and by distributivity, which does not involve any unitary stimuli. A class of representations more general than rank-dependent utility (RDU) is found in which monotonic functions of increments U(x)-U(y), where U is an order preseving representation of gambles, and joint receipt play a role. This form and its natural generalization to gambles with n > 2 consequences, which is also axiomatized, appear to encompass models of configural weights and decision affect. When joint receipts are not commutative, somewhat similar representations of stimuli arise, and joint receipts are shown to have a conjoint additive representation and in some cases a constant bias independent of signal intensity is predicted. (shrink)

The enormous scale of the available information and products on the Internet has necessitated the development of algorithms that intermediate between options and human users. These algorithms attempt to provide the user with relevant information. In doing so, the algorithms may incur potential negative consequences stemming from the need to select items about which it is uncertain to obtain information about users versus the need to select items about which it is certain to secure high ratings. This tension is an (...) instance of the exploration–exploitation trade‐off in the context of recommender systems. Because humans are in this interaction loop, the long‐term trade‐off behavior depends on human variability. Our goal is to characterize the trade‐off behavior as a function of human variability fundamental to such human–algorithm interaction. To tackle the characterization, we first introduce a unifying model that smoothly transitions between active learning and recommending relevant information. The unifying model gives us access to a continuum of algorithms along the exploration–exploitation trade‐off. We then present two experiments to measure the trade‐off behavior under two very different levels of human variability. The experimental results inform a thorough simulation study in which we modeled and varied human variability systematically over a wide rage. The main result is that exploration–exploitation trade‐off grows in severity as human variability increases, but there exists a regime of low variability where algorithms balanced in exploration and exploitation can largely overcome the trade‐off. (shrink)

A detailed theoretical analysis is presented of what five utility representations – subjective expected utility (SEU), rank-dependent (cumulative or Choquet) utility (RDU), gains decomposition utility (GDU), rank weighted utility (RWU), and a configural-weight model (TAX) that we show to be equivalent to RWU – say about a series of independence properties, many of which were suggested by M. H. Birnbaum and his coauthors. The goal is to clarify what implications to draw about (...) the descriptive aspects of the representations from data concerning these properties. The upshot is a sharp rejection of SEU and RDU and no clear choice between GDU and TAX, but a list of 8 properties is given that should receive more attention to discriminate between the latter two models. (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 theory. (...) I will show that the orthodoxy can be made to accommodate all of the preferences that Buchak’s theory can accommodate. (shrink)

Matthew Adler's Measuring Social Welfare is an introduction to the social welfare function (SWF) methodology. This essay questions some ideas at the core of the SWF methodology having to do with the relation between the SWF and the measure of well-being. The facts about individual well-being do not single out a particular scale on which well-being must be measured. As with physical quantities, there are multiple scales that can be used to represent the same information about well-being; no one scale (...) is special. Like physical laws, the SWF and its ranking of distributions cannot depend on exactly which of these scales we use. Adler and other theorists in the SWF tradition have used this idea to derive highly restrictive constraints on the shape of the SWF. These constraints rule out seemingly plausible views about distributive justice and population ethics. I argue, however, that these constraints stem from a simple but instructive mistake. The SWF should not be applied to vectors of numbers such as 1 and 2, but rather to vectors of dimensioned quantities such as 1 util and 2 utils. This seemingly pedantic suggestion turns out to have far-reaching consequences. Unlike the orthodox SWF approach, treating welfare levels as dimensioned quantities lets us distinguish between real changes in well-being and mere changes in the unit of measurement. It does this without making the SWF depend on the scale on which welfare is measured, and in a way that avoids the restrictive constraints on the shape of the SWF. (shrink)

A substantial body of empirical evidence shows that individuals overweight extreme events and act in conflict with the expected utility theory. These findings were the primary motivation behind the development of a rank-dependent utility theory for choice under uncertainty. The purpose of this paper is to demonstrate that some simple empirical rules of thumb for choice under uncertainty are consistent with the rank-dependent utility theory.

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...) also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity. (shrink)

The aim of the paper is to propose a preferences representation model under risk where risk perception can be past experience dependent. A first step consists in considering a one period decision problem where individual preferences are no more defined only on decisions but on pairs (decision, past experience). The obtained criterion is used in the construction of a dynamic choice model under risk. The paper ends with an illustrative example concerning insurance demand. It appears that our model allows (...) to explain modifications in the insurance demand behavior over time observed on the insurance markets for catastrophic risk and difficult to justify with standard models. (shrink)

In many real-world gambles, a non-trivial amount of time passes before the uncertainty is resolved but after a choice is made. An individual may have a preference between gambles with identical probability distributions over final outcomes if they differ in the timing of resolution of uncertainty. In this domain, utility consists not only of the consumption of outcomes, but also the psychological utility induced by an unresolved gamble. We term this utility anxiety. Since a reflective decision maker (...) may want to include anxiety explicitly in analysis of unresolved lotteries, a multiple-outcome model for evaluating lotteries with delayed resolution of uncertainty is developed. The result is a rank-dependent utility representation (e.g., Quiggin, 1982), in which period weighting functions are related iteratively. Substitution rules are proposed for evaluating compound temporal lotteries. The representation is appealing for a number of reasons. First, probability weights can be interpreted as the cognitive attention allocated to certain outcomes. Second, the model disaggregates strength of preference from temporal risk aversion and thus provides some insight into the old debate about the relationship between von Neumann–Morgenstern utility functions and strength of preference value functions. (shrink)

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

Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. First, (...) a probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent method. (shrink)

We investigate risk attitudes when the underlying domain of payoffs is finite and the payoffs are, in general, not numerical. In such cases, the traditional notions of absolute risk attitudes, that are designed for convex domains of numerical payoffs, are not applicable. We introduce comparative notions of weak and strong risk attitudes that remain applicable. We examine how they are characterized within the rank-dependent utility model, thus including expected utility as a special case. In particular, we (...) characterize strong comparative risk aversion under rank-dependent utility. This is our main result. From this and other findings, we draw two novel conclusions. First, under expected utility, weak and strong comparative risk aversion are characterized by the same condition over finite domains. By contrast, such is not the case under non-expected utility. Second, under expected utility, weak comparative risk aversion is characterized by the same condition when the utility functions have finite range and when they have convex range. By contrast, such is not the case under non-expected utility. Thus, considering comparative risk aversion over finite domains leads to a better understanding of the divide between expected and non-expected utility, more generally, the structural properties of the main models of decision-making under risk. (shrink)

This paper merges the non-expected utility approach (Tversky and Kahneman, J Risk Uncertain 5:297–323, 1992 and Quiggin, J Econ Behav Organ 3:323–343, 1982) into Akerlof’s (Quart J Econ 84:488–500, 1970) model of Market for Lemons. We derive the results for different probability weighting functions and analyze the phenomenon of market failure in light of non-expected utility maximization. Our main finding suggests that when the proportion of traded lemons is high (low), the problem of market failure is mitigated (enhanced). (...) In addition, for the case of Cumulative Prospect Theory, we show that (a) the higher the loss aversion is, the more pronounced is the market failure; (b) gain-domain elevation is negatively related to the extent of market failure; and (c) the value function is (i) negatively monotonic in the gain-domain diminishing sensitivity parameter when the market is characterized by a high proportion of “peaches,” and (ii) positively monotonic in the loss-domain diminishing sensitivity parameter when the market is characterized by a high proportion of “lemons.”. (shrink)

The paper characterizes axiomatically a class of temptation-driven preferences. The key (but not the only) novelty of the paper is the idea that the alternative which tempts when an item x is consumed may not be the same as the alternative which tempts when another item y is consumed. For any single item to be ultimately consumed, the other items can be ranked by how much they tempt. An individual contemplates, as an alternative consumption, only the item that tempts most. (...) The utility of a menu is then equal to the utility of the item that is consumed less a (psychological) cost of resisting temptation; this cost depends on both: the item to be consumed and the item that tempts. Unlike most of the existing literature, the axioms are imposed on deterministic menus, not on menus of lotteries. (shrink)

In order to accommodate empirically observed violations of the independence axiom of expected utility theory Becker and Sarin (1987) proposed their model of lottery dependent utility in which the utility of an outcome may depend on the lottery being evaluated. Although this dependence is intuitively very appealing and provides a simple functional form of the resulting decision criterion, lottery dependent utility has been nearly completely neglected in the recent literature on decision making under risk. (...) The goal of this paper is to revive the lottery dependent utility model. Therefore, we derive first a sound axiomatic foundation of lottery dependent utility. Secondly, we develop a discontinuous variant of the model which can accommodate boundary effects and may lead to a lexicographic non-expected utility model. Both analyses are accompanied by considering some functional specifications which are in accordance with recent experimental results and may have significant applications in business and management science. (shrink)

Savage's framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence€. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of states), and numeric utilities assigned to consequences. (...) Savage's derivation, however, is based on a highly problematic well-known assumption not included among his postulates: for any consequence of an act in some state, there is a "constant act" which has that consequence in all states. This ability to transfer consequences from state to state is, in many cases, miraculous -- including simple scenarios suggested by Savage as natural cases for applying his theory. We propose a simplification of the system, which yields the representation theorem without the constant act assumption. We need only postulates P1-P6. This is done at the cost of reducing the set of acts included in the setup. The reduction excludes certain theoretical infinitary scenarios, but includes the scenarios that should be handled by a system that models human decisions. (shrink)

The possibility to interpret expected and nonexpected utility theories in purely probabilistic terms has been recently investigated. Such interpretation proposes as guideline for the Decision Maker the comparison of random variables through their probability to outperform a stochastic benchmark. We apply this type of analysis to the model of Becker and Sarin, showing that their utility functional may be seen as the probability that an opportune random variable, depending on the one to be evaluated, does not outperform a (...) non-random benchmark. Further, the consequent choice criterion is equivalent to a sort of probability of ruin. Possible interpretations and financial examples are discussed. (shrink)

State-dependent utility is a problem for the behavioural branch of decision theory under uncertainty. It questions the very possibility that beliefs be revealed by choice data. According to the current literature, all models of beliefs are equally exposed to the problem. Moreover, the problem is solvable only when the decision-maker can influence the resolution of uncertainty. This article gives grounds to reject these two views. The various models of beliefs can be shown to be unequally exposed to the (...) problem of state-dependent utility. The problem can be argued to be solved even when the decision-maker has no influence over the resolution of uncertainty. The implications of such reappraisal for a philosophical appreciation of the revealed preference methodology are discussed. (shrink)

Much behavioral welfare economics assumes that expected utility theory does not accurately describe most human choice under risk. A substantial literature instead evaluates welfare consequences by taking cumulative prospect theory as the natural default alternative, at least where description is concerned. We present evidence, based on a review of previous literature and new experimental data, that the most empirically adequate hypothesis about human choice under risk is that it is heterogeneous, and that where EUT does not apply, more choice (...) is characterized by rank-dependent utility models than by CPT. Most of the apparently loss-averse choice behavior results from probability weighting rather than from direct disutility experienced when an outcome is framed as a loss against an idiosyncratic reference point. We then consider implications of this finding for methodological debates about how to model welfare effects of policies, and argue that abandonment of a dogmatic belief in CPT as the correct theory of risk human choice exposes a conceptual error that is widespread in behavioral welfare economics. We provide concluding reflections on second-order, philosophical issues around the grounding of normative commitments in policy-focused economics. (shrink)

In Pelota matches, bets are made between viewers through a middleman who receives 16% of the finally paid amount. In this paper, a description of the way bets are made and an explanation of the existence of those markets are presented. Taking betting markets as a simplified analogy for financial markets we have searched for the explanation in a world where both sides of the market are not different in believes and preferences. We find that for a bet to exist (...) when bettors are rank dependent expected utility maximizers, they have to be optimistic. Taking observations from actually made bets a preliminary analysis about the biases of those markets is presented. (shrink)

One aspect of the utility of gambling may evidence itself in failures of idempotence, i.e., when all chance outcomes give rise to the same consequence the `gamble' may not be indifferent to its common consequence. Under the assumption of segregation, such gambles can be expressed as the joint receipt of the common consequence and what we call `an element of chance', namely, the same gamble with the common consequence replaced by the status quo. Generalizing, any gamble is indifferent to (...) the joint receipt of its element of chance and a certain consequence, which is called the `kernel equivalent' of the gamble. Under idempotence, the kernel equivalent equals the certainty equivalent. Conditions are reported (Theorem 4) that are sufficient for the kernel equivalents to have the kind of utility representation first discussed by Luce and Fishburn (1991), including being idempotent. This utility representation of the kernel equivalents together with the derived form of utility over joint receipts yields a utility representation of the original structure. Possible forms for the utility of an element of chance are developed. (shrink)

Utility functions often lack additive separability, presenting an obstacle for decision theoretic axiomatizations. We address this challenge by providing a representation theorem for utility functions of quasi-separable preferences of the form $$u(x,y,z)=f(x,z) + g(y,z)$$ on subsets of topological product spaces. These functions are additively separable only when holding z fixed but are cardinally comparable for different values of z. We then generalize the result to spaces with more than three dimensions and provide applications to belief elicitation, inequity aversion, (...) intertemporal choice, and rank-dependent utility. (shrink)

This paper reports an experimental comparison of attitudes toward time and toward money in experience-based decisions. Preferences were elicited under rank-dependent utility for prospects with two or three consequences expressed either in time or in monetary units. Probabilities were unknown but learned through sampling. More specifically, time and money were compared under two conditions. In a first experiment, both consequences and probabilities of prospects were unknown and learned through sequential sampling. In a second experiment, the possible consequences (...) were revealed after the sampling. A real incentive system was implemented for both time and money. The heterogeneity of preferences was assessed for time and for money through individual and mixed modeling estimations. We observe that the nature of consequences (time or money) modifies probability weighting in terms of elevation and sensitivity. Subjects exhibit more optimism and less sensitivity to probability changes when deciding about time than about money. Revealing the consequences impacts the shape of the utility function and leaves probability weighting unchanged. We also observe that the real incentives have no effect except for the reduction in decision errors. This effect is stronger for money than for time. (shrink)

The Expected Shortfall or Conditional Value-at-Risk (CVaR) has been playing the role of main risk measure in the recent years and paving the way for an enormous number of applications in risk management due to its very intuitive form and important coherence properties. This work aims to explore this measure as a probability-dependent utility functional, introducing an alternative view point for its Choquet Expected Utility representation. Within this point of view, its main preference properties will be characterized (...) and its utility representation provided through local utilities with an explicit dependence on the assessed revenue’s distribution (quantile) function. Then, an intuitive interpretation for the related probability dependence and the piecewise form of such utility will be introduced on an investment pricing context, in which a CVaR maximizer agent will behave in a relativistic way based on his previous estimates of the probability function. Finally, such functional will be extended to incorporate a larger range of risk-averse attitudes and its main properties and implications will be illustrated through examples, such as the so-called Allais Paradox. (shrink)

Risk preferences of Australian academics are elicited by analyzing the aggregate distribution of their retirement funds across available investment options. Not more than 10 % of retirement funds are invested as if their owners maximize expected utility under the assumption of constant relative risk aversion with an empirically plausible level of risk aversion. An implausibly high level of risk aversion is required to rationalize any investment into bonds when stocks are available. Not more than 36.54 % of all investments (...) can be rationalized by a model of loss averse preferences. Moreover, the levels of loss aversion typically reported in the experimental studies imply overinvestment in bonds, which is not observed in the data. Up to 67.18 % of all investments can be rationalized by rank-dependent utility or Yaari’s dual model with empirically plausible parameters. A median Australian academic behaves as if maximizing rank-dependent utility with parameter γ∈[0.76,0.79]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma \in [0.76, 0.79]$$\end{document} in a Tversky and Kahneman probability weighting function. (shrink)

In this paper, I investigate the betting behavior of a decision-maker who can influence the likelihood of the events upon which she is betting. In decision theory, this is best known as a situation of moral hazard. Focusing on a particularly simple case, I sketch the first systematic analysis of moral hazard in the canonical Savage framework. From the results of this analysis, I draw two philosophical conclusions. First, from an observational and a descriptive point of view, there need to (...) be no incompatibility between moral hazard and the Savage framework. This qualifies the incompatibility view, that is ubiquitous in decision theory. Second, in general, moral hazard is not sufficient to overcome the challenges posed by state-dependent utility to the behavioral identification of beliefs. This qualifies the sufficiency view, that is influential in decision theory. These two philosophical conclusions are the main contributions of my paper. (shrink)

Despite Fisher's (1930) psychological intuitions of and the formal treatment given by Yaari (1965, Review of Economic Studies 32, 137), the intertemporal model of choice is mainly a model with certain lifetime. The purpose of this paper is to reconsider this assumption, starting from a very simple two-period model of choice with lifetime uncertainty. We examine the comparative statics of the model at the first two orders and replace the concept of `pure time preference' by taking into account the subjective (...) treatment of the probability of survival. (shrink)

Many quantitative scales are constructed using cutoffs on a continuum with scores assigned to the cutoffs. This paper develops a framework for using or constructing such scales from a decision-making standpoint. It addresses questions such as: How many distinct thresholds or cutoffs on a scale (i.e., what levels of granularity) are useful for a rational agent? Where should these thresholds be placed given a rational agent’s preferences and risk-orientation? Do scale score assignments have any bearing on decision-making and if so, (...) how should scores be assigned? Given two possible states of nature , an ordered collection of alternatives from which one is to be selected depending on the probability that A is the case, a simple expected utility condition stipulates when adjacent alternatives are distinguishable and determines the threshold odds separating them. Threshold odds and utilities are mapped onto scale scores via a simple distance model. The placement of the thresholds reflects relative concern over decisional consequences given A versus consequences given ∼ A. Likewise, it is shown that scale scores reflect risk-aversion or risk-seeking not only with respect to A versus ∼ A but also with respect to the rank of the R j . Connections are drawn between this framework and rank-dependent expected utility (RDEU) theory. Implications are adumbrated for both machine and human decision-making. (shrink)

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision (...) weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism. (shrink)

We develop an algorithm that can be used to approximate a decisionmaker’s beliefs for a class of preference structures that includes, among others, α-maximin expected utility preferences, Choquet expected utility preferences, and, more generally, constant additive preferences. For both exact and statistical approximation, we demonstrate convergence in an appropriate sense to the true belief structure.

A usual argument in finance refers to no arbitrage opportunities for the positivity of the bid-ask spread. Here we follow the decision theory approach and show that if positivity of the bid-ask spread is identified with strong risk aversion for an expected utility market-maker, this is no longer true for a rank-dependent expected utility one. For such a decision-maker only a very weak form of risk aversion is required, a result which seems more in accordance with (...) his actual behavior. We conclude by showing that the no-trade interval result of Dow and Werlang (1992a) remains valid for a rank-dependent expected utility market-maker merely exhibiting this weak form of risk aversion. (shrink)

Which is better: a guarantee of a modest amount of moral value, or a tiny probability of arbitrarily large value? To prefer the latter seems fanatical. But, as I argue, avoiding such fanaticism brings severe problems. To do so, we must decline intuitively attractive trade-offs; rank structurally identical pairs of lotteries inconsistently, or else admit absurd sensitivity to tiny probability differences; have rankings depend on remote, unaffected events ; and often neglect to rank lotteries as we already know (...) we would if we learned more. Compared to these implications, fanaticism is highly plausible. (shrink)

This article uses Lancaster's characteristics approach to rank sets of alternative combinations of commodity characteristics. It is assumed that there exists a reference point or reference level from which the individual evaluates set expansions in appropriate directions. We provide an axiomatic characterization for such a case.

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

The aim of this paper is to apply a general methodology for constructing statistical methods, which is based on decision theory, to give a statistical description of preferential rankings, with a focus on the rankings’ dependence on categorical variables. In the paper, I use functions of description errors that are based on the Kemeny and Hamming distances between preferential orderings, but the proposed methodology can also be applied to other methods of estimating description errors.

The so-called Final Ranking of the Philebus offers Socrates’ final evaluation of the relative merits of pleasure and reason in the best life. I begin by examining two common lines of interpretation as they address the criterion according to which the final ranking is organized. I then discuss the role ‘similarity’ has in organizing the investigation throughout the dialogue, from the initial comparison of the two lives (of reason and pleasure singly) down through the final ranking. I then consider the (...) thematic discussions of pleasure and reason separately, arguing that their treatments display an intriguing structural similarity. Next, I propose my own reading of the final ranking, whereby the ‘dependence’ relation at work in those two specific discussions may be see as the through-line of all (now five) tiers of the final ranking. I conclude by suggesting that this interpretation is able to preserve what is worthwhile in the two traditional lines of interpretation, while avoiding the pitfalls that tend to accompany them. (shrink)