We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. (...) We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. (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)

We distinguish three qualitatively different types of uncertainty—ethical, option and state space uncertainty—that are distinct from state uncertainty, the empirical uncertainty that is typically measured by a probability function on states of the world. Ethical uncertainty arises if the agent cannot assign precise utilities to consequences. Option uncertainty arises when the agent does not know what precise consequence an act has at every state. Finally, state space uncertainty exists when the agent is unsure how to construct an exhaustive state space. (...) These types of uncertainty are characterised along three dimensions—nature, object and severity—and the relationship between them is examined. We conclude that these different forms of uncertainty cannot be reduced to empirical uncertainty about the state of the world without inducing an increase in its severity. (shrink)

Many fine-grained decisions concerning climate change involve significant, even severe, uncertainty. Here, we focus on modelling the decisions of single agents, whether individual persons or groups perceived as corporate entities. We offer a taxonomy of the sources and kinds of uncertainty that arise in framing these decision problems, as well as strategies for making a choice in spite of uncertainty. The aim is to facilitate a more transparent and structured treatment of uncertainty in climate decision making.

In some severely uncertain situations, exemplified by climate change and novel pandemics, policymakers lack a reasoned basis for assigning probabilities to the possible outcomes of the policies they must choose between. I outline and defend an uncertainty averse, egalitarian approach to policy evaluation in these contexts. The upshot is a theory of distributive justice which offers especially strong reasons to guard against individual and collective misfortune.

The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist (“classical”) statistics have strong cases on these grounds. In this article, we instead approach the debates in the “Statistics Wars” from a largely unexplored angle: simulations of different methodologies’ performance in the short to medium run. We conducted a large number of simulations using a straightforward decision problem based (...) around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson’s version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player functions as a benchmark: a statistical methodology should at least outperform a crude form of induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. Unlike that study, we were able to use Big Data methods to mitigate problems of random error in the simulation results. The Williamsonian player, who is a novel element of our study, also had no systematic differences in their performance, provided that they use a low confidence level. These players performed similarly even in the very short run, when players were making different decisions. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics. However, the frequentist and Williamsonian performed poorly when their confidence levels were high, and the Bayesian was surprisingly harmed by biased priors, providing some unexpected lessons for these methodologies when facing this type of decision problem. (shrink)

This note argues that, under some circumstances, it is more rational not to behave in accordance with a Bayesian prior than to do so. The starting point is that in the absence of information, choosing a prior is arbitrary. If the prior is to have meaningful implications, it is more rational to admit that one does not have sufficient information to generate a prior than to pretend that one does. This suggests a view of rationality that requires a compromise between (...) internal coherence and justification, similarly to compromises that appear in moral dilemmas. Finally, it is argued that Savage's axioms are more compelling when applied to a naturally given state space than to an analytically constructed one; in the latter case, it may be more rational to violate the axioms than to be Bayesian. (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)

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds. We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: learning observable evidence obtained by (...) repeated sampling from the unknown distribution; and learning higher-order information about the distribution. The first changes only the plausibility map, but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions, as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning. (shrink)

The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference and judgment (...) aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s :410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed. (shrink)

In the standard formulation of game theory, agents use mixed strategies in the form of objective and probabilistically precise devices to conceal their actions. We introduce the larger set of probabilistically imprecise devices and study the consequences for the basic results on normal form games. While Nash equilibria remain equilibria in the extended game, there arise new Ellsberg equilibria with distinct outcomes, as we illustrate by negotiation games with three players. We characterize Ellsberg equilibria in two-person conflict and coordination games. (...) These equilibria turn out to be related to experimental deviations from Nash equilibrium play. (shrink)

Journal of Political Philosophy, Volume 30, Issue 3, Page 370-394, September 2022.

We consider a setting where a decision maker’s uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well known to suffer from problems. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural (...) approach to determining the weights. We then show how this representation can be used in decision making, by modifying a standard approach to decision making—minimizing expected regret—to obtain minimax weighted expected regret. We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case. (shrink)

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

In this paper I offer an alternative - the ‘dispositional account’ - to the standard account of imprecise probabilism. Whereas for the imprecise probabilist, an agent’s credal state is modelled by a set of credence functions, on the dispositional account an agent’s credal state is modelled by a set of sets of credence functions. On the face of it, the dispositional account looks less elegant than the standard account – so why should we be interested? I argue that the dispositional (...) account is actually simpler, because the dispositional choice behaviour that fixes an agent’s credal state is faithfully depicted in the model of that agent’s credal state. I explore some of the implications of the account, including a surprising implication for the debate over dilation. (shrink)

Recent literature has examined the problem facing decision makers with bounded awareness, who may be unaware of some states of nature. A question that naturally arises here is whether a value of awareness, analogous to value of information, can be attributed to changes in awareness. In this paper, such a value is defined. It is shown that the sum VOA +\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+$$\end{document} VOI is constant and, except for scale effects, independent of the (...) choice set. It follows that the larger is VOA, the smaller is VOI. This point is illustrated for a simple two-state case, then proved for general classes of compact convex choice sets, and for alternative interpretations of the concept of unawareness. (shrink)

We study decision under uncertainty in an Anscombe–Aumann framework. Two binary relations characterize a decision-maker: one incomplete relation, reflecting her objective rationality, and a second complete relation, reflecting her subjective rationality. We require the latter to be an extension of the former. Our key axiom is a dominance condition. Our main theorem provides a representation of the two relations. The objectively rational relation has a Bewley-style multiple prior representation. Using this set of priors, we fully characterize the subjectively rational relation (...) in terms of the most optimistic and most pessimistic expected utilities. (shrink)

As illustrated by the famous Ellsberg paradox, many subjects prefer to bet on events with known rather than with unknown probabilities, i.e., they are ambiguity averse. In an experiment, we examine subjects’ choices when there is an additional source of ambiguity, namely, when they do not know how much money they can win. Using a standard assumption on the joint set of priors, we show that ambiguity-averse subjects should continue to strictly prefer the urn with known probabilities. In contrast, our (...) results show that many subjects no longer exhibit such a strict preference. (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is “completely (...) ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)

Epistemic rationality is typically taken to be immodest at least in this sense: a rational epistemic state should always take itself to be doing at least as well, epistemically and by its own light, than any alternative epistemic state. If epistemic states are probability functions and their alternatives are other probability functions defined over the same collection of proposition, we can capture the relevant sense of immodesty by claiming that epistemic utility functions are (strictly) proper. In this paper I examine (...) what happens if we allow for the alternatives to an epistemic state to include probability functions with different domains. I first prove an impossibility result: on minimal assumptions, I show that there is no way of vindicating strong immodesty principles to the effect that any probability function should take itself to be doing at least as well than any alternative probability function, regardless of its domain. I then consider alternative, weaker generalizations of the traditional immodesty principle and prove some characterization results for some classes of epistemic utility functions satisfying each of the relevant principles. (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)

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

The degrees of belief of rational agents should be guided by the evidence available to them. This paper takes as a starting point the view—argued elsewhere—that the formal model best able to capture this idea is one that represents degrees of belief using Dempster–Shafer belief functions. However degrees of belief should not only respect evidence: they also guide decision and action. Whatever formal model of degrees of belief we adopt, we need a decision theory that works with it: that takes (...) as input degrees of belief so represented. The task of this paper is to develop such a decision theory for the belief function model of degrees of belief. This is not the first paper to attempt that task, but compared to the existing literature it takes a more abstract route to its destination, via a consideration of the very idea of rational decision making in light of one’s beliefs and desires. After presenting the new decision theory and comparing it to existing views, the paper goes on to consider diachronic decision situations. (shrink)

I consider games with ambiguous payoffs played by non-Expected Utility decision makers. Three equilibrium solutions are studied. Nash equilibrium in which equilibrium mixed strategies must be best responses, Crawford equilibrium in beliefs and pure equilibrium in beliefs in which equilibrium strategies are mixtures of best responses, with the latter restricting best responses to pure actions. I study the interactions between ambiguity preferences on one side and equilibrium properties on the other. I show how the equilibrium concepts differ, computing necessary and (...) sufficient conditions for existence and equivalence. I also show how these solution concepts fare against two fundamental principles of Nash equilibrium in standard games: the principle of indifference and the reduction principle. Given both are central to the computation of Nash equilibrium in games with Expected Utility players, their failure indicates how relaxing the Expected Utility hypothesis may disrupt standard game theoretic results such as the characterization of equilibria in two-player games. (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)

Grant and Quiggin suggest that agents employ heuristics to constrain the set of acts under consideration before applying standard decision theory, based on their restricted model of the world to the remaining acts. The aim of this paper is to provide an axiomatic foundation, and an associated representation theorem, for the preference model proposed by Grant and Quiggin. The unawareness of the agent is encoded both in the specification of the states and in an elaboration of the set of consequences. (...) We illustrate how the representation can be applied to rationalize two notions of the precautionary principle that were proposed and discussed in Grant and Quiggin. (shrink)

Integrated assessment models play a major role in the science and policy of climate change. Similarly to other widely used computational tools for addressing socially relevant problems, IAMs need to account for the key uncertainties characterizing processes and socio-economic responses. In the case of climate change, these are particularly complex given the very long-term nature of climate and the deep uncertainty characterizing technological and human systems. Here we draw from philosophical discussion of mathematical modeling of social problems and review the (...) role of uncertainty in climate-economic modeling. In agreement with the literature, we highlight the crucial role of epistemic uncertainty in IAMs. We posit that the normative components of models, more than the physical and socio-techno-economic ones, are the most fraught by uncertainty and yet the least understood. We suggest a research agenda to explore uncertainties of evaluation frameworks, transcending the current implicit normativity of IAMs. (shrink)

The Precautionary Principle is typically construed as a conservative decision rule aimed at preventing harm. But Martin Peterson (JME 33: 5–10, 2007; The ethics of technology: A geometric analysis of five moral principles, Oxford University Press, Oxford, 2017) has argued that the principle is better understood as an epistemic rule, guiding decision-makers in forming beliefs rather than choosing among possible acts. On the epistemic view, he claims there is a principle concerning expert disagreement underlying precautionary-based reasoning called the ecumenical principle: (...) all expert views should be considered in a precautionary appraisal, not just those that are the most prominent or influential. In articulating the doxastic commitments of decision-makers under this constraint, Peterson precludes any probabilistic rule that might result in combining expert opinions. For combined or consensus probabilities are likely to provide decision-makers with information that is more precise than warranted. Contra Peterson, I argue that upon adopting a broader conception of probability, there is a probabilistic rule, under which expert opinions are combined, that is immune to his criticism and better represents the ecumenical principle. (shrink)

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker’s risk and (...) ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article. (shrink)

Les comportements individuels et collectifs en présence d’incertitude peuvent paraître irrationnels ou se modifier au cours du temps à la suite de nouvelles informations ou d’événements plus ou moins en lien avec ces incertitudes. Ceci pose la question des moyens mis à disposition des autorités publiques pour prévenir et gérer ces situations. Dans cet article, nous nous intéressons aux comportements des individus face aux situations incertaines en mettant en avant la manière dont la population peut percevoir ces incertitudes et les (...) informations provenant de sources diverses. Nous reprenons la littérature économique des comportements et prises de décision dans un environnement incertain afin de mettre en évidence les difficultés de la mise en place de politiques notamment d’incitation à la prévention. (shrink)

Using a subclass of the α-maximin expected-utility preference model, in which the decision maker’s degree of ambiguity and degree of pessimism are each parameterized, we present a theory of religious choice in the Pascalian decision theory tradition, one that can resolve dilemmas, address the “many Gods objection,” and address the ambiguity inherent in religious choice. Parameterizing both the degree of ambiguity and the degree of pessimism allows one to examine how the two interact to impact choice, which is useful regardless (...) of the application. Applying this model to religious choice is a move beyond subjective expected-utility theory, allowing us to show that a change in either the degree of ambiguity or the degree of pessimism can lead a decision maker to “convert” from one religion to another. (shrink)

This paper presents the results of two experiments designed to test violations of Subjective Expected Utility Theory (SEUT) within a sample of Italian trade union delegates and leaders. Subjects priced risky and ambiguous prospects in the domain of gains. Risky prospects were based on games of chance, while ambiguous prospects were built on the standard Ellsberg paradox and on event lotteries whose outcomes were based either on the results of a fictional election or on the future results of the 1999 (...) European Parliamentary election in Italy and the U.K. The experiments show that, although risky prospects were priced at their expected values on average, trade union delegates and leaders did violate SEUT when assessing ambiguous prospects. Moreover, their behaviour depended on the source of uncertainty (Ellsberg paradox vs. electoral results; fictional vs. real election; Italy vs. U.K. election outcomes). We discuss the implications of these results for the economic theory of the trade union. (shrink)

This paper provides a general framework for analyzing self-confirming policies. We study self-confirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. We characterize stationary monetary policies in a linear-quadratic setting.

Tribute to Jean-Yves Jaffray by the French Group of Decision Theory.

We provide a simple model to measure the impact of aggregate risks. We consider agents whose rankings of lotteries over vectors of outcomes satisfy expected utility and separability. Such rankings are characterized in terms of aggregative utilities that measure sensitivity to aggregate uncertainty in a straightforward way. We consider applications to models of product variety, portfolio choice, and public attitudes towards catastrophic risks. The framework lends support to precautionary measures that penalize policies for exposure to correlation. The model rationalizes a (...) number of behavioral and policy patterns as attempts to hedge against aggregate uncertainty. (shrink)

Maxmin Expected Utility was first axiomatized by Gilboa and Schmeidler in an Anscombe–Aumann setup Anscombe and Aumann which includes exogenous probabilities. The model was later axiomatized in a purely subjective setup, where no exogenous probabilities are assumed. The purpose of this note is to show that in all these axiomatizations, the only assumptions that are needed are the basic ones that are used to extract a cardinal utility function, together with the two typical Maxmin assumptions, Uncertainty Aversion and Certainty Independence, (...) applied only to 0.5:0.5 mixtures. For the purely subjective characterizations, this means that assumptions involving an unbounded number of variables can be replaced with assumptions that involve only a finite number thereof. (shrink)

For (S, Σ) a measurable space, let ${\cal C}_1$ and ${\cal C}_2$ be convex, weak* closed sets of probability measures on Σ. We show that if ${\cal C}_1$ ∪ ${\cal C}_2$ satisfies the Lyapunov property , then there exists a set A ∈ Σ such that minμ1∈ ${\cal C}_1$ μ1(A) > maxμ2 ∈ ${\cal C}_2$ (A). We give applications to Maxmin Expected Utility (MEU) and to the core of a lower probability.

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in (...) which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance. (shrink)

This article analyzes investors’ portfolio selection problems in a two-period dynamic model of Knightian uncertainty. We account for the existence of portfolio inertia in this two-period framework. Furthermore, by incorporating investors’ updating behavior, we analyze how observing new information in the first period will affect investors’ behavior. By this analysis, we show that observing new information in the first period will expand portfolio inertia in the second period compared with the case in which observing new information has not been gained (...) in the first period if the degree of Knightian uncertainty is sufficiently large. (shrink)

Models of electoral competition between two opportunistic, office-motivated parties typically predict that both parties become indistinguishable in equilibrium. I show that this strong connection between the office motivation of parties and their equilibrium choice of identical platforms depends on two—possibly false—assumptions: Issue spaces are uni-dimensional and Parties are unitary actors whose preferences can be represented by expected utilities. I provide an example of a two-party model in which parties offer substantially different equilibrium platforms even though no exogenous differences between parties (...) are assumed. In this example, some voters’ preferences over the 2-dimensional issue space exhibit non-convexities and parties evaluate their actions with respect to a set of beliefs on the electorate. (shrink)

For non-additive set functions, the independent product, in general, is not unique and the Fubini theorem is restricted to slice-comonotonic functions. In this paper, we use the representation theorem of Gilboa and Schmeidler (Math Oper Res 20:197–212, 1995) to extend the Möbius product for non-additive set functions to non-finite spaces. We extend the uniqueness result of Ghirardato (J Econ Theory 73:261–291, 1997) for products of two belief functions and weaken the requirements on the marginals necessary to obtain the Fubini property (...) in the product. More importantly, we show that for the Möbius product one side of the Fubini theorem holds for all integrable functions if one of the marginals either is a probability or a convex combination of a chain of unanimity games, i.e., we relax the requirement of slice-comonotonicity and enrich the set of possible applications. (shrink)

Most decisions concerning insurance and self-protection have to be taken in situations in which the effort exerted precedes the moment uncertainty realizes, and the probabilities of future states of the world are not perfectly known. By integrating these two characteristics in a simple theoretical framework, this paper derives plausible conditions under which ambiguity aversion raises the demand for insurance and self-protection. In particular, it is shown that in most usual situations where the level of ambiguity does not increase with the (...) level of effort, a simple condition of ambiguity prudence known as decreasing absolute ambiguity aversion is sufficient to give a clear and positive answer to the question: Does ambiguity aversion raise the optimal level of effort? (shrink)

Uncertain or ambiguous events cannot be objectively measured by probabilities, i.e. different decision-makers may disagree about their likelihood of occurrence. This paper proposes a new decision-theoretical approach on how to measure ambiguity that is analogous to axiomatic risk measurement in finance. A decision-theoretical measure of ambiguity is a function from choice alternatives to non-negative real numbers. Our proposed measure of ambiguity is derived from a novel assumption that ambiguity of any choice alternative can be decomposed into a left-tail ambiguity and (...) a right-tail ambiguity. This decomposability assumption is combined with two standard assumptions: ambiguity sources are independent from outcomes and any elementary increase in uncertainty necessarily increases ambiguity. (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our new (...) elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

We provide a new behavioral foundation for subjective expected utility within the Anscombe–Aumann framework. In contrast to the original axiomatization of SEU, our behavioral foundation establishes that to be consistent with SEU maximization, we need not explicitly assume that preferences satisfy the independence axiom over the domain of all acts. Rather, the substantive implications of independence for an SEU representation may equivalently be derived from less demanding conditions over certain smaller classes of acts. These acts, which we refer to as (...) uncertainty-free comparable acts, have the property that they are relatively simple for a decision maker to compare because she can rank acts within any such class based on her risk preferences alone, without having to consider the underlying uncertainty. Acts of this kind comprise constant acts and acts that are almost identical in the sense that they differ from one another in at most one state. (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.