Reflective coherence and Newcomb problems: A simple solution

Assignments of greater expected value to dominated options in Newcomb problems are analyzed as manifestations of reflective incoherence. The prospect of a greater reward by choosing a dominated option is illusory, since any ill gotten, i.e. irrational, gains can be leeched away by submitting the agent to a dynamic Dutch Book. In the Appendix, a proof is given which shows that if the agent is to avoid the Dutch Book in Newcomb situations, his degrees of belief are reflectively coherent if and only if his desirabilities at the time of choice align with his desirabilities at the time of action.     

Hidden Assumptions in the Dutch Book Argument

Probabilistic theories of rationality claim that degrees of belief have to satisfy the probability axioms in order to be rational. A standard argument to support this claim is the Dutch Book argument. This paper tries to show that, in spite of its popularity, the Dutch Book argument does not provide a foundation for normative theories of rationality. After a presentation of the argument and some of its criticisms a problem is pointed out: the Dutch Book argument applies only to situations with a specific formal structure. Several attempts to justify the argument for more general situations are considered and rejected. The only way to remedy the shortcoming, it is argued, seems to be the acceptance of a far-reaching and highly implausible empirical hypothesis.     

Conditional Desirability

Conditional attitudes are not the attitudes an agent is disposed to acquire in event of learning that a condition holds. Rather they are the components of agent's current attitudes that derive from the consideration they give to the possibility that the condition is true. Jeffrey's decision theory can be extended to include quantitative representation of the strength of these components. A conditional desirability measure for degrees of conditional desire is proposed and shown to imply that an agent's degrees of conditional belief are conditional probabilities. Rational conditional preference is axiomatised and by application of Bolker's representation theorem for rational preferences it is shown that conditional preference rankings determine the existence of probability and desirability measures that agree with them. It is then proven that every conditional desirability function agrees with an agent's conditional preferences and, under certain assumptions, every desirability function agreeing with an agent's conditional preferences is a conditional desirability function agreeing with her unconditional preferences.     

Cognitive rationality and alternative belief measures

In this article, we first examine the various criticisms of the probabilistic model. Then we introduce capacities in order to show that if a probability measure corresponds to anesthetizing the belief of the agent's knowledge, it is then possible to suggest another type of rationality—namely, being able to describe a wise and a rash behavior when facing risk—and therefore another model of belief under uncertainty. While trying to specify various alternative measures, possibility, necessity, and measures resulting from a triangular norm or from a triangular conorm, we finally try to define the field of application of the probabilistic model as well as a sign of the rationality choice: constraint of mass-unity for traditional rationality, and constraint of duality for the one we present.This article is a revised version of a paper presented during the FUR V Congress, Duke University, North Carolina, USA, June 10–13, 1990. I am indebted to Bertrand Munier, Alain Chateauneuf, Olivier Favereau, Jacques-François Thisse, Bernard Walliser, and Kip Viscusi for helpful comments on earlier versions of this article.     

Deriving Harsanyi’s Utilitarianism from De Finetti’s Book-Making Argument

The book-making argument was introduced by de Finetti as a principle to prove the existence and uniqueness of subjective probabilities. It has subsequently been accepted as a principle of rationality for decisions under uncertainty. This note shows that the book-making argument has relevant applications to welfare: it gives a new foundation for utilitarianism that is alternative to Harsanyi’s, it generalizes foundations based on the theorem of the alternative, and it avoids arguments based on expected utility.     

Single Case Probabilities and the Social World: The Application of Popper's Propensity Interpretation

This paper is a re-examination of Popper's propensity interpretation of probability in respect of its potential methodological value in social science. A long standing problem for the (standard) frequency interpretation of probability is that whilst it is able to treat both aggregate and individual phenomena as having measurable properties, it cannot explain the ontological relationship between such concrete individual cases and aggregates. Popper's interpretation treats single cases as both real, but also as realisations of a propensity to occur. The frequency and propensity interpretations are compared and whilst some common objections raised must be upheld, they do not devalue the importance of the propensity interpretation as at least a metaphysical basis for probabilistic claims in social science. However the value of the approach may also lie in its methodological potential. Here I sugest that single case probabilities must be analysed in terms of the anterior probabilities of prior constituent events. In this I move beyond Popper's own programme, but suggest that such a move is theoretically compatible with recent complexity approaches in social science and goes some way toward meeting anti-naturalist concerns about intentionality.     

Arbitrage,rationality, and equilibrium

No-arbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, no-arbitrage is synonymous with subjective expected utility maximization in personal decisions, competitive equilibria in capital markets and exchange economies, and correlated equilibria in noncooperative games. The arbitrage principle directly characterizes rationality at the market level; the appearance of deliberate optimization by individual agents is a consequence of their adaptation to the market. Concepts of equilibrium behavior in games and markets can thus be reconciled with the ideas that individual rationality is bounded, that agents use evolutionarily-shaped decision rules rather than numerical optimization algorithms, and that personal probabilities and utilities are inseparable and to some extent indeterminate. Risk-neutral probability distributions, interpretable as products of probabilities and marginal utilities, play a central role as observable quantities in economic systems.     

Aggregation theorems and multidimensional stochastic choice models

In many choice situations, the options are multidimensional. Numerous probabilistic models have been developed for such choices between multidimensional options and for the parallel choices determined by one or more components of such options. In this paper, it is assumed that a functional relation exists between the choice probabilities over the multidimensional options and the choice probabilities over the associated component unidimensional options. It is shown that if that function satisfies a marginalization property then it is essentially an arithmetic mean, and if the function satisfies a likelihood independence property then it is a weighted geometric mean. The results are related to those on the combination of expert opinion, and various probabilistic models in the choice literature are shown to have the geometric mean form.     

A Characterization for the Spherical Scoring Rule

Strictly proper scoring rules have been studied widely in statistical decision theory and recently in experimental economics because of their ability to encourage assessors to honestly provide their true subjective probabilities. In this article, we study the spherical scoring rule by analytically examining some of its properties and providing some new geometric interpretations for this rule. Moreover, we state a theorem which provides an axiomatic characterization for the spherical scoring rule. The objective of this analysis is to provide a better understanding of one of the most commonly available scoring rules, which could aid decision makers in the selection of an appropriate tool for evaluating and assessing probabilistic forecasts.      

Coherent decision analysis with inseparable probabilities and utilities

This article explores the extent to which a decision maker's probabilities can be measured separately from his/her utilities by observing his/her acceptance of small monetary gambles. Only a partial separation is achieved: the acceptable gambles are partitioned into a set of belief gambles, which reveals probabilities distorted by marginal utilities for money, and a set of preference gambles, which reveals utilities reciprocally distorted by marginal utilities for money. However, the information in these gambles still enables us to solve the decision maker's problem: his/her utility-maximizing decision is the one that avoids arbitrage (i.e., incoherence or Dutch books).     

A theory of subjective expected utility with vague preferences

This paper shows how notions of vagueness in preferences and judgments of personal probabilities can be accommodated within an axiomatization of subjective expected utility by the use of extraneous scaling probabilities and gambles on consequences. The representational form obtained says that the subjective expected utility of one act exceeds the subjective expected utility of a second act whenever the first is preferred to the second. The paper also explores the possibility of obtaining this representational form under Savage's formulation, which does not use extraneous probabilities, and discusses difficulties encountered in this approach.     

Rediscovering debates in the international studies: Morton Kaplan's system epistemology revisited

In this four-part paper I attempt to recover the notion of debate as a method of philosophical analysis for the international studies. In part one, it is argued that discursive reasoning is indispensable to the task of attempting to say what international relations might consist in. Three reasons are given for this, viz., that there is an important connection between such debates and rationality; that it is a constitutive feature of natural language to want to use it for self-conscious reflections; and that it seems to be the only way of identifying the key concepts in terms of which any theorizing about international relations is to be expressed. Parts two and three are intended to show one of the uses to which discursive reasoning may be put in establishing, beyond a shadow of a doubt, the incoherence of Morton Kaplan's systems epistemology for international relations. Establishing the incoherence of one conception of what international relations consists in will go one step closer towards saying more fully what international relations is. Part four suggests, but does not attempt to make compelling, that an Aristotelian conception of the subject matter is a quite defensible one.     

Probabilities and beliefs

Choice-theoretic definitions of subjective probabilities originated with the work of Ramsey and de Finetti and attained their definitive form in the work of Savage. These probabilities are intended to provide a numerical representation of a decision maker's beliefs regarding the likely realization of alternative events. In this article, I argue that the choice-theoretic definitions of subjective probabilities involve a tacit convention—namely, state-independent utility functions—that is not implied by the axioms, and, as a consequence, choice-theoretic subjective probabilities, even when they exist, do not necessarily represent the decision makers' beliefs.     

Nondegenerate Intervals of No-Trade Prices for Risk Averse Traders

According to the local risk-neutrality theorem an agent who has the opportunity to invest in an uncertain asset does not buy it or sell it short iff its expected value is equal to its price, independently of the agent's attitude towards risk. Contrary to that it is shown that, in the context of expected utility theory with differentiable vNM utility function, but without the assumption of stochastic constant returns to scale, nondegenerate intervals of no-trade prices may exist. With a quasiconcave expected utility function they do if, and only if, the agent is risk averse of order one.     

The role of risk preferences in bargaining when acceptance of a proposal requires less than unanimous approval

The role of risk preferences in determining the outcome to bargaining is examined for the case in which acceptance of a proposal requires less than unanimous approval. Using an n-agent extension of the Ståhl-Rubinstein alternating offer model, we find that risk preferences play a fundamentally different role when bargaining is settled using a nonunanimity voting rule. Risk preferences determine not only an agent's reservation price but also the likelihood that he is made part of the winning coalition. An implication of this analysis is that when the preferences of the agents are not too diverse, it is advantageous for an agent to be relatively risk-averse.The helpful comments and suggestions of Rich McLean and an anonymous referee are gratefully acknowledged. This article was presented as a paper at the 1988 Winter Econometric Society Meetings.     

Estimating subjective probabilities

Subjective probabilities play a central role in many economic decisions and act as an immediate confound of inferences about behavior, unless controlled for. Several procedures to recover subjective probabilities have been proposed, but in order to recover the correct latent probability one must either construct elicitation mechanisms that control for risk aversion, or construct elicitation mechanisms which undertake “calibrating adjustments” to elicited reports. We illustrate how the joint estimation of risk attitudes and subjective probabilities can provide the calibration adjustments that theory calls for. We illustrate this approach using data from a controlled experiment with real monetary consequences to the subjects. This allows the observer to make inferences about the latent subjective probability, under virtually any well-specified model of choice under subjective risk, while still employing relatively simple elicitation mechanisms.     

Information,risk perceptions,and smoking choices of youth

Conventional wisdom maintains that youths take risks because they underestimate probabilities of harm. Presumably if they knew the true probabilities, they would behave differently. We used the National Longitudinal Survey of Youth 1997 to assess whether differences between subjective and objective probabilities that an adverse outcome to self will occur are systematically related to a harmful behavior, initiating smoking. We find that youths are generally pessimistic about probabilities of their own deaths and being violent crime victims. After smoking initiation, youths increase subjective probabilities of death by more than the objective increase in mortality risk, implying recognition of potential harms. Virtually all 12–14 year-olds know that smoking causes heart disease. The minority who believe that smoking causes AIDS are less likely to become smokers; i.e., risk misperceptions deter rather than cause smoking initiation. Messages designed to deter smoking initiation should stress other disadvantages of smoking than just probabilities of harm.     

Choices at various levels of uncertainty: An experimental test of the restated diversification theorem

Our “Restated diversification theorem” (Skogh and Wu, 2005) says that risk-averse agents may pool risks efficiently without assignment of subjective probabilities to outcomes, also at genuine uncertainty. It suffices that the agents presume that they face equal risks. Here, the theorem is tested in an experiment where the probability of loss, and the information about this probability, varies. The result supports our theorem. Moreover, it tentatively supports an evolutionary theory of the insurance industry—starting with mutual pooling at uncertainty, turning into insurance priced ex ante when actuarial information is available.