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).     

De Finetti was Right: Probability Does Not Exist

De Finetti's treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals. De Finetti defined subjective probabilities in terms of the rates at which individuals are willing to bet money on events, even though, in principle, such betting rates could depend on state-dependent marginal utility for money as well as on beliefs. Most later authors, from Savage onward, have attempted to disentangle beliefs from values by introducing hypothetical bets whose payoffs are abstract consequences that are assumed to have state-independent utility. In this paper, I argue that de Finetti was right all along: PROBABILITY, considered as a numerical measure of pure belief uncontaminated by attitudes toward money, does not exist. Rather, what exist are de Finetti's `previsions', or betting rates for money, otherwise known in the literature as `risk neutral probabilities'. But the fact that previsions are not measures of pure belief turns out not to be problematic for statistical inference, decision analysis, or economic modeling. This revised version was published online in June 2006 with corrections to the Cover Date.     

A New Method for Determining Why Length of Life is More Unequal in Some Populations Than in Others

Why is there greater variability in individual longevity in some populations than in others? We propose a decomposition method designed to address that question by quantifying the effects of population differences in the spread, allocation, and timing of the principal causes of death. Applying the method to the United States and Sweden, we find that spread effects account for about two-thirds of the greater variance in age at death among American adults, meaning that two-thirds of the U.S.-Sweden difference would persist if the two countries differed only with respect to within-cause variance among adults. The remainder of the difference is due largely to allocation effects, with the greater incidence of homicides and fatal traffic accidents alone accounting for more than one-fourth of the greater variance in age at death among adults in the United States.     

A theorem for Bayesian group decisions

This paper presents a natural extension of Bayesian decision theory from the domain of individual decisions to the domain of group decisions. We assume that each group member accepts the assumptions of subjective expected utility theory with respect to the alternatives from which they must choose, but we do not assume, a priori, that the group as a whole accepts those assumptions. Instead, we impose a multiattribute utility independence condition on the preferences of the group with respect to the expected utilities of its actions as appraised by its members. The result is that the expected utility of an alternative for the group is a weighted average of the expected utilities of that alternative for its members. The weights must be determined collectively by the group. Pareto optimality is not assumed, though the result is consistent with Pareto optimality.     

The incoherence of agreeing to disagree

The agreeing-to-disagree theorem of Aumann and the no-expected-gain-from-trade theorem of Milgrom and Stokey are reformulated under an operational definition of Bayesian rationality. Common knowledge of beliefs and preferences is achieved through transactions in a contingent claims market, and mutual expectations of Bayesian rationality are defined by the condition of joint coherence,i.e., the collective avoidance of arbitrage opportunities. The existence of a common prior distribution and the impossibility of agreeing to disagree follow from the joint coherence requirement, but the prior must be interpreted as a risk-neutral distribution: a product of probabilities and marginal utilities for money. The failure of heterogenous information to create disagreements or incentives to trade is shown to be an artifact of overlooking the potential role of trade in constructing the initial state of common knowledge.     

Leveraging corporate influence

Movement scholars have become increasingly interested in the way in which social movement actors target non-state entities, particularly corporations. The reason for this is quite simple: globalization, neoliberal policies adopted by the state, and new legal protections via court rulings have allowed businesses to exert considerable influence across all facets of society. In light of these changes, movements have found targeting the state less effective than directly pressuring business interests. Scholarship suggests that one of the most effective ways to ensure that corporations attend to movement concerns is through market pressures. While negatively impacting stock returns is perhaps the most effective means of achieving such pressure, there is surprisingly little empirical research linking stock price outcomes to movement success. Here, we use Qualitative Comparative Analysis and examine 35 labor strikes to determine if the ability of the union to negatively impact stock price affected their ability to win new gains for members (or, to prevent concessions). Our findings reveal that it is the characteristics of the targeted firm, not the actions of the unions themselves, that is most closely associated with success.     

Wealth transfer receipt and later life wealth

Wealth ownership is highly concentrated in the U.S. and this inequality may be reproduced in subsequent generations through wealth transfers. Yet we do not know how households respond to the receipt of a wealth transfer and whether time amplifies the initial benefit of a wealth transfer. Using the Survey of Consumer Finances, we test whether wealth transfer recipients gain an advantage that cumulates with time. We find that the positive association between transfer amount and present net worth weakens as time elapsed since transfer receipt increases. The larger the wealth transfer, the more its association with net worth is diminished by time since transfer receipt. Though wealth transfers provide recipients with a significant initial advantage, households appear to adapt to wealth transfer receipt by some combination of reduced savings and increased consumption. We demonstrate an association between receiving a larger wealth transfer and one type of increased consumption, gift-giving.     

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.