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.     

Complementarity of behavioral biases

I investigate the complementarity of behavioral biases in a simple investment problem. The agent has incomplete knowledge about the correlation between fitness and the decision environment. Nature endows the agent with a decision procedure so that the induced action can reflect this correlation. I show that the agent with this decision procedure always exhibits (i) present biased time preference, (ii) distorted beliefs, and (iii) cognitive dissonance. The three biases are complements and the absence of one of them destroys the value of the other two. The decision procedure also provides insights into the non-fungibility of savings.     

The likelihood of various stock market return distributions, part 1: Principles of inference

This is the first of two articles which apply certain principles of inference to a practical, financial question. The present article argues and cites arguments which contend that decision making should be Bayesian, that classical (R. A. Fisher, Neyman-Pearson) inference can be highly misleading for Bayesians as can the use of diffuse priors, and that Bayesian statisticians should show remote clients with a variety of priors how a sample implies shifts in their beliefs. We also consider practical implications of the fact that human decision makers and their statisticians cannot fully emulate Savage's rational decision maker.     

Are beliefs a matter of taste? A case for objective imprecise information

We argue, in the spirit of some of Jean-Yves Jaffray’s work, that explicitly incorporating the information, however imprecise, available to the decision maker is relevant, feasible, and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker’s attitude toward imprecise information.     

Instrumental rationality and cognitive rationality

Beside instrumental rationality, concerned with consistency between available means and pursued objectives, cognitive rationality, concerned with consistency between current beliefs and detained information, is nowadays bursting in economic theory. For an individual decision, the two notions are expressed structurally in similar forms, but they heavily interact in the deliberation process, especially when the agent is searching relevant information on his environment and his own determiners. In a game framework, the players' representations are formalized in a more and more sophisticated way, and are closely interwoven with their preferences in contemporary equilibrium notions as well as in selection between corresponding equilibrium points.     

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.     

Causality in the logic of decision

In recent years there has been an active debate between proponents of two different models of rational decision. One model is evidential decision theory, which is characterized by the fact that it holds the principle of maximizing expected utility to be appropriate whenever the states are probabilistically independent of the acts. The other model, causal decision theory, holds that the principle of maximizing expected utility is appropriate whenever the states are causally independent of the acts. The proponents of evidential decision theory include Richard Jeffrey and Ellery Eells, who claim that evidential decision theory has significant advantages over causal decision theory. In this paper I discuss the two main advantages which have been claimed for evidential decision theory, and show that in fact evidential decision theory does not possess either of these advantages.     

Negotiation and Defeasible Decision Making

In economically meaningful interactions negotiations are particularly important because they allow agents to improve their information about the environment and even to change accordingly their own characteristics. In each step of a negotiation an agent has to emit a message. This message conveys information about her preferences and endowments. Given that the information she uses to decide which message to emit comes from beliefs generated in previous stages of the negotiation, she has to cope with the uncertainty associated with them. The assessment of the states of the world also evolves during the negotiation. In this paper we analyze the intertwined dynamics of beliefs and decision, in order to determine conditions on the agents that allow them to reach agreements. The framework for decision making we consider here is based on defeasible evaluation of possibilities: an argument for a choice defeats another one if it is based on a computation that better uses all the available information.     

Effortful Bayesian updating: A pupil-dilation study

Journal of Risk and Uncertainty - When confronted with new information, rational decision makers should update their beliefs through Bayes’ rule. In economics, however, new information often...     

A Theory of Rational Choice under Ignorance

This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called `Simultaneous Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons.     

Re-examining the law of iterated expectations for Choquet decision makers

Yoo (Economic Letters 37:145–149, 1991) argues that the law of iterated expectations must be violated if the probability measure of a Choquet decision maker is non-additive. In this article, we prove the positive result that the law of iterated expectations is satisfied for Choquet decision makers whenever they update their non-additive beliefs in accordance with the Sarin and Wakker (Journal of Risk and Uncertainty 16:223–250, 1998) update rule. The formal key to this result is the act-dependence of the Sarin–Wakker update rule, which does not hold for the update rules considered by Yoo (1991).     

Residential Respite Care: The Caregiver's Last Resort

Understanding the beliefs that caregivers of people with dementia have in regard to the use of residential respite may inform strategies to address low service utilisation. In this article, the application of theory in qualitative research with 36 caregivers provides insight into why most delay service use. Although some believe that service use may increase caregiving longevity, others position service use in conflict with normative values, and may hold beliefs that negative outcomes will result from utilisation. To address caregivers' beliefs to support service use, improvements are required to service promotion, as well as to models of care.     

Residential respite care: the caregiver's last resort

Understanding the beliefs that caregivers of people with dementia have in regard to the use of residential respite may inform strategies to address low service utilisation. In this article, the application of theory in qualitative research with 36 caregivers provides insight into why most delay service use. Although some believe that service use may increase caregiving longevity, others position service use in conflict with normative values, and may hold beliefs that negative outcomes will result from utilisation. To address caregivers' beliefs to support service use, improvements are required to service promotion, as well as to models of care.     

Putting culture back into acculturation: Identifying and overcoming gaps in the definition and measurement of acculturation

The concept of acculturation is widely used in the health and social sciences to explain various health and behavioral outcomes. A review of the literature highlights weaknesses in current acculturation research including the failure to ground the concept in a theory of culture, failure to specify the pathways through which acculturation impacts on outcomes and reliance on methodological tools that do not measure the core construct of interest. Building on cognitive and evolutionary anthropological theories and methods of measuring the distribution of cultural beliefs, we suggest that a research program focused on acculturation needs to initially aim at measuring beliefs, attitudes, and norms, and not on behavior. Researchers should empirically examine the distribution of beliefs across presumed cultural groups, and specify how these might impact on outcomes of interest. By parceling beliefs as distinct from behavior, our approach advances culture as but one possible hypothesis to account for outcomes.     

Great Expectations. Part I: On the Customizability of Generalized Expected Utility

We propose a generalization of expected utility that we call generalized EU (GEU), where a decision maker’s beliefs are represented by plausibility measures and the decision maker’s tastes are represented by general (i.e., not necessarily real-valued) utility functions. We show that every agent, “rational” or not, can be modeled as a GEU maximizer. We then show that we can customize GEU by selectively imposing just the constraints we want. In particular, we show how each of Savage’s postulates corresponds to constraints on GEU.     

The Processual Origins of Social Representations

Referring to some perceived difficulties in social representation theory, this paper offers an account of the genesis of social representations in a theory of valuing. Drawing on influential but previously largely unconnected ideas from interactionist theory, personal construct theory, and Rokeach's theory of values, it is suggested that a process of valuing can be presented as a crucial link between the individual and social levels of analysis, a present theoretical disjuncture that has been of concern to some commentators in social representations and widespread beliefs.     

Gender, Status, and Leadership

More than a trait of individuals, gender is an institutionalized system of social practices. The gender system is deeply entwined with social hierarchy and leadership because gender stereotypes contain status beliefs that associate greater status worthiness and competence with men than women. This review uses expectation states theory to describe how gender status beliefs create a network of constraining expectations and interpersonal reactions that is a major cause of the "glass ceiling." In mixed-sex or gender-relevant contexts, gender status beliefs shape men's and women's assertiveness, the attention and evaluation their performances receive, ability attributed to them on the basis of performance, the influence they achieve, and the likelihood that they emerge as leaders. Gender status beliefs also create legitimacy reactions that penalize assertive women leaders for violating the expected status order and reduce their ability to gain complaince with directives.     

信仰及其秩序的构成——中国信仰社会学的理论视角

对于中国历史、文化的"和谐"现象及其概念理解,信仰问题的理解与认识,乃是其中的关键。中国信仰及其社会实践方式,与中国社会历史、文化秩序的和谐建构紧密相关。实际上,"和谐"既可以指一种价值目标,也可以是一种社会现实,同时也是一种信仰方式;而基于某种信仰关系、道德秩序、政治秩序、权力秩序等层面的和谐建构,则是社会、文化和谐的基本要素。因此,从信仰社会学的理论视角,来探讨中国文化和谐秩序中诸种信仰关系在和谐秩序构成中的具体地位及其作用,有利于把握中国社会与中国信仰双重变迁的某些规律。