Estimating Subjective Probabilities

Subjective probabilities play a role in many economic decisions. There is a large theoretical literature on the elicitation of subjective probabilities, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover subjective probabilities, but stresses the need to make strong auxiliary assumptions or "calibrating adjustments" to elicited reports in order to recover the latent probability. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We illustrate how the joint estimation of risk attitudes and subjective probabilities using structural maximum likelihood methods can provide the calibration adjustments that theory calls for. This allows the observer to make inferences about the latent subjective probability, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective beliefs assuming that choices are made consistently with expected utility theory or rank-dependent utility theory. Inferred subjective probabilities are significantly different when calibrated according to either theory, thus showing the importance of undertaking such exercises. Our findings also have implications for the interpretation of probabilities inferred from prediction markets.

Words or numbers? Communicating probability in intelligence analysis

Intelligence analysis is fundamentally an exercise in expert judgment made under conditions of uncertainty. These judgments are used to inform consequential decisions. Following the major intelligence failure that led to the 2003 war in Iraq, intelligence organizations implemented policies for communicating probability in their assessments. Virtually all chose to convey probability using standardized linguistic lexicons in which an ordered set of select probability terms (e.g., highly likely) is associated with numeric ranges (e.g., 80-90%). We review the benefits and drawbacks of this approach, drawing on psychological research on probability communication and studies that have examined the effectiveness of standardized lexicons. We further discuss how numeric probabilities can overcome many of the shortcomings of linguistic probabilities. Numeric probabilities are not without drawbacks (e.g., they are more difficult to elicit and may be misunderstood by receivers with poor numeracy). However, these drawbacks can be ameliorated with training and practice, whereas the pitfalls of linguistic probabilities are endemic to the approach. We propose that, on balance, the benefits of using numeric probabilities outweigh their drawbacks. Given the enormous costs associated with intelligence failure, the intelligence community should reconsider its reliance on using linguistic probabilities to convey probability in intelligence assessments. Our discussion also has implications for probability communication in other domains such as climate science

A quantum-like model for complementarity of preferences and beliefs in dilemma games

We propose a formal model to explain the mutual influence between observed behavior and subjects' elicited beliefs in an experimental sequential prisoner's dilemma. Three channels of interaction can be identified in the data set and we argue that two of these effects have a non-classical nature as shown, for example, by a violation of the sure thing principle. Our model explains the three effects by assuming preferences and beliefs in the game to be complementary. We employ non-orthogonal subspaces of beliefs in line with the literature on positive-operator valued measure. Statistical fit of the model reveals successful predictions

Measuring Subjective Expectations in Developing Countries: A Critical Review and New Evidence

The majority of economic decisions taken by individuals are forward looking and thus involve their expectations of future outcomes. Understanding the expectations that individuals have is thus of crucial importance to designing and evaluating policies in health, education, finance, migration, social protection, and many other areas. However, the majority of developing country surveys are static in nature and do not contain information on the subjective expectations of individuals. Possible reasons given for not collecting this information include fears that poor, illiterate individuals do not understand probability concepts, that it takes far too much time to ask such questions, or that the answers add little value. This paper provides a critical review and new analysis of subjective expectations data from developing countries and refutes each of these concerns. The authors find that people in developing countries can generally understand and answer probabilistic questions, such questions are not prohibitive in time to ask, and the expectations are useful predictors of future behavior and economic decisions. The paper discusses the different methods being tried for eliciting such information, the key methodological issues involved, and the open research questions. The available evidence suggests that collecting expectations data is both feasible and valuable, suggesting that it should be incorporated into more developing country surveys.Subjective Expectations; Survey Methodology; Development.

Subjective expectations in the context of HIV/AIDS in Malawi

In this paper we present a newly developed interactive elicitation methodology for collecting probalistic in expectations in a developing country context with low levels of literacy and numeracy, and we evaluate the feasibility and success of this method for a wide range of outcomes in rural Malawi. We find that respondents' answers about their subjective expectations take into account basic properties of probabilities, and vary meaningfully with observable characteristics and past experience. From a substantive point of view, the elicited expectation's indicate that individuals are generally aware of differential risks. For example, individuals with lower incomes and less land rightly feel at greater risk of financial distress than people with higher socioeconomic status (SES), and people who are divorced or widowed rightly feel at greater risk of being infected with HIV than currently married individuals. Meanwhile many expectations - including the probability of being currently infected with HIV - are well-calibrated compared to actual probabilities, but mortality expectations are substantially overestimated compared to life table estimates. This overestimation maylead individuals to underestimate the benefits of adopting HIV risk-reduction strategies. The skewed distribution, of expectations about condom use also suggests that a small group of innovators are the forerunners in the adoption of condoms within marriage for HIV prevention. © 2009 Adeline Delavande & Hans-Peter Kohler

Gifts as Economic Signals and Social Symbols

Gift-giving has often puzzled economists, especially because efficient gifts-like cash or giving exactly what a person asks for-seem crass or inappropriate. It is shown in a formal game-theoretic model that gifts serve as "signals" of a person's intentions about future investment in a relationship, and inefficient gifts can be better signals. Other explanations for the inefficiency of gift giving are advanced, and some stylized facts about gift-giving practices are described (many of which are consistent with the signaling view of gifts)