Sharing beliefs and the absence of betting in the Choquet expected utility model

Choquet expected utility maximizers tend to behave in a more “cautious” way than Bayesian agents, i. e. expected utility maximizers. We illustrate this phenomenon in the particular case of betting behavior. Specifically, consider agents who are Choquet expected utility maximizers. Then, if the economy is large, Pareto optimal allocations provide full insurance if and only if the agents share at least on prior, i. e., if the intersection of the core of the capacities representing their beliefs is non empty. In the expected utility case, this is true only if they have a common prior. Received: July 2000; revised version: May 2001     

Inductive Inference: An Axiomatic Approach

A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of finitely many past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality–case pairs, as follows. Given a memory, each eventuality is ranked according to the sum of the numbers in its row, over cases in memory. The number attached to an eventuality–case pair can be interpreted as the degree of support that the past case lends to the plausibility of the eventuality. Special instances of this result may be viewed as axiomatizing kernel methods for estimation of densities and for classification problems. Interpreting the same result for rankings of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with rankings by the likelihood functions.     

Probabilities as Similarity‐Weighted Frequencies

A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the belief formation process follows a simple formula: beliefs are a similarity‐weighted average of the beliefs induced by each past case.     

No-betting Pareto under ambiguity

It has been argued that Pareto-improving trade is not as compelling under uncertainty as it is under certainty. The former may involve agents with different beliefs, who might wish to execute trades that are no more than betting. In response, the concept of no-betting Pareto dominance was introduced, requiring that putative Pareto improvements must be rationalizable by some common probabilities, even though the participants’ beliefs may differ. In this paper, we argue that this definition might be too narrow for use when agents are not Bayesian. Agents who face ambiguity might wish to trade in ways that can be justified by common ambiguity, though not necessarily by common probabilities. We accordingly extend the notion of no-betting Pareto dominance to characterize trades than are “no-betting Pareto” ranked according to the maxmin expected utility model.

     

Making statements and approval voting

We assume that people have a need to make statements, and construct a model in which this need is the sole determinant of voting behavior. In this model, an individual selects a ballot that makes as close a statement as possible to her ideal point, where abstaining from voting is a possible (null) statement. We show that in such a model, a political system that adopts approval voting may be expected to enjoy a significantly higher rate of participation in elections than a comparable system with plurality rule.     

The predictive role of counterfactuals

We suggest a model that describes how counterfactuals are constructed and justified. The model can describe how counterfactual beliefs are updated given the unfolding of actual history. It also allows us to examine the use of counterfactuals in prediction, and to show that a logically omniscient reasoner gains nothing from using counterfactuals for prediction.     

What are axiomatizations good for?

Theory and Decision - Do axiomatic derivations advance positive economics? If economists are interested in predicting how people behave, without a pretense to change individual decision making, how...     

ACADEMIC ADMISSIONS STANDARDS: IMPLICATIONS FOR OUTPUT,DISTRIBUTION, AND MOBILITY

We examine the trade‐offs implicit in academic admissions standards when students are charged cost‐based tuition and offered loans that remove liquidity constraints. Lowering entry requirements while holding graduation requirements fixed increases aggregate output and promotes a more equal distribution of wages, but reduces relative income mobility and diminishes the scope for affirmative action. Lowering admissions standards while raising graduation requirements, so that the number of graduates remains constant, has little direct effect on output, distribution, or mobility, but again reduces the scope for affirmative action. Income‐based affirmative action offers a better trade‐off between output and relative mobility than income‐neutral admissions. (JEL: D31, H42, I23, I28, J24)     

Quantitative Assessment of the Risk of Release of Foot‐and‐Mouth Disease Virus via Export of Bull Semen from Israel

Various foot‐and‐mouth disease (FMD) virus strains circulate in the Middle East, causing frequent episodes of FMD outbreaks among Israeli livestock. Since the virus is highly resistant in semen, artificial insemination with contaminated bull semen may lead to the infection of the receiver cow. As a non‐FMD‐free country with vaccination, Israel is currently engaged in trading bull semen only with countries of the same status. The purpose of this study was to assess the risk of release of FMD virus through export of bull semen in order to estimate the risk for FMD‐free countries considering purchasing Israeli bull semen. A stochastic risk assessment model was used to estimate this risk, defined as the annual likelihood of exporting at least one ejaculate of bull semen contaminated with viable FMD virus. A total of 45 scenarios were assessed to account for uncertainty and variability around specific parameter estimates and to evaluate the effect of various mitigation measures, such as performing a preexport test on semen ejaculates. Under the most plausible scenario, the annual likelihood of exporting bull semen contaminated with FMD virus had a median of 1.3 * 10^?7 for an export of 100 ejaculates per year. This corresponds to one infected ejaculate exported every 7 million years. Under the worst‐case scenario, the median of the risk rose to 7.9 * 10^?5, which is equivalent to the export of one infected ejaculate every 12,000 years. Sensitivity analysis indicated that the most influential parameter is the probability of viral excretion in infected bulls.