Abstract
The central question of this paper is whether a rational agent under uncertainty can exhibit ambiguity aversion (AA). The answer to this question depends on the way the agent forms her probabilistic beliefs: classical Bayesianism (CB) vs modern Bayesianism (MB). We revisit Schmeidler's coin-based example and show that a rational MB agent operating in the context of a "small world", cannot exhibit AA. Hence we argue that the motivation of AA based on Schmeidler's coin-based and Ellsberg's classic urn-based examples, is poor, since they correspond to cases of "small worlds". We also argue that MB, not only avoids AA, but also proves to be normatively superior to CB because an MB agent (i) avoids logical inconsistencies akin to the relation between her subjective probability and objective chance, (ii) resolves the problem of "old evidence" and (iii) allows psychological detachment from actual evidence, hence avoiding the problem of "cognitive dissonance". As far as AA is concerned, we claim that it may be thought of as a (potential) property of large worlds, because in such worlds MB is likely to be infeasible.
Highlights
Since 1961, year which Ellsberg introduced the concept of "ambiguity aversion" (AA) in the form of his well-known thought experiments, economists, psychologists and decision theorists have been trying to provide answers to the following two questions: (i) is AA empirically documented by means of formal experimentation and (ii) does AA violate the standard Bayesian conditions of rationality, or is it consistent with rationality when properly modi...ed?With respect to the ...rst question, Machina and Siniscalchi (2014) o¤er an extensive survey of the empirical literature that spans over a period of 50 years
As far as the second question is concerned, the main argument in favor of AA being consistent with rational probabilistic beliefs is the following: AA implies that probabilistic beliefs are not sophisticated, in the sense that they cannot be represented by a unique prior probability measure
If the Modern Bayesianism (MB) strategy is unrealistic within the Global Bayesianism (GB) framework, is it possible that there is another framework, say it Local Bayesianism (LB), within which the MB strategy is likely to work? Before we answer this question, let us ...rst describe, following Garber (1983) how LB might be de...ned: "Typically when scientists or decision makers apply Bayesian methods to the clari...cation of inferential problems, they do so in a much more restricted scope than global Bayesianism suggests, dealing only with the sentences and degrees of belief that they are concerned with, those that pertain to the problem at hand
Summary
Since 1961, year which Ellsberg introduced the concept of "ambiguity aversion" (AA) in the form of his well-known thought experiments (see Ellsberg 1961), economists, psychologists and decision theorists have been trying to provide answers to the following two questions: (i) is AA empirically documented by means of formal experimentation and (ii) does AA violate the standard Bayesian conditions of rationality, or is it consistent with rationality when properly modi...ed?. IB should not include any actual outcomes of the experiment or information about the objective chances (e.g. coin is fair) This information is speci...c information or relevant evidence and should be thought of as part of IS : The question of whether to allow both IB and IS or only IB to a¤ect the generation of the agent’s prior belief function is crucial for deciding whether AA is (or can be made) consistent with rationality. For the purposes of the present paper, a "world" is de...ned to be the domain (language) L of the agent’s probabilistic beliefs This domain includes all the hypotheses of interest Hi, all the relevant evidential statements Ej, together with the corresponding (logical) entailment relations between Hi and Ej. A world is small if (a) the number of hypotheses in L is small and (b) L does not evolve over time.
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