Abstract
The present model of individual decision is based on the assumption according to whichthe agent's preferences over sets of alternatives are stochastic in a multiself sense and leadto choice probabilities describing past decisions. Then, using this recorded information inan optimal way, it is first shown to imply some auto-experiment which modifies the termsof the current choice. Actually, the relative desirability of alternatives in competition issupposed to be learnt by the agent step by step. Hence, competition among alternatives canhere be formalized in terms of contests which may involve alternatives and/or bundles ofalternatives, and in which only chosen bundles (decisions) are observed. The specific natureof desirability is left unspecified, and is treated simply as an abstract measure which isincreased monotonically for decisions and left unaltered for all others. Under the keyassumption that the intensification of chosen alternatives' desirability increases with thedesirability of the unchosen bundles, the main result is to establish the existence of certainbiased competitions which are uniformly informative in the sense that the agent's confidence(subjective probability) about the best alternative is increased regardless of the decision ofthe competition (where no competition is allowed to end in a draw). In addition, it is shownthat when there is a highly frequent alternative (called a hard alternative) with sufficientlystrong desirability relative to all other alternatives, there exists no biased competition favoringless frequent alternatives which are uniformly informative.
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Billot, A. Autobiased choice theory. Annals of Operations Research 80, 85–103 (1998). https://doi.org/10.1023/A:1018936503162
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DOI: https://doi.org/10.1023/A:1018936503162