Autobiased choice theory

The present model of individual decision is based on the assumption according to which the agent’s preferences over sets of alternatives are stochastic in a multiself sense and lead to choice probabilities describing past decisions. Then, using this recorded information in an optimal way, it is first shown to imply some auto-experiment which modifies the terms of the current choice. Actually, the relative desirability of alternatives in competition is supposed to be learnt by the agent step by step. Hence, competition among alternatives can here be formalized in terms of contests which may involve alternatives and/or bundles of alternatives, and in which only chosen bundles (decisions) are observed. The specific nature of desirability is left unspecified, and is treated simply as an abstract measure which is increased monotonically for decisions and left unaltered for all others. Under the key assumption that the intensification of chosen alternatives' desirability increases with the desirability of the unchosen bundles, the main result is to establish the existence of certain biased 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 of the competition (where no competition is allowed to end in a draw). In addition, it is shown that when there is a highly frequent alternative (called a hard alternative) with sufficiently strong desirability relative to all other alternatives, there exists no biased competition favoring less frequent alternatives which are uniformly informative.