The social choice theory has focused in the past on the problem of devising methods to determine how individual preferences are transformed into collective ones. In some investigations, scholars provided methods for expressing the social choice function, that, given a set of individual preferences, computes the resulting collective choice. Other studies focused on determining under which conditions the social choice function is efficiently computable. In this paper, we concentrate on the specific case of collective decisions, when we assume that the agents are rational: they do not express random preferences, and they do not make random choices. In this context, we define four logical problems derived and study their computational complexity: (1) Determining the rationality of a given choice, (2) Establishing a possible rational maximal subset of a given choice, (3) Computing the votes on a rational proposal, and (4) Determining a priori the winning conditions of a given rational choice.
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