Are Choice Rationality and Social Consistency the Two Faces of a Same Coin?

This paper aims at proving that a society cannot be consistent if it is constituted of decision-makers who are not rational. For that purpose, we propose to justify social interactions by means of individual preferences. More precisely, we establish that individual choice rationality is logically equivalent, i.e. is a necessary and sufficient condition, to social consistency--when individual rationality means that preferences are completely ordered (as in standard microeconomics) and social consistency that there is a one-to-one mapping from the list of actual communities to the underlying particular interaction (unique, reflexive and symmetric) between all individuals of the society