European Journal of Political Economy 7 (1991) 191-198. North-Holland Choice functions on pairwise disjoint domains and G-rationalizability Stefano Vannucci* Dipartimento di zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Economia Politica, Uniuersitci di Siena, 53100 Siena, Italy Accepted for publication January 1991 It is shown that any choice function defined on a pairwise disjoint domain is fully G-rationalizable by many distinct total preorderings. Some implications of this fact are discussed at length. Examples of plausible pairwise disjoint domains are provided. 1. Introduction Choice functions do represent the choice behaviour of decision-making units, both individual and collective. A thorough analysis of choice functions was at first motivated by the theory of revealed preference for competitive consumers, pioneered by Samuelson in the late ’30s. Substantial contribu- tions originating from the other main source of interest in choice functions, namely social choice theory, only started surfacing much later, in the late ’60s. Perhaps as a result of this history, the notion of (full) rationality for a choice function has been identified with (full) G-rationalizability, i.e., with maximization with respect to a fixed binary relation (total preordering). The aim of this note is to show that the relevance of such a notion of rationality is highly sensitive to the specification of the choice function’s domain. Namely, even full rationality-as-consistent-maximization trivializes whenever the domain of the relevant choice function is pairwise disjoint. It follows that, whenever a relevant class of choice problems turns out to have a pairwise disjoint domain, the traditional view of rationality-as-consistency does not put any restriction whatsoever on observable behaviour and has therefore - under the most favourable interpretation - to be supplemented with a richer theory. The final section of this paper is devoted to the presentation of some choice problems which conceivably admit a pairwise disjoint domain. In particular, the first example consists in an agenda *Currently visiting the Department of Economics, Georgetown University, Washington, D.C. 20057. USA. 01762680/91/303.50 0 1991-Elsevier Science Publishers B.V. (North-Holland)