Domain Closedness Conditions and Rational Choice
Series/Report no.Cahier de recherche #2005-21
The rationalizability of a choice function on an arbitrary domain under various coherence properties has received a considerable amount of attention both in the long-established and in the recent literature. Because domain closedness conditions play an important role in much of rational choice theory, we examine the consequences of these requirements on the logical relationships among different versions of rationalizability. It turns out that closedness under intersection does not lead to any results differing from those obtained on arbitrary domains. In contrast, closedness under union allows us to prove an additional implication.
BOSSERT, Walter et SUZUMURA, Kotaro, «Domain Closedness Conditions and Rational Choice», Cahier de recherche #2005-21, Département de sciences économiques, Université de Montréal, 2005, 19 pages.