In this paper we characterize choice behaviour that picks the second largest element if there is a uniquely largest; otherwise, the largest elements are picked. Having defined our choice function, we offer a complete characterization of the latter in terms of pure choice function conditions. Similarities to and divergences from conventional choice theory are explained. We discuss the motivations underlying our exercise and provide several examples for the axiomatized choice behaviour.
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Helpful discussions with R. Deb, M. R. Johnson, P. K. Pattanaik, A. Sen, Y. Xu, and participants at a seminar on individual and social choice in Osnabrück, November 1993, are gratefully acknowledged. One of the authors wishes to thank the British Council and the University of Osnabrück for financial support. We are also grateful to the Department of Economics at Queen Mary and Westfield College, London, for its hospitality.