CHOICE FUNCTIONS AND UPPER CHOICE FUNCTIONS

John N. Mordeson (), Terry D. Clark (), Jennifer M. Larson () and Mark J. Wierman ()
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John N. Mordeson: Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA
Terry D. Clark: Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA
Jennifer M. Larson: Department of Government, Harvard University, Cambridge Massachusetts 02138, USA
Mark J. Wierman: Department of Computer Science, Creighton University, Omaha, Nebraska 68178, USA

New Mathematics and Natural Computation (NMNC), 2008, vol. 04, issue 02, 177-190

Abstract: Choice functions play an important role in political science. We present structure results of choice functions following an algebraic approach. It is logical that rational political actors are not able to perceive every alternative in a set of alternativesX. They may also choose to exclude some alternatives from consideration. LetSbe a subset ofXthat some set of political actors are not able to perceive. Then the complementX\Sis the set comprising those alternatives considered in the decision process. IfCis a choice function onX, thenC(X\S)are the alternatives chosen andX\C(X\S)are those that are not. We are thus led to the concept of an upper choice function. We define upper choice functions in terms of choice functions and we give relationships between them.

Keywords: Choice function; C-subspace; C-basis; upper choice functions; conditions α; β; γ; Arrow; WARP; path independence (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S179300570800101X

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