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Choice Functions And Upper Choice Functions

Author

Listed:
  • 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)

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.

Suggested Citation

  • John N. Mordeson & Terry D. Clark & Jennifer M. Larson & Mark J. Wierman, 2008. "Choice Functions And Upper Choice Functions," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 177-190.
    • Handle: RePEc:wsi:nmncxx:v:04:y:2008:i:02:n:s179300570800101x
    DOI: 10.1142/S179300570800101X
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