Utility representation via additive or multiplicative error functions

  • Authors:

  • Fuad Aleskerov;Yusufcan Masatlioĝlu

  • Affiliations:

  • Department of Economics, Bogaziçi University, Bebek, 80815 Istanbul, Turkey and Russian Academy of Sciences, Institute of Control Sciences, 65 Porfsoyuznaya St., Moscow 117806, Russia;Department of Economics, New York University, 269 Mercer Street, 7th Floor, New York, NY

  • Venue:
  • Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
  • Year:
  • 2003

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Abstract

The aim of this article is to study two distinct cases of utility representations where the error functions are assumed to display characteristics different than usual. These characteristics depend respectively on the feasible set and the two alternatives compared. Thus, in the first case the error functions are additive and in the second they are multiplicative.Our study of additive error functions shows that a very narrow class of choice functions can be represented in this form. Also we introduce a new class of binary relations, called simple semiorders, to fill the relevant gap in the literature. As for the case of multiplicative error functions, we study the cases where the error function is directly and inversely proportional to the utility function. We show that these classes of binary relations display characteristics of interval orders, semiorder, or regular semiorders depending on the case studied.