6 - Satisficing
Published online by Cambridge University Press: 05 January 2012
Summary
Two souls, alas, do dwell within his breast; The one is ever parting from the other.
– Goethe Faust, Part IOptimization is the sine qua non of decision theory. The list of contributors to the concept is a veritable who's who of mathematics that includes Fermat, Newton, Gauss, Euler, Lagrange, Fourier, Edgeworth, Pareto, von Neumann, Wiener, Dantzig, Kantorovich, Bellman, Kalman, Arrow, Nash, and others. Indeed, optimization has played a central role in virtually every decision-making procedure and enjoys uncontested mathematical respectability. As Euler noted, “Since the fabric of the world is the most perfect and was established by the wisest Creator, nothing happens in this world in which some reason of maximum or minimum would not come to light” (cited in Polya, 1954).
With the exception of work based on the results of Edgeworth, Pareto, von Neumann, Arrow, and Nash, however, optimization theory has focused on the behavior of a single decision maker. Indeed, the concept of optimization is an individual concept. In group scenarios, the issues become more complex: If a group wishes to optimize, it must act as if it were a single entity. As Arrow's (1951) impossibility theorem establishes, however, it is not generally possible to define a preference ordering for a group in terms of the preference orderings of its individual members. Consequently, the concept of optimization in group settings is often expressed through such concepts as equilibrium, nondominance, and social welfare, none of which enjoy the type of global superlativeness that the term optimization typically connotes.
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- Theory of Conditional Games , pp. 139 - 173Publisher: Cambridge University PressPrint publication year: 2011