The instability of instability
By: Craig A. Tovey
Contributors: Naval Postgraduate School (U.S.). Dept. of Operations Research
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1991
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 40
Subjects: Decision theory; Decision making
Other titles: NPS-OR-91-15.
Description: Democratic simple majority voting is perhaps the most widely used method of group      decision making in our time. Current theory, based on instability theorems, predicts that      a group employing this method will almost always fail to reach a stable conclusion.      There is one case that the classical instability theorems do not treat: an even number of      voters in 2 dimensions. We resolve this remaining case, proving that instability occurs      with probability converging rapidly to 1 as the population increases. But empirical      observations do not support the gloomy predictions of the instability theorems. We      show that the instability theorems are themselves unstable in the following sense: if the      model of voter behavior is altered however slightly to incorporate any of several      plausible characteristics of decision-making, then the instability theorems do not hold      and in fact the probability of stability converges to 1 as the population increases, when      the population is sampled from a centered distribution. The assumptions considered are:      a cost of change; bounded rationality; perceptual thresholds; a cost of uncertainty; a      discrete proposal space, and others. One consequence of this work is to render precise      and rigorous the solution proposed by Tullock (63,64) and refined by Arrow (2) to the      impossibility problem. The stability results all hold for arbitrary dimension, and      generalize to establish a tradeoff between the characteristics and the degree of      noncenteredness of a population. As a by-product of the analysis, we establish the      statistical consistency of the sample yolk radius.
Notes: Title from cover.

"NPS-OR-91-15."

"May 1991."

AD A236 902.

Includes bibliographical references (p. 35-40).

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