On the fundamental thought behind voting rules
The theme is Arrow's requirement in his theorem of 1951 on methods for group choice, that the choice be independent of irrelevant alternatives. The attention is drawn to (1) his own explanation of this requirement in 1972, which is a quite different understanding than has been discussed in the voluminous literature on the theorem, (2) that Arrow, in fact, in 1985 showed an understanding for how “irrelevant alternatives” might in a meaningful way influence the group choice, (3) that admittedly the border-line between irrelevant and relevant alternatives in Arrow's original statement is arbitrary, and (4) that Arrow, if he had observed the final thought in the origin of the group theory by Borda, which he admittedly did not, might have realized that Borda's method stringently estimates the relevance of each alternative for the result.
The author expresses his surprise that a theoretical conclusion based on an arbitrary fundament has been admired so long.
KeywordsTheoretical Conclusion Group Choice Irrelevant Alternative Fundamental Thought
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