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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.

Borda's vote method was used by the French Academy from 1796 to 1803 when Napoleon got it abolished. In the laws and regulations of the Academy there are stipulations regarding the election of new members. The practice is demonstrated by some examples from the protocols. In fact, Borda presented two vote methods which he showed would give the same conclusion. The method which has not been in the limelight proves to be the same one as is used for selecting the best player in chess tournaments.

In a letter to the author Arrow makes an important recognition regarding the question of irrelevant alternatives by expressing his view that alternatives which are not among the superior ones can, in fact, affect the choice of the best alternative (it is a question of choosing the best chess player).