The Condorcet Method
SIR,—The 'brace ot American academics' must concede either 'Anglo-Saxon arrogance' or, what is worse, ignorance, with respect to M. Guilbaud's formula for the percentage of cyclical majorities. Now that the SPICIAIOR (January 14) has called it to our attention, however, we don't really feel greatly enlightened. M. Guilbaud does not give the deriva- tion of his equation, and we have been unable to work it out for ourselves. Further, his formula, giving a limit of 8.7 per cent for the proportion of cycles, is in conflict with the results we obtained from our computers. With three candidates we obtained more than 8.7 per cent cycles for twenty-one, twenty- three, .twenty-five, twenty-seven and twenty-nine voters: The possibility of sampling error in our results does exist, but we doubt that his figure is the actual limit of the series.
The editor, like so many other people, would like to find the general function himself. One thing that can be said for certain is that the formula given by Guilbaud is not truly general. It applies only to the situation in which there are three candi- dates or proposals. If the number is larger than three, then the equation gives a negative answer. The problem thus is still an open one even if M. Gail- baud's results are accepted. We will try to beat the editor of the SPECTATOR to the answer, but we must admit that our work so far has not given us any great confidence in our success.
oottooN TEILF_OCIC Col IN CAMPBELL University of Virginia. Charlottesville. Va