VOTING PARADOXES:

11 John Bull. Let us now resume our discussion of the electoral system, Socrates. Socrates. It is indeed an honour for me to discuss this interesting matter with so worthy a representative of this great nation, and I hope my remaining perplexities will be resolved. You will recall, Mr. Bull, that during our previous conversation we established that it is possible in principle for the most unpopular candidate to be elected. You assured me, however, that this would not occur in practice, and you undertook to find some evidence with which to demonstrate this point. I.E. I have some bad news, Socrates. I have scrupulously checked my calculations, and I find that this absurd possibility may well have occurred in practice in a British General Election. S. What evidence led you to this remarkable conclusion? I.B. The evidence concerns the order of preference in which a voter places the candidates. Butler and Stokes, in their book Political Change in Britain, report the results of a survey based upon a very large, self-weighting, multi-stage, stratified sample of the adult population of England, Wales and Scotland shortly after the 1966 General Election. Of those who voted Conservative, 76 per cent. preferred Liberal to Labour; of those who voted Labour, 74 per cent. preferred Liberal to Conservative; and among Liberal voters, 56 per cent. preferred Labour to Conservative. I have assumed that these percentages hold for voters within any particular constituency. S. Is it possible to make that assumption? J.B. In statistical work, Socrates, one is entitled to make whatever plausible assumptions are required. S. I see. J.B. With this data we can estimate the number of voters who considered a particular candidate to be the worst choice in any con-