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The circumstances of the author's discovery of the median voter theorem and the steps which led from there to his Theory of Committees and Elections are set out. His theory is presented in the form of the `statistical thesis' that the best choice procedure selects the option which `on average' is highest on the committee members' schedules. As there is more than one concept of average, so there is more than one acceptable committee procedure. The author's way of proceeding is compared and contrasted with Arrow's.

We have already considered the election of a single candidate to represent a constituency. Now we turn to the problem of choosing the group of representatives who will best reflect the political opinions held throughout a country or constituency. The desirability of proportional representation, ceteris paribus, we take to be self-evident; a change in the electoral system that makes the legislative bodies more truly reflect the citizens' opinions will certainly be desirable, provided the party system and the system of cabinet government remain as effective after the change as they had been before. Of course, the source of difficulty, the opponents of proportional representation would add, is that when proportional representation is introduced other things do not remain the same: instead a degeneration of the party and cabinet system sets in.These "dynamic changes" include alterations in party structure, a heightening or lessening of the political interest of the voters, alterations in the type of persons who stand for Parliament, new problems of cabinet formation, and increased or lesser control by the electorate over the course of government. And we readily concede that these are the aspects of the problem that it is most important to investigate to decide whether proportional representation would, in practice, do good or harm. The present paper will make no reference to them, and is not, indeed, much concerned to answer the broad question of whether proportional representation would, in any particular circumstances, be a good thing or a bad thing. A proper scientific procedure permits the treatment in isolation of particular aspects of each wider problem; and our concern is with the "statics" of the problem. (We only consider one or two small dynamic changes which are intimately connected with the course of the argument.)

Which candidate ought to be elected in a single-member constituency if all that we take into account is the order in which each of the electors ranks the various candidates? The most reasonable answer, I think, is that that candidate ought to be elected who, on the whole or on the average, stands highest on the electors' schedules of preferences.At the very outset of the argument we try to move from the is to the ought and to jump the unbridgeable chasm between the universe of science and that of morals. Some discussion of this step should be given, even though it does no more than point out the assumptions under which the jump is made.We assume that, in a constituency which is to elect a single member, we know the order in which the candidates are ranked on the schedule of preferences of each elector. If the electors had only been allowed to cast a single vote and the record of this was all the information at our disposal, inevitably, I think, we would have to conclude that the candidate most deserving of election was the one with the greatest number of first-preference votes. As against this, however, our assumption will be that each elector expresses his attitude to each of the candidates in the field, and that we have this record of the electors' attitudes.