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.