ther three States; and, under these circumstances,
the party will return 15 senators, the exact number to which it is
entitled. It may happen to be under the assumed proportion in only two
of the States and over in the other four, and that the party will get
one more senator than it is entitled to; but it is extremely improbable
that it will get two more, and virtually impossible that it will get
three more senators than its just proportion. Mr. M'Cay's conclusion
that proportional representation can only be used in electorates
returning an odd number of representatives is shown to be entirely
unwarranted. Equally fallacious is Professor Nanson's rebutting
statement that "scientific proportionalists recommend odd electorates."
While the number of States remains even, the mathematical chance of a
minority securing one-half of the representation is precisely the same
whether the States return an odd or an even number of senators. As a
matter of fact, the danger of a minority securing one-half of the
representation is much greater at the intermediate elections for the
Senate, when each State returns three senators, the reason being the
smaller field.

We have dwelt at some length on the preceding example, because it serves
to refute another error into which some of the proportionalists have
fallen. It is held that the unit of representation should be ascertained
by dividing the total votes, not by the number of seats, but by the
seats increased by one. This unit is generally known as the Droop quota,
having been proposed in a work published by Mr. H.R. Droop in 1869.
Since one vote more than one-half of the total votes is sufficient for
election in a single-seat electorate, it is argued that one vote more
than one-third suffices in a two-seat electorate, one vote more than
one-fourth in a three-seat electorate, and so on. The unit in a six-seat
electorate would be one-seventh of the votes instead of one-sixth, and
it is pointed out that by this means the whole six seats would be filled
by whole units, leaving an unrepresented residuum of one-seventh of the
votes divided between the two parties.

The error lies precisely as before in concentrating attention on one of
the electorates, and in neglecting the theory of probability. The Droop
quota introduces the condition that each party must pay a certain
minimum number of votes for each seat, and the real distinction is that,
instead of the minority and the majority having a