The novel scheme for proportional representation developed by Professor Steven J. Brams (PS, Summer, 1970, pp. 321–335) has at least two major advantages in comparison with most electoral plans:

1 The plan permits the voter to give effect to the intensity of his support for individual candidates. Each voter has at his disposal a number of votes equal to the number of offices to be filled, but, assuming that fractions are not allowed, the voter has as many alternative means for distributing his votes as there are mathematical combinations for the set of numbers represented by the number of votes to be cast. For example, let us assume that six seats on the APSA board are to be filled. The voter may cast his six votes, one for each of six candidates, or he may cast six votes for a single candidate, or he may distribute his votes equally or unequally among several candidates.

2 Professor Brams presents a mathematical analysis to demonstrate that the plan under specified conditions facilitates representation of differing interests, including minority interests, in rough proportion to their numerical strengths, provided the interests are effectively organized, have accurate information as to the voting strengths of the competing interests, and are able to make and implement maximizing choices regarding the voting decisions. As in gaming, the aim of such organized effort is to maximize the chances of the opposition electing only a minimum number of its chosen candidates. For example, if three candidates are to be elected, a minority group able to poll a united vote of 26 per cent is able to muster 3 x 26 = 78 votes. If the other 74 per cent of the votes are united in organized opposition, they may divide their 3 x 74 = 222 votes in the following alternative arrangements:

a) 222 votes for one candidate.

b) 111 votes for each of two candidates.

c) 74 votes for each of three candidates.

It is evident that the minority, if able to concentrate its effort behind a single candidate (3 x 26 = 78 votes), will elect its candidate in spite of any strategy which the majority interest may choose.