Many in the scholarly and legal communities argue that, under straight voting, single-member districts allow minority voters to elect minority representatives more easily than do multimember districts.
All voters have the same number of votes as in the straight voting case (two in this example), but they have more options as to how they can distribute their votes among the candidates.(8)
In this article we examine theoretically and empirically both cumulative voting and straight voting in multimember district elections.
We show that the tendencies to plump votes in straight voting and to cumulate votes in cumulative voting are related directly to the conditional probabilities of which candidates, in the event of a tie, are likely to tie for the last seat rather than first place.
We consider the voting equilibria in multimember districts under straight voting and then under cumulative voting.
Our configuration also allows us to test the argument, presented earlier, that multimember districts with straight voting are biased against the election of minority candidates.(16)
In each election under straight voting, a voter can either abstain or cast one vote each for up to two candidates.
We can identify five possible equilibria in straight voting, labeled points 1, 2, 3, 4, and 5 in Figure 1 and summarized in Table 2.
The important conclusion from this discussion is that there are a number of straight voting equilibria in which the minority candidate is expected to be in a close three-way race and thus has a positive (and high) probability of being selected for one of the seats in the multimember district.
PROPOSITION 1: Under straight voting, the voting game results in voting equilibria that are consistent with two expected electoral outcomes: D[approximately equal to]R[much greater than]S and D[approximately equal to]R[approximately equal to]S.
As with straight voting, the less difference minority voters perceive between the two majority candidates, the more likely are equilibria to exist in which the minority candidate has a high probability of winning.