Previous investigations of strategic voting equilibria in mass elector
ates have looked only at single-member districts. I shall investigate
such equilibria in multimember districts operating under the single no
ntransferable vote system. What appear to be the most natural equilibr
ia conform to the M + 1 rule, according to which strategic voting in M
-seat districts produces exactly M + 1 vote-getting candidates in equi
librium, any others having their support totally undercut. This result
provides the beginnings of a formal underpinning for Reed's recent ex
tension of Duverger's Law to the Japanese case. The model also generat
es specific and empirically testable hypotheses concerning the excepti
ons to the M + 1 rule that one ought to expect in equilibrium. I test
these hypotheses with Japanese data. Finally, the model also reveals a
type of strategic voting that is specific to multimember districts. I
use Japanese data again to explore the empirical importance of this k
ind of strategic voting.