Previous investigations of strategic voting equilibria in mass elector
ates have looked only at elections held under plurality-rule electoral
laws. This paper investigates such equilibria in multimember district
s operating under Various largest-remainders methods of proportional r
epresentation (PR). In principle, strategic voting imposes a limit on
the number of viable lists under PR, just as it imposes a limit on the
number of viable candidates under plurality rule, as noted long ago.
The results proved here provide some formal underpinning for this idea
and yield specific hypotheses, for each electoral system, concerning
the maximum number of lists/candidates consistent with equilibrium lev
els of strategic voting. Our results also clarify the conditions under
which these theoretical upper bounds on the number of lists/candidate
s are binding in practice. We use Colombian and Japanese electoral dat
a to test the model's predictions.