Compared to the attention they have lavished on strategic voting in single- member simple plurality elections, scholars have neglected strategic voting in multimember districts. We do have the Leys-Sartori conjecture - the thesis that strategic voting will be politically significant, acting to reduce the number of competitors, under PR systems with low district magnitudes, high thresholds, or other features that militate against the success of small parties. But there is not much systematic empirical evidence to back this claim up. Indeed, neither Leys nor Sartori cite or adduce any evidence at all; their conjecture is based on their own insight and an informal appeal to logic.