A systematic analysis of the relationships between the main electoral system variables (electoral formula, district magnitude, and ballot structure) and electoral outcomes (the degrees of disproportionality and multipartism) in the 20 Western democracies from 1945 to 1985—representing 32 distinct electoral systems (an electoral system being defined as a set of elections held under basically the same rules)—shows that the effects of both formula and magnitude on proportionality are very strong, much stronger than Douglas W. Rae and subsequent researchers have suggested; that on the other hand, their effects on the number of parties participating in elections is surprisingly weak; and that ballot structure affects the degree of multipartism only in single-member district systems. These findings suggest that strategic behavior by politicians and voters plays a less important role in reducing multipartism than is usually assumed.
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