APSA2003
McElwain
19
statistically significant at conventional levels, although the sign is in the correct direction
(positive). Thus when bonus differential under SPM increases in small doses, the probability of
electoral reform actually increases. If Country differed from Country only in that there was
a majoritarian party with a bonus differential of .25, the likelihood of electoral change would be
a relatively high 17.5%. In contrast, if bonus differential is very large, the probability of
electoral reform decreases; if bonus differential for Country rose to 1.3, the likelihood of
change falls to 6.6%. The effect that bonus differential has on the probability of electoral rule
change, conditional on SPM = 1, is presented in Graph 2 (the null, where SPM=0, would be as
presented in Graph 1).
[Graph 2 about here.]
Hypothesis 1b posits that when the party with the largest vote share does not have the
largest bonus ratio, then the probability of electoral rule change increases. The variables bonus
loser and bonus loser * bonus differential operationalize this concept, and the latter is
statistically significant at the 10% level. The former variable can be interpreted
straightforwardly: when the largest vote-getting party has a smaller bonus ratio than the second
party, the probability of electoral rule change is higher. The interaction term emphasizes this
effect, indicating that when there is a bonus loser, the more negative the bonus differential
(keeping in mind that the values are always negative in the case of bonus losers), the higher the
probability of change. In other words, as the extent to which the largest vote-getter loses out
from the electoral system increases, the more likely we can predict electoral reform. If Country
differed from Country only in that the former’s largest party was a bonus loser with a bonus
differential of –.07 (compared to .015 in ), Country ’s probability of rule change would be a
higher 8.0%. Graph 3 presents the effect of increasing bonus differential when bonus loser = 1,
holding other variables at their median values.
[Graph 3 about here.]
Bonus differential change supports Hypothesis 2, which states that a change in bonus
differential from (t-1) to (t) should lead to a greater likelihood of electoral system manipulation.
Convention