Signalling, incumbency advantage, and optimal reelection rules

Much literature on political behavior treats politicians as motivated by reelection, choosing actions to signal their types to voters. We identify two novel implications of models in which signalling incentives are important. First, because incumbents only care about clearing a reelection hurdle, signals will tend to cluster just above the threshold needed for reelection. This generates a skew distribution of signals leading to an incumbency advantage in the probability of election. Second, voters can exploit the signalling behavior of politicians by precommitting to a higher threshold for signals received. Raising the threshold discourages signalling effort by low quality politicians but encourages effort by high quality politicians, thus increasing the separation of signals and improving the selection function of an election. This precommitment has a simple institutional interpretation as a supermajority rule, requiring that incumbents exceed some fraction of votes greater than 50% to be reelected.