Are parliaments with more parties cheaper to bribe?

We collect data about 172 countries: their parliaments, level of corruption, perceptions of corruption of parliament and political parties. We find weak empirical evidence supporting the conclusion that corruption increases as the number of parties increases. To provide a theoretical explanation of this finding we present a simple theoretical model of parliaments formed by parties, which must decide whether to accept or reject a proposal in the presence of a briber, who is interested in having the bill passed. We compute the number of deputies the briber needs to persuade on average in parliaments with different structures described by the number of parties, the voting quota, and the allocation of seats among parties. We find that the average number of seats needed to be bribed decreases as the number of parties increases. Restricting the minimal number of seats a party may have, we show that the average number of seats to be bribed is smaller in parliaments without small parties. Restricting the maximum number of seats a party may have, we find that under simple majority the average number of seats needed to be bribed is smaller for parliaments in which one party has majority, but under qualified majority it hardly changes.

A computational approach to unbiased districting

In the context of discrete districting problems with geographical constraints, we demonstrate that determining an (ex post) unbiased districting, which requires that the number of representatives of a party should be proportional to its share of votes, turns out to be a computationally intractable (NP-complete) problem. This raises doubts as to whether an independent jury will be able to come up with a “fair” redistricting plan in case of a large population, that is, there is no guarantee for finding an unbiased districting (even if such exists). We also show that, in the absence of geographical constraints, an unbiased districting can be implemented by a simple alternating-move game among the two parties.