Corruption in representative democracy

A parliament with n members, distributed among two parties, decides whether to accept or reject a certain proposal. Each member of the parliament votes in favour or against. If there are at least t members in favour, the proposal is accepted; otherwise it is rejected. A non-member of the parliament, the briber, is interested in having the proposal accepted. To this end, he is willing to bribe members to induce them to vote in favour. It is compared a parliament with party discipline, where members vote according to the party line, and a parliament without party discipline, where members vote according to their own opinion. The paper determines, for given values of n and t , the average number of members that the briber has to bribe in each case (with the average taken with respect to all the possible allocations of members between parties and their votes, and also with respect to those allocations inducing the briber to bribe). The results show that a parliament with parties with party discipline is more costly for the briber to be bribed.