This article on Reuters about Chinese villagers complaining that they were no longer receiving bribes from candidates in local elections got me thinking about how best to model bribery in an election process. I’ve not done any research at this point, so I wouldn’t be the least bit surprised if someone had already done this in considerably more detail, but here are some initial thoughts …

Assume that the local government offers no public goods or public services to the voters, but instead acts either as a gatekeeper for business permits or as a guide through an externally imposed beauracracy. In either case, further assume that elected officials make a lot of money through bribery and in particular, more than their outside options.

The candidate that hands out the most to the voters wins the election and gets the bribes from business. Without a credible commitment between the candidates to not give handouts, the incentive will always be to give a handout and the only stable equilibrium will be for everyone to give a handout.

If the size of the bribe from business is universally known ex ante, or if it is uncertain but it’s expected value is commonly known and the candidates are risk-neutral, the candidates will all give handouts until their expected return matches their outside options. The result (a coin-toss since all candidates handed out the same amount) will be that the guy who wins the election gets a bucket of money, the voters each get a bit and the other candidates all lose money. e.g. Outside option for all candidates = 0, (Expected) Bribe from business = 100, Number of candidates = 4, Number of voters = 1000. Each candidate will give each voter 0.025 (so each voter will get 0.1 and the total handouts to voters will be 100). The candidate who wins will get 75 (100 – 25) and the candidates who lose will get -25.

I’ve assumed above that all candidates are the same in a) their risk aversion; b) their expectation of the value of the bribe from business; and c) their outside option. If the expected bribe and outside options are common but candidates vary in their level of risk aversion, the least risk averse candidate will win. If candidates vary only on their expected bribe, the candidate with the largest expectation will win. If candidates vary only in their outside option, the candidate with the lowest outside option will win.

Obvious extensions would be to include not just ex ante handouts but promises of handouts ex post and to suppose that some (or all) of the candidates also owned the businesses that would have to pay the bribes.

As always, any thoughts or comments are welcome.