Electoral bribery - a tale of two games?

Anecdotal evidence from electoral politics in many Indian states appears to indicate that all the contesting candidates pay reasonably similar amounts of cash bribes to all the voters.

On the face of it, this appears surprising since only one candidate can finally win the electoral race and the electoral race is high stakes and ultra-competitive. In the circumstances, conventional wisdom would have it that atleast some candidates renege on their bribe payments. Further, there should have been a bidding war among contestants to outbid each other in the payment of bribes. So what is the underlying story? Why do "all candidates" bribe "all voters"? Why are the bribes "reasonably similar"?

I am inclined to believe that there are two games being played here. On the one hand, candidates have to weigh the consequence of not making payments given the uncertainty associated with the response of the other side. On the other hand, candidates face the possibility of a potential bidding war in bribe payments.

Consider the first game, which is a defection game. Candidates rationalize bribing voters on the ground that voters have been socialized into expecting bribes and are likely to react negatively (turn against them) if their expectations are not met by any of the candidates. The undeniable reality of an availability bias associated with electoral bribing means that there is a strong likelihood for voters to form expectations about receiving some amount as a bribe. In fact, this expectation is likely to be more pronounced with the incumbent legislator.

The trend is widely pervasive in most parts of India, so much so that any candidate who defects, by not paying or paying less, is perceived to face certain defeat. The table below models a two-candidate electoral game where the decision point is about whether to bribe or not.



This brings us to the second game, the co-operation game. Interestingly, political parties too appear to have internalized the dynamics of the electoral game. Given the inevitability of bribe payments, all of them realize the massive costs associated with a bidding war where one party tries to outbid the other. Since these games are all repeat games, with the same parties fighting over multiple elections, there are sufficient incentives for all sides to embrace an equilibrium and co-operate. The result is an implicit understanding about the magnitude of their bribe payouts. The table below captures this game.



However, there is a small Bayesian twist to this tale which highlights the slippery slope down which both candidates and voters have slipped. Since all parties bribe voters, and voters have to make an electoral choice, they end up making their actual choices based on other considerations. But this choice is conditional on the receipt of bribes. In other words, while voters may make their choice based on several factors, this choice is mostly restricted to those who have paid the bribes. If this line of analysis is true, then all candidates end up defecting and bribing, resulting in a Nash equilibrium. Ironically, atleast in the short-run, the real winner in this is the voter!

So, conditional on receipt of the bribes, what are the factors that drive voting choices? A few intuitive answers include those who paid the larger amount, those perceived as leading the electoral race, those who have struck a chord with some local or emotional issue, and sometimes even those who are perceived as extremely corrupt. Given this, do we have a window of opportunity here to align the individual incentives of voters with general public interest and drive the agenda of contesting candidates accordingly?