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?

Optimizing transportation networks

I have blogged earlier about this (pdf here) fascinating study of unco-ordinated transportation systems by Hyejin Youn, Michael T. Gastner, Hawoong Jeong. They analyzed the 246 road links and 88 nodes of Boston's transportation network and their conclusion is striking and has significant lessons for urban transport planners,

"Uncoordinated individuals in human society pursuing their personally optimal strategies do not always achieve the social optimum, the most beneficial state to the society as a whole. Instead, strategies form Nash equilibria which are often socially suboptimal. Society, therefore, has to pay a price of anarchy for the lack of coordination among its members. Here we assess this price of anarchy by analyzing the travel times in road networks of several major cities. Our simulation shows that uncoordinated drivers possibly waste a considerable amount of their travel time. Counter intuitively, simply blocking certain streets can partially improve the traffic conditions. We analyze various complex networks and discuss the possibility of similar paradoxes in physics."

They find that contrary to conventional wisdom, the interaction of utility maximizing road users do not result in optimal traffic outcomes. Transportation flows can in reality be far from optimal even if all individuals search for the quickest paths and if complete information about the network and other users’ behaviors is available. In other words, "traffic networks can be inherently inefficient". In a game theoretic framework, they find that the Nash equilibrium (arising from self-interested road use decisions of driver) is different from the social optimum (minimized cost to society per unit transport time).

The study highlights the importance of the Braess Paradox which states that adding capacity to a network in which all the moving entities rationally seek the most efficient route can sometimes reduce the network’s overall efficiency. The graphic below highlights how certain road links add to traffic congestion due to drivers propensity to selfishly optimize on their travel times (which ironically enough, in turn results in higher travel times for the collective).



In many respects, urban transport market is a classic free-market of vehicle and road users - completely unregulated, but rife with information asymmetry (among drivers). Which routes to use and which to not use at any point in time? Which routes are best traversed through public transit as opposed to private vehicles? Which roads can be made one-way? How do we regulate vehicle flows in a road circuit?

The larger lesson it conveys to urban transport planners is about the importance of co-ordination among vehicle-users in reducing traffic congestion. Such co-ordination can be achieved by both bridging the information asymmetry between drivers and through interventions to optimize flows within transport networks.

In the prevailing "build your way out of traffic congestion" paradigm, there is very little attention paid to bridging this information asymmetry and scientifically optimizing the configuration of traffic flow networks. It is therefore not surprising that, like other unregulated free-markets, market failures (manifesting as traffic congestions) abound in this market.

The third batting power play and game theory!

One of the interesting debates on the sidelines of the Cricket World Cup relates to the timing of when batting team captains should use their third power play (PP) of five overs. The third PP, to be availed at the request of the batting team, imposes a restriction that the fielding team can have only three fielders outside the thirty yard circle.

The dilemma for batting captains is to use it earlier, say in the 30-40 over period, or preserve it for the slog overs. Apart from the argument that since the ball is changed in the 34 th over (and since a harder ball is easier to hit), it may be effective to take PP early, there has not been much analysis of the issue. However, a simple balance sheet of the costs and benefits of both alternatives to each side reveals that the choice is not as hard as it appears.

The benefits for the batting side are several and significant

1. With or without field restrictions, slog overs are a form of PP in themselves, atleast from the mental frame of the batsmen. It may therefore be more effective to take an early PP and get more runs earlier than otherwise would have been the case. The batting team effectively gets two PPs! The batting team can also carry the momentum on to the slog overs - the bowling side will have to mentally recover after the PP.

2. The bowling side is forced to call on its best bowlers much earlier than they would have preferred. Typically, the best bowlers have three spells - opening burst, slog overs, and a containing or wicket searching spell in the middle. If the PP is taken in the slog overs, it coincides with the bowlers final planned spell. However, an early PP, especially if the bowler has already completed his middle spell, can wreck the best laid plans of the bowling captain. Forced into dividing their ten overs into four spells, the best bowlers will have less overs for the slog.

3. Even without field restrictions, slog overs generally yield more runs. The incremental benefit, in terms of runs scored, with PP restrictions are not likely to be substantial. However, in the earlier overs, without field restrictions, batting sides are likely to score only modestly (3-4 runs an over in an average scoring match and 5-6 runs an over in a high scoring one). The incremental benefit of early PP is therefore significant.

4. Finally, the harder the ball, the easier is it to strike. Since the ball is replaced in the 34 th over, it is surely more sensible to opt for an early PP.

The negative side of the equation for the batting side is the risk of losing wickets in the PP and being left with limited fire-power to take advantage of the slog overs. However, this is more a question of the batsman's judgement of the PP situation, an issue of mental orientation. An element of representativeness bias in the batsman's mind anchors the third PP to slog overs.

It needs to be borne in mind that batting PP are not slog overs. In slog overs, batsmen throw caution to the winds safely in the knowledge that the end of the innings is near. But early PPs are followed by more overs. The risks being taken need to be weighed accordingly.

Consider this 2X2 matrix of the two alternatives - early and slog overs PP - from the perspective of the batting and bowling sides.



As can be seen, the early PP is the dominant strategy for the batting side - for the batting side, its benefits are singificant while for the bowling side, the costs are just as high!