'Backwards induction' is a useful solution concept in game theory. Games that have a finite number of turns can often be straightforwardly solved by looking at the final outcome, working out the optimal play in the previous turn, then using that to work out the optimal play in the turn before that and so on. Games like the Rubinstein bargaining model, or the finitely-repeated prisoners' dilemma (PD), raise interesting insights when solved with backwards induction. In the Rubinstein game, the relative power of the last mover 'infects' the rest of the game and leads to a division of spoils in their favour even if agreement is reached on turn one. In the repeated PD, co-operation can be sustained as long as there is the prospect of further games. But where there is a known final game - be it ever so far away - the co-operative solution can 'unravel' from the end and lead to a destructive 'defection' solution from the start.

A Hive of Inactivity(Photo by David Iliff. License: CC-BY-SA 3.0)
The timing of political elections, and its ramifications for legislative activity, are often analysed using a similar approach. There is little incentive to pass legislation at the end of a parliament: there is no time for the incumbents to gain political capital from it, and if they lose the opposition will either get the credit or simply reverse the decision on taking power. In the UK, there has been talk of a 'zombie parliament' while MPs wait for the election. The US's four-yearly electoral cycle produces a similar torpor in the election year - with the added dampener that in the second term there is no prospect for the incumbent to be re-elected. There is no question, of course, of giving governments total freedom to decide the timing of elections: this would be an invitation to perpetual delay and functional tyranny.

Game theory provides a possible solution though. In the repeated PD, if you randomly decide whether or not the game will be played once more, the 'backwards induction' effect disappears (provided the probability of a repeat is above a certain level). We could easily implement this for the UK. It would require a National Lottery-style ball tumbler containing 61 balls, two of which would be labelled 'ELECTION'. Each morning, before parliamentary business begins, two balls would be drawn. If both are the 'ELECTION' balls then an election would be called in - say - six months time. This would produce parliaments every five years on average, although sometimes you'd have elections very close to one another, and other times they would drag on for considerably longer.

The main advantage would be the elimination of 'zombieism': every day, the expected length of time till the next election would be the same. Watching the draw would also make for a fun five-minute coffee break for politicos. What would the disadvantages be? Why couldn't we randomise elections?

Edit (9am): six months is probably too long; it would simply replicate the problem. Perhaps two weeks would be better? What would the optimal time be?