Randomization is a standard solution in problems of game theory. In this context, randomization is used to baffle an adversary, who would be able to counter any deterministic strategy (assuming that that strategy was known to her) more effectively than she would be able to counter a randomized strategy. Thus, randomization is a maximin strategy: it guarantees the randomizer the best possible worst-case outcome. Sortition – a randomized strategy for selecting political delegates – can be advocated on similar grounds.
In a standard conception of the problem of selecting delegates, the people can assess the quality of any possible delegate set. They do so and then choose the delegation that maximizes that quality. Thus, in this conception, delegation is a maximization problem.
An alternative conception is one where the quality of potential delegations is difficult to assess. In such a situation, selecting a delegation requires some way to handle the uncertainty. One such way is to assume that even if quality is not observable, an estimate of the quality can be made, and the estimate can then be used instead of the quality itself as an objective for maximization. This setup is theoretically consistent as long as the uncertainty about the quality of delegations is unbiased – i.e., as long as the uncertainly in quality is not correlated with the perception of quality. Corruption, however, is not an unbiased process. As the maxim “power corrupts” reflects, corruption is a dynamic process which depends on many factors, including, significantly, the level of distinction of the person or group in question. A person or group that are perceived as having the highest quality as a potential delegate or delegation could be more susceptible to corruption than a person or group that are perceived as average.
Thus, the process of corruption can be realistically likened to an adversary which counters methods for selecting delegations by corrupting those delegations that are most likely to be selected. This phenomenon may be due to natural tendencies of individuals or groups, or to the existence of true adversaries, i.e., individuals or groups that have an interest in subverting the quality of government and which actively work to corrupt potential delegates. Whatever underlying mechanism is, the outcome is a situation in which perceptions of quality are wholly unreliable – not even as noisy unbiased estimates.
In such a situation, just like in an adversarial game, the safest strategy to pursue is a maximin strategy – i.e., a strategy which guarantees a best worst-case outcome. If corruption affects a subset of the possible delegations, but it is impossible to identify which delegations would be corrupt, then it is most prudent to choose a delegation by randomization, since any deterministic choice makes it possible that the same distinguishing characteristic that is used for selection of the delegates also makes them more susceptible for corruption.
This argument may be used to justify various forms of randomization, depending on various assumptions about the distribution of competence in the population and about the way the process of corruption affects it. At an extreme case, an equal-chance lottery among the entire set of possible delegations minimizes the chance of having a corrupt delegation. Moving away from that extreme, a mechanism in which some groups – that are considered as having very low competence, such as children – are excluded can be considered as aiming at achieving a balance between reducing the chance of corruption while not giving up completely on the application of some judgement of competence. Approaching determinism, a mechanism in which the lottery is limited to some elite group, such as was employed in the city-states of Italy, can still be seen as enjoying some anti-corruption benefits. Weighted lotteries can also be seen as lying on the spectrum between a completely deterministic process and a completely random process.