Cycles of risk

Conclusion

Much of the social choice literature has tried to skirt around the main conclusion which it has come up with. The literature seems to imply that the world is in disequilibrium, yet it keeps trying to model the process in terms of equilibrium models and to search for conditions which guarantee equilibria. The conditions which have been found for equilibrium when only pure strategies are used are so servere, we would seldom expect them to be met. But if the conditions for equilibria over pure strategies are servere, then the conditions for equilibria over risky strategies must be even more so, for risky strategies can, atbest, disrupt existing equilibria. In this paper, we have attempted to accept the deductions of the model, and to investigate, instead, the implications of this lack of equilibrium. We have argued that, in a large class of situations, it seems that we will get convergence in risk even if there is no euqilibrium. Moreover, the point to which the risk will converge may not be entirely arbitrary, i.e., the area of intransitivities, given that candidates adopt optimal responses to each other, may be a fairly localized region in the space.