First, the Athenians did not randomise policy, but deliberated and voted for against proposals in the Assembly of the Demos. Service in the Council of Five Hundred was restricted to two terms over the lifetime, but not in consecutive years, and once in other magistracies, although there was no limit on the number of times one could be elected general.
Be that as it may, like all proposals for institutional reforms, whether introduction of random selection will be undertaken depends on whether the constitutional framers expect to benefit from it.
Along with policy making by the Assembly of the demos, the hallmark of the Athenian democracy was appointment to public office by lot. Hence, they can make only moderate demands on fellow citizens lessening government coercion. As a result, the decision of the sample will be perceived as standing for the population as a whole.
Sortition is a mechanism that can help secure this right for everyone. After all, many non-democratic poleis had assemblies as well. Thus, sortition inevitably diminished the status of the offices of archons and opened them up to all citizen classes, significantly, poorer members of the demos.
Councillors, jurors of the Court and members of some boards received a fee for their days of service.
Democracy as a right is not mentioned throughout the convention. More formally, in a model where a citizen divides his time between private work and work from public office, Tridimas shows that a contestant for office prefers to be subject to the luck of the draw instead of fighting for it in an election, when the probability of winning the election is less than the probability of winning the lot by a factor that accounts for the cost of election campaign net of the intrinsic utility from public office.