Political equality requires that each citizen has an equal chance of exerting political influence, in some sense. Aggregating equally weighted votes, one per person, is a familiar way of doing this. A simple, non-aggregative alternative would be to randomly select whose vote will count as the winning one. So long as everyone has an equal chance of being chosen, that seems to satisfy political equality, even if most people do not thereby get to actually contribute to determining the outcome. (After all, coin-flipping is widely recognized as a fair way to settle disputes, when all else is equal.) This principle is crucial for securing the democratic legitimacy of citizens juries and the like, given that only a random subset of the population get to actually participate in them.
My question is this: how far back in time can we push the random selection? How about the "genetic lottery"? Could even aristocracies and racist regimes count as satisfying political equality, so long as everyone had an equal chance of being born into the privileged class? If not, why not?
One might suggest that I never really had a chance of being born a prince -- the apparent possibility may be merely epistemic. (That is, the scenario is conceivable, but not one that ever had a real chance of eventuating.) But it would be a bit odd for questions of political justice to be held hostage to such abstruse modal metaphysics.
So I see two basic options here. One is to bite the bullet and simply accept that there's nothing intrinsically illegitimate or unfair about aristocracies and the like. Their flaws are purely pragmatic: unaccountable rulers tend to do a crummy job.
Alternatively, we could reconceive of political equality, in a more demanding fashion, as concerned with the ongoing relationship between the rulers and the ruled. It's not enough that everyone initially has an equal chance of influence, or whatever. Political equality must be maintained, by limiting the extent (power and duration) of the inevitable actual inequalities. In particular, those who receive power must be precluded from exercising it in an oppressive fashion. On this conception, political equality requires civic respect: the ongoing recognition of other citizens' political agency or potential to contribute to future decision-making.
What this means in practice is that political inequalities, though unavoidable, must never be entrenched. The moral requirement of "equal chances" cannot be ultimately satisfied by any one chance of selection. Instead, the chances must be revisited and maintained, so that those who are powerless today retain a real chance of becoming empowered tomorrow. In short: the ideal of political equality requires that our actual inequalities of power be always in flux.