  Voters from m disjoint constituencies (regions, federal states, etc.) are
represented in an assembly which contains one delegate from each constituency
and applies a weighted voting rule. All agents are assumed to have
single-peaked preferences over an interval; each delegate's preferences match
his constituency's median voter; and the collective decision equals the
assembly's Condorcet winner. We characterize the asymptotic behavior of the
probability of a given delegate determining the outcome (i.e., being the
weighted median of medians) in order to address a contentious practical
question: which voting weights w_1, ..., w_m ought to be selected if
constituency sizes differ and all voters are to have a priori equal influence
on collective decisions? It is shown that if ideal point distributions have
identical median M and are suitably continuous, the probability for a given
delegate i's ideal point \lambda_i being the Condorcet winner becomes
asymptotically proportional to i's voting weight w_i times \lambda_i's density
at M as $m\to \infty$. Indirect representation of citizens is approximately
egalitarian for weights proportional to the square root of constituency sizes
if all individual ideal points are i.i.d. In contrast, weights that are linear
in-- or, better, induce a Shapley value linear in-- size are egalitarian when
preferences are sufficiently strongly affiliated within constituencies.
