A large population of voters with single-peaked preferences are partitioned into disjoint constituencies. Collective decisions are taken by their representatives, one from each constituency, according to a weighted voting rule. It is assumed that each representative’s ideal point perfectly...

Indices that evaluate the distribution of power in simple games are commonly required to be monotonic in voting weights when the game represents a voting body such as a shareholder meeting, parliament, etc. The standard notions of local or global monotonicity are bound to be violated, however,...