Strict Proportional Power and Fair Voting Rules in Committees

In simple weighted committees with a finite number $n$ of members, fixed weights and changing quota, there exists a finite number $r$ of different quota intervals of stable power ($r \le 2^{n}-1$) with the same sets of winning coalitions for all quotas from each of them. If in a committee the sets of winning coalitions for different quotas are the same, then the power indices based on pivots, swings, or minimal winning coalitions are also the same for those quotas. If the fair distribution of voting weights is defined, then the fair distribution of voting power means to find a quota that minimizes the distance between relative voting weights and relative voting power (optimal quota). The problem of the optimal quota has an exact solution via the finite number of quotas from different intervals of stable power.