2020/10/17 by Alex Arnell, Arnell, Alex, Richard Chen +9
Computer Science · Economics, Econometrics and Finance · #Complexity and Algorithms in Graphs #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Voting Systems #Internet Traffic Analysis and Secure E-voting #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2010.08672
openalex publication_date 2020/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Banzhaf and Shapley-Shubik power indices were first introduced to measure the power of voters in a weighted voting system. Given a weighted voting system, the fixed point of such a system is found by continually reassigning each voter's weight with its power index until the system can no longer be changed by the operation. We characterize all fixed points under the Shapley-Shubik power index of the form (a,b,…,b) and give an algebraic equation which can verify in principle whether a point of this form is fixed for Banzhaf; we also generate Shapley-Shubik fixed classes of the form (a,a,b,…,b). We also investigate the indices of divisor voting systems of abundant numbers and prove that the Banzhaf and Shapley-Shubik indices differ for some cases.