Powers of subgroups in voting bodies

✍ Scribed by P. C. Fishburn; W. V. Gehrlein

• Publisher: Springer
• Year: 1984
• Tongue: English
• Weight: 499 KB
• Volume: 1
• Category: Article
• ISSN: 0176-1714
• DOI: 10.1007/bf00452880

✦ Synopsis

This paper discusses the power p, of an n-member subgroup B, of an N-member voting body, N odd and 1 \\\_ n \_< N. In contrast to bloc voting, we assume that the members vote independently with equal probability "for" and "against" a given issue. Power Pn is defined as the probability that the outcome of a vote changes if all members of B, reverse their votes. Theorems: p, + 1 = P, for odd nPm+, if m+n<N; p,+l/p~(n+l)/n as N ~ oo for fixed even n; for rational 0 < 2 < 1, PaN ~ 2re-1 sin-1 21/2 as N ~ oo. A simple summation formula is given for p~.