Matpic
mathematics, in pictures
Concept

Weighted voting

A voting rule in which each member casts a fixed number of votes and a motion passes when the votes for it reach a quota. A member's power to decide outcomes need not follow its share of the votes, and can even be zero.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A share of the votes, and a share of the power. Three weighted assemblies, each with the members' share of the votes beside their share of the power counted two independent ways.

A share of the votes is not a share of the power

Give three members four, four and one vote, with five needed to pass. Every winning coalition needs exactly two of them, so all three have equal power — and one of them holds a ninth of the votes.

applied · Shapley value Luxembourg's votes and Luxembourg's power, 1958 to 1995. Paired bars for Luxembourg at five enlargements of the Council: vote share falling and power share rising from nothing in 1958 to 0.95% in 1973 and 3.02% in 1981.

A vote worth nothing until it was outnumbered

From 1958 to 1973 Luxembourg held one vote of seventeen in the Council of the European Communities and could never once change an outcome. When the Council grew, Luxembourg's share of the votes fell and its share of the power rose from nothing. Power is not a quantity a member holds; it is a property of the whole assembly, and changing the assembly moves it in directions nobody would guess.

applied · Shapley value

Named alongside it

The objects these essays reach for when they reach for this one.

Marginal contributionQuotaBanzhaf indexCoalitionCooperative gameCounterexampleDummy playerExhaustive searchMonotonicityParityPivotal playerShapley shubik index

All concepts