WOLFRAM|DEMONSTRATIONS PROJECT

Power in Weighted Voting Systems

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power index
ShapleyShubik
Banzhaf
players
3
4
5
6
quota
no. votes A
no. votes B
no. votes C
no. votes D
no. votes E
no. votes F
show details
For the weighted voting system [51 : 50,49,1] ,
the Shapley-Shubik power is distributed as follows:
name ofplayer
proportion of votesheld by player
no. of coalitions in which player is pivotal
Shapley-Shubik power index of player
A
0.500
4
0.667
B
0.490
1
0.167
C
0.0100
1
0.167
A weighted voting system consists of a number of players, each with a certain number of votes, and a quota of votes needed to pass a measure. There are various methods of measuring the "power" that an individual in a weighted voting system has. This Demonstration lets you compare the proportion of votes a player has versus that player's power as measured by the Shapley–Shubik and Banzhaf power indices. The thumbnail shows the famous example [51: 50, 49, 1] of a system with three players having 50, 49, and 1 votes, respectively, and with the quota set at 51 votes. Note that the distribution of power of the voters is very different than the distribution of votes.