WOLFRAM|DEMONSTRATIONS PROJECT

Probability of Election in a Vote

​
voters (N)
7
required votes for election (M)
4
number of simulations
10000
50000
100000
200000
choose a simulation
1
2
3
4
5
6
7
8
9
10
candidates
P(election)
2
1.
3
0.5177
4
0.2869
5
0.1642
6
0.1087
7
0.0716
A group of
N
people wishes to elect one of their members as their leader. Each member of the group can vote for any member in a smaller set of candidates of size
n≤N
. Candidates can vote for themselves. At least
M
votes are needed to elect a leader. Suppose that each of the
N
people votes for one of the
n
candidates randomly. The result shows the approximate probability of election as a function of
n
.