Max Phragmen

It has been suggested that this article be merged with Phragmén's Method. (Discuss)

Potentially first defined here.

Definition

Let:

• V voters
• C candidates
• W winners, 0<W<C
• Each voter approves or disapproves each candidate.
• Assume each voter approves at least one candidate.

A "load distribution" is a two-dimensional array X_{v,c} v=1..V, c=1..C such that:

1. 0 <= X_{v,c} <= 1
2. X_{v,c}=0 unless v approves c
3. DoubleSum X_{v,c} = W
4. for each candidate c, Sum_v X_{v,c} = 1 if c is a winner, otherwise =0.

The winner set is the set which minimizes the SUM_v MAX_c X_{v,c}.