Max Phragmen

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Potentially first defined here.

Definition[edit | edit source]


  • 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}.