Ebert's method: Difference between revisions

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==Definition==
Let:
* V voters
* C candidates
* W winners, 0<W<C
Each voter approves or disapproves each candidate.
Assume* eachEach voter approves ator leastdisapproves oneeach candidate.
Each* Assume each voter approves orat disapprovesleast eachone candidate.
 
A "load distribution" is a two-dimensional array X_{v,c} v=1..V, c=1..C such that:
# 0 <= X_{v,c} v<=1..V, c=1..C
2. # X_{v,c}=0 unless v approves c
such that
3. # DoubleSum X_{v,c} = W
4. # for each candidate c, Sum_v X_{v,c} = 1 if c is a winner, otherwise =0.
 
minimizeThe winner set is the set which minimizes the SUM_v ( SUM_c X_{v,c} )^2.
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.
 
minimize the SUM_v ( SUM_c X_{v,c} )^2.
 
==Variants==