Ebert's method: Difference between revisions

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m (Add Approval methods category)
m (Clean up math with TeX)
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* Assume each voter approves at least one 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:
A "load distribution" is a two-dimensional array <math>X_{v,c}</math> with <math>v=1\ldots V,\,c=1\ldots C</math> such that:
# 0 <= X_{v,c} <= 1
# <math> 0 \leq X_{v,c} \leq 1</math>
# X_{v,c}=0 unless v approves c
# <math>X_{v,c}=0</math> unless v approves c
# DoubleSum X_{v,c} = W
# <math>\sum_{v}\sum_{c}\,X_{v,c} = W</math>
# for each candidate c, Sum_v X_{v,c} = 1 if c is a winner, otherwise =0.
# for each candidate c, <math>\sum_{v} X_{v,c} = 1</math> if c is a winner, otherwise <math>=0</math>.


The winner set is the set which minimizes the SUM_v ( SUM_c X_{v,c} )^2.
The winner set is the set which minimizes <math>\sum_{v}(\sum_{c} X_{v,c} )^2</math>.


==Variants==
==Variants==