View source for Ebert's method

Ebert's Method is a system of [[proportional representation]] that uses [[approval voting]] as a modification of [[Phragmén's Method]] and uses the same concept of loads. It was first knowingly defined by Bjarke Dahl Ebert in 2003.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/076356.html|title=Alternate view of Phragmén's method|website=Election-methods mailing list archives|date=2003-10-02|last=Ebert|first=Bjarke D.}}</ref>

Each elected candidate has a “load” of 1 that is spread equally among their approvers (every elected candidate must be approved by at least one voter). For example, if an elected candidate is approved by 100 voters, each of these voters would have a load of 1/100 from this candidate, which would be added to their loads from the other winning candidates. The winning set of candidates is the one that minimises the sum of the squared voter loads. For example, if a voter approves two elected candidates who each had 100 approvers, this voter would have a squared load of (1/100 + 1/100)^2 = 1/2500. This would be added to the squared loads of every other voter.

==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 <math>X_{v,c}</math> with <math>v=1\ldots V,\,c=1\ldots C</math> such that:
# <math> 0 \leq X_{v,c} \leq 1</math>
# <math>X_{v,c}=0</math> unless v approves c
# <math>\sum_{v}\sum_{c}\,X_{v,c} = W</math>
# 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 <math>\sum_{v}(\sum_{c} X_{v,c} )^2</math>.

==Variants==

There is a Sequential version called [[Sequential Ebert]].

There is also a modified version by Toby Pereira called [[PAMSAC]]<ref>[https://arxiv.org/abs/1602.05248 PAMSAC]</ref>

There is also a version called ABC+A+B+C (and a sequential version of it) where the score is modified so that to the total sum of squared loads we add the sums of squared loads if only individual candidates were elected.

== Further reading ==
Two variants of Ebert's method are discussed [https://aaai.org/ocs/index.php/AAAI/AAAI17/paper/view/14757 here]. One is a change to the quality function and the other is a sequential implementation. In this paper they call Ebert's method  var-Phragmen.

== References ==
<references />
[[Category:Approval PR methods]]