# [EM] MOP-F2 definition

Juho Laatu juho.laatu at gmail.com
Tue Jul 9 01:21:04 PDT 2019

```In order to keep definitions clear, I wrote a compact definition of the MOP-F2 method.

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MOP-F2

1) Votes are ranked votes with one cutoff. Candidates above the cutoff are called protected candidates. The default position of the cutoff is at the beginning of the vote (i.e. no protected candidates).

2) Count the margins (for each pair of candidates). This is based on the rankings only.

3) Modify the margins using function f, where
- f(m,p) = m + sign(m) * (1-p/N) * 2 * N
- m is the original pairwise margin
- p is the number of votes that identified both candidates as protected candidates
- N is the number of votes
- sign(x) is +1 if x>0, -1 if x<0, and 0 if x=0

4) Use the Minmax algorithm to find the winner (i.e. the candidate whose worst defeat (based on the modified margins) is smallest).

* Note that function f will modify only the strength of the defeats. The direction of the defeats will not change.
* Note that function f can be simplified to (a shorter but maybe less intuitive) form f(m,p) = m + sign(m) * 2 * (N-p)
* Note that function f stretches the range of defeat strength values from [-N, N] to [-3*N, 3*N]
* In the name of the method MOP refers to "Modified Overall Preferences", F refers to word Favourites, and 2 refers to the "stretch factor" 2

```

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