Proportional Subset Voting: Difference between revisions

Ballot uses range [0%,100%]. <math>\begin{equation}N\end{equation}</math> is the number of winners.

For each vote, and for each subset of <math>\begin{equation}N\end{equation}</math> candidates:

* create a list of <math>\begin{equation}G_i\end{equation}</math> groups, 1 for each percentage, multiple of <math>\begin{equation}\frac{100\%}{N}\end{equation}</math> ''(eg for N = 4 the groups are 0%, 25%, 50%, 75%, 100%)''.

* for each <math>\begin{equation}G_i\end{equation}</math>, the voters with a total approval <math>\begin{equation}=G_i\end{equation}</math> are counted getting <math>\begin{equation}C_i\end{equation}</math> <math>\begin{equation}(\ \mathrm{ total\ approval\ of\ the\ N\ candidates}=\frac{\mathrm{ratings\ sum}}{N}\ )\end{equation}</math>. Each <math>\begin{equation}C_i\end{equation}</math> is then divided by the number of voters.

* find the group with the lowest percentage <math>\begin{equation}G_{min}\end{equation}</math> containing <math>\begin{equation}C_{min}>0\end{equation}</math>, and associate <math>\begin{equation}S_{min}=\{G_{min},C_{min}\}\end{equation}</math> to the subset.

* find the group with the highest percentage <math>\begin{equation}G_{max}\end{equation}</math> containing <math>\begin{equation}C_{max}>0\end{equation}</math>, and associate <math>\begin{equation}S_{max}=\{G_{max},C_{max}\}\end{equation}</math> to the subset.

Sort the subsets from major to minor based on the <math>\begin{equation}S_{min}\end{equation}</math> value; if there are tied subsets then sort them from minor to major based on the <math>\begin{equation}S_{max}\end{equation}</math> value. The subset that is first after sorting wins.

If there are any tied subsets, <math>\begin{equation}P\end{equation}</math> is calculated which is the sum of the products between <math>\begin{equation}G_i\end{equation}</math> and <math>\begin{equation}C_i\end{equation}</math>. The subset that has highest <math>\begin{equation}P\end{equation}</math> wins.

* the total approval of a voter for N candidates must be somehow rounded up to a multiple of <math>\begin{equation}\frac{100\%}{N}\end{equation}</math>, in order to be counted in the list of <math>\begin{equation}G_i\end{equation}</math> groups.

Find <math>\begin{equation}\{S_{min},S_{max}\}\end{equation}</math> and sort: