Editing Task:Define voting procedure for Community Council elections
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== Proposal: RRV == | == Proposal: RRV == | ||
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=== Variables === | === Variables === | ||
- | * | + | *<math>l</math>: number of voters |
- | * | + | *<math>m</math>: number of candidates |
- | * | + | *<math>n</math>: number of seats |
- | * | + | *<math>i</math>: index of voters (<math>1 \le i \le l</math>) |
- | * | + | *<math>j</math>: index of candidates (<math>1 \le j \le m</math>) |
- | * | + | *<math>k</math>: index of seats (and rounds) (<math>1 \le k \le n</math>) |
=== Parameters === | === Parameters === | ||
- | + | A range for votes is selected by two limits, <math>a_{max}</math> and <math>a_{min}</math>. | |
+ | Reasonable choices include: | ||
+ | *<math>a_{min}=0</math>, <math>a_{max}=1</math> (unbalanced, normalized) | ||
+ | *<math>a_{min}=-1</math>, <math>a_{max}=1</math> (balanced) | ||
+ | *<math>a_{min}=0</math>, <math>a_{max}=100</math> (unbalanced percentage; potentially useful if ratings were to be quantized) | ||
+ | The effects of the voting system are generally independent of the limits selected, but a balanced range ''may'' be preferred by some voters to permit unknown candidates to be rated 0 with known, disliked candidates rated negative. Obviously this effect may be accomplished in an unbalanced range by rating unknown candidates <math>\tfrac{a_{min} + a_{max}}{2}</math>. Some calculations are simplified by using the unbalanced, normalized range, which makes it preferable from a numerical perspective. | ||
- | A ballot from voter | + | A ballot from voter <math>i</math> consists of <math>m</math> ratings <math>a_{ij}</math> for the <math>m</math> candidates, such that <math>a_{min} \le a_{ij} \le a_{max}</math>. |
=== Procedure === | === Procedure === | ||
- | After all ballots are collected, | + | After all ballots are collected, <math>n</math> rounds are held to choose the winners <math>w_{k}</math>, with one winner chosen per round. In the first round, the weighted ratings for each voter are initialized as <math>b_{ij1}=a_{ij}</math>. The weighted scores in each round are summed: |
- | + | <math>B_{jk}=\sum_{i=1}^{l}b_{ijk}</math> | |
The highest-scoring candidate not yet elected wins; this is not simple to express formally: | The highest-scoring candidate not yet elected wins; this is not simple to express formally: | ||
- | + | <math>w_k = \max ( B_{jk} \ni j \notin w_{1 \cdots k-1})</math> | |
The weighted scores for each succeeding round are calculated by de-emphasizing ballots according to the portion in which they've already won: | The weighted scores for each succeeding round are calculated by de-emphasizing ballots according to the portion in which they've already won: | ||
- | + | <math>b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}\tfrac{a_{iw_p}-a_{min}}{a_{max}-a_{min}}}</math> | |
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- | + | In the case of an unbalanced range (<math>a_{min} = 0</math>), <math>b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}\tfrac{a_{iw_p}}{a_{max}}}</math>, and in the normalized case (<math>a_{max} = 1</math>), <math>b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}a_{iw_p}}</math>. | |
== Discussions == | == Discussions == | ||
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[[Category:Community]] | [[Category:Community]] | ||
[[Category:maemo.org]] | [[Category:maemo.org]] | ||
- | [[Category: | + | [[Category:Council]] |
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