Task:Define voting procedure for Community Council elections

This is an ongoing task, planned to be completed during the current maemo.org development sprint. Any help is appreciated!
Please see the talk page for discussion.

Due to the noise generated by the voting procedure from the first election, the procedure needs to be reevaluated and a better system needs to be put in place for the next election.

1 Proposal: RRV
2 Discussions

Proposal: RRV

Variables

$l$ : number of voters
$m$ : number of candidates
$n$ : number of seats
$i$ : index of voters ( $1 \le i \le l$ )
$j$ : index of candidates ( $1 \le j \le m$ )
$k$ : index of seats (and rounds) ( $1 \le k \le n$ )

Parameters

A range for votes is selected by two limits, $a m a x$ and $a m i n$ . Reasonable choices include:

$a m i n = 0$ , $a m a x = 1$ (unbalanced, normalized)
$a m i n = - 1$ , $a m a x = 1$ (balanced)
$a m i n = 0$ , $a m a x = 100$ (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 $\tfrac{a_{min} + a_{max}}{2}$ . Some calculations are simplified by using the unbalanced, normalized range, which makes it preferable from a numerical perspective.

A ballot from voter $i$ consists of $m$ ratings $a i j$ for the $m$ candidates, such that $a_{min} \le a_{ij} \le a_{max}$ .

Procedure

After all ballots are collected, $n$ rounds are held to choose the winners $w k$ , with one winner chosen per round. In the first round, the weighted ratings for each voter are initialized as $b i j 1 = a i j$ . The weighted scores in each round are summed:

$B_{jk}=\sum_{i=1}^{l}b_{ijk}$

The highest-scoring candidate not yet elected wins; this is not simple to express formally:

$w_k = \max ( B_{jk} \ni j \notin w_{1 \cdots k-1})$

The weighted scores for each succeeding round are calculated by de-emphasizing ballots according to the portion in which they've already won:

$b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}\tfrac{a_{iw_p}-a_{min}}{a_{max}-a_{min}}}$

In the case of an unbalanced range ( $a m i n = 0$ ), $b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}\tfrac{a_{iw_p}}{a_{max}}}$ , and in the normalized case ( $a m a x = 1$ ), $b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}a_{iw_p}}$ .