Task:Define voting procedure for Community Council elections

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.

Proposal: RRV

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

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 <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

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:

<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:

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

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

• Defining the Maemo Community Council voting procedure - Internet Tablet Talk