Talk:Task:Define voting procedure for Community Council elections

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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>.
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>.
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=== Discussion ===
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It seems to me like this voting system requires voters to understand at least a little game theory. It looks far too complicated to be used in a real-life election.
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The voting system used should, in my opinion, require the voter to do one of three things:
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* Choose candidates in order of preference (1, 2, 3...)
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* Choose 1 favourite candidate
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* Choose their N favourite candidates from the electorate (the GNOME system)
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Of the three choices, the GNOME system is my least favourite, and the straight vote seems a little limiting. I prefer simple preferential voting.
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Of the simple preferential voting systems, my favourite is single transferable vote. It's better than Condorcet, in my opinion, because it is understandable quite easily by the electorate and does not produce unexpected results (such as someone who was no-one's favourite candidate getting elected).
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--[[User:dneary|Dave Neary]] 18:39, 3 December 2008 (UTC)

Revision as of 18:39, 3 December 2008

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Contents

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, amax and amin. Reasonable choices include:

  • amin = 0, amax = 1 (unbalanced, normalized)
  • amin = − 1, amax = 1 (balanced)
  • amin = 0, amax = 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 aij 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 wk, with one winner chosen per round. In the first round, the weighted ratings for each voter are initialized as bij1 = aij. 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 (amin = 0), b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}\tfrac{a_{iw_p}}{a_{max}}}, and in the normalized case (amax = 1), b_{ij(k+1)}=\frac{a_{ij}}{1+\sum_{p=1}^{k}a_{iw_p}}.

Discussion

It seems to me like this voting system requires voters to understand at least a little game theory. It looks far too complicated to be used in a real-life election.

The voting system used should, in my opinion, require the voter to do one of three things:

  • Choose candidates in order of preference (1, 2, 3...)
  • Choose 1 favourite candidate
  • Choose their N favourite candidates from the electorate (the GNOME system)

Of the three choices, the GNOME system is my least favourite, and the straight vote seems a little limiting. I prefer simple preferential voting.

Of the simple preferential voting systems, my favourite is single transferable vote. It's better than Condorcet, in my opinion, because it is understandable quite easily by the electorate and does not produce unexpected results (such as someone who was no-one's favourite candidate getting elected).

--Dave Neary 18:39, 3 December 2008 (UTC)

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