Single distributed vote: Difference between revisions
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Dr. Edmonds (talk | contribs) (→Motivation for specific parameter choice: typographical error) |
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# Acquire candidate score form voters and normalize them in [0,1] into a matrix. Voter, v,
# Determine candidate with max summed (over voters) score.
# Update the entire score matrix. The v,c entry of the new matrix is
#: <math>\begin{equation}
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# Go back to step 2 until desired number of winners have been elected.
===Verbal Description===
The first winner is the score winner. Then we allow ballot weight to be distributed between the first winner and all potential next winners according to the score given. The the second winner is the candidate who has the highest sum score when it is down weighted by the ballot weight they are supported with by each voter. Then we allow ballot weight to be distributed between the first two winner and all potential next winners according to the score given. The the third winner is the candidate who has the highest sum score when it is down weighted by the ballot weight they are supported with by each voter. And so on…▼
▲The first winner is the
==Distribution Example==▼
▲===Distribution Example===
To illustrate how ballot weight is distributed it will now be shown how the scores are distributed across candidates. The formula for score matrix reweighting can be properly viewed as the original score matrix times a candidate and voter dependant ballot weight. ▼
▲To illustrate how ballot weight is distributed it will now be shown how the scores are distributed across candidates. The formula for score matrix reweighting can be properly viewed as the original score matrix times a
<math>\begin{equation}
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==Generalization==
The most general form of the
<math>\begin{equation}
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A desirable property of a sequential system is to conserved vote power across rounds. The most literal interpretation of this concept is [[Vote unitarity]]. An alternative idea is that instead of spending the amount of ballot it is distributed between previous winners and potential winners. The distribution would follow the rule that the total is preserved. Whichever potential winner has the most distributed vote power available to them wins. This concept is maintained in SPAV and highest average party list systems. Each voter has their vote split between all their approved winners and the next potential one. The formula for their ballot weight is 1/(1+W). It is not clear if this conservation of ballot weight was what lead Thiele to proposing SPAV.
This rule is that for each voter the sum
To continue in the above derivation it would seem logical that when the score given is 0 we do not want the ballot to have any weight assigned to that candidate.
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<math>\begin{equation}
\frac{
\end{equation}</math>
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<math>\begin{equation}
\frac{S_{v,c} \times ( S_{v,c})}{
\end{equation}</math>
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This last undetermined constant, K, was discussed above in the variant section. The value of 2 would give Webster reweighting. This is a common debate when designing a system intended to produce something like [[Proportional representation]].
The key is to consider what the natural threshold should be in specific scenarios. Consider a 2 seat race with two factions Red and Blue. Assume Red is the larger party so it will win one of the seats. What fraction of votes does
{| class="wikitable"
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! Party list !! [[Monroe's method | Quota systems]] !! Psi/Harmonic voting !! [[Single distributed
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| Sainte-Laguë/Webster || Hare || Δ=½ || K=2 || 3/4
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The 3/4 threshold systems are
==Comparison to [[Reweighted Range Voting]]==
This system is very similar to Reweighted Range Voting. The logic for the theoretical motivation is laid out above. While the concept of an underlying conserved ballot might be compelling theoretically it is worth considering the practical differences. While results are similar in most situation it is worth noting that [[Single distributed vote]]
One clear benefit is that [[Single distributed vote]] is scale invariant
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