User:Matijaskala/Probabilistic Approval Voting: Difference between revisions
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'''Probabilistic Approval Voting''' is a sequential [[Proportional representation|proportional voting system]] that uses either [[Approval ballot|approval]] or [[Score voting|score]] ballots. Probabilistic calculations are used as a tool to predict potential power balance of elected political factions. The method itself is deterministic. |
'''Probabilistic Approval Voting''' is a sequential [[Proportional representation|proportional voting system]] that uses either [[Approval ballot|approval]] or [[Score voting|score]] ballots. Probabilistic calculations are used as a tool to predict potential power balance of elected political factions. The method itself is deterministic. The system is 2-level [[Summability criterion|precinct-summable]] and passes the [[universally liked candidate criterion]]. |
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== Derivation == |
== Derivation == |
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* <math display="inline">V(A \and B)</math> ... number of voters who approve of both A and B |
* <math display="inline">V(A \and B)</math> ... number of voters who approve of both A and B |
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Let's say that |
Let's say that a candidate A proposes a decision. The probability that a candidate supports the decision equals <math display="inline">\frac{V(A \and B)}{V(B)}</math>. Expected number of votes that the decision gets equals <math display="inline">\sum_{B \in W}\frac{V(A \and B)}{V(B)}</math> or <math display="inline">\frac{\sum_{B \in W}\frac{V(A \and B)}{V(B)}}{V(A)}</math> per voter. To minimize number of votes per voter we elect the candidate with the highest score <math>\frac{V(A)}{1+\sum_{X \in W} \frac{V(A \and X)}{V(X)}}</math>. |
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In practice, electing a candidate whose inverse score is at least as low as inverse Hare quota will not always be possible. In that case we need to either add fail-safe approvals which we previously didn't consider or elect the candidate with the lowest inverse score and hope it is low enough. |
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A reasonable choice for P(A,B) would be <math display="inline">\frac{V(A \and B)}{V(B)}</math> which would give <math>\frac{V(A)}{1+\sum_{X \in W} \frac{V(A \and X)}{V(X)}}</math> as the formula for the score of candidate A. In each step we elect the candidate with the highest score. This version of the system is 2-level [[Summability criterion|precinct-summable]] and passes the [[universally liked candidate criterion]]. |
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In [[party list case]] P(A,B) equals 1 if A and B belong to the same party and 0 otherwise. Because of that the system decays into [[D'Hondt]]. |
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== Example == |
== Example == |