User:Matijaskala/Probabilistic Approval Voting: Difference between revisions
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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 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 |
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 maximize <math>\frac{V(A)}{1+\sum_{X \in W} \frac{V(A \and X)}{V(X)}}</math> for each newly elected candidate. |
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== Example == |
== Example == |
Latest revision as of 12:22, 26 February 2024
Probabilistic Approval Voting is a sequential proportional voting system that uses either approval or 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 precinct-summable and passes the universally liked candidate criterion.
Derivation
Given:
- ... the set of all candidates
- ... the set of already elected candidates
- ... number of voters who approve of A
- ... number of voters who approve of both A and B
Let's say that a candidate A proposes a decision. The probability that a candidate supports the decision equals . Expected number of votes that the decision gets equals or per voter. To minimize number of votes per voter we maximize for each newly elected candidate.
Example
29 AB
1 B
14 C
In each step we elect the candidate with the highest .
First seat:
A:
B:
C:
B is elected
Second seat:
A:
C:
A is elected
Score ballots
Probabilistic voting can be done with score ballots. We start by treating maximum score as approval. Once every candidate's score falls below Hare quota we progressively add lower scores.