Distributed Voting: Difference between revisions
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Dr. Edmonds (talk | contribs) No edit summary |
Aldo Tragni (talk | contribs) (Added sections: Free Riding (and Surplus Handling), IWA example, Cardinal Voting (comparison). Removed "Related Systems - Cumulative voting" because it's already indicated in the initial description that it's a vote in Cumulative form. Removed "Related Systems - Baldwin's method" because the example concerned Borda and not DV; in this regard, a specific example for DV has been added in the "IWA example" section.) |
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==Procedure specification== |
==Procedure specification== |
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===Example normalization of a single vote=== |
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Given an initial vote of this type, with candidates A,B,C,D,E: |
Given an initial vote of this type, with candidates A,B,C,D,E, are removed in order E,D,C, and 100 points proportionally redistributed each time: |
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A[0] B[1] C[3] D[6] E[90] |
A[0] B[1] C[3] D[6] E[90] |
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===Normalization formula=== |
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v0 := old value of candidate X. |
v0 := old value of candidate X. |
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\end{equation}</math> |
\end{equation}</math> |
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It’s possible to divide by 100 all the points present in the initial votes, and use the following simplified formula throughout the counting process: |
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<math>\begin{equation} |
<math>\begin{equation} |
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\end{equation}</math> |
\end{equation}</math> |
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During counting, points can be represented in decimal form. |
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If the only candidate C with 0 points is eliminated from a vote like this A[80] B[20] C[0], there are 2 forms that the vote can take: |
If the only candidate C with 0 points is eliminated from a vote like this A[80] B[20] C[0], there are 2 forms that the vote can take: |
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It's recommended to use the honest form, also because the vote from the beginning may not have candidates with 0 points. |
It's recommended to use the honest form, also because the vote from the beginning may not have candidates with 0 points. |
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===Vote with only 0 points=== |
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If the only candidate C with points is eliminated from a vote like this A[0] B[0] C[100], you can proceed in 2 ways: |
If the only candidate C with points is eliminated from a vote like this A[0] B[0] C[100], you can proceed in 2 ways: |
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The two procedures return the same winners, but in the [[Multi-Member System|multi-winner]] case the winners can have different % of victory; in this case it's better to use procedure 1 for the reasons indicated above. |
The two procedures return the same winners, but in the [[Multi-Member System|multi-winner]] case the winners can have different % of victory; in this case it's better to use procedure 1 for the reasons indicated above. |
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===Tie during counting=== |
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Cases of parity can occur during counting, as in the following example: |
Cases of parity can occur during counting, as in the following example: |
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==Other properties== |
==Other properties== |
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===Tactical vote resistance=== |
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In the Distributed Voting, given an honest vote with this distribution of points [50 30 15 5 0], a tactical vote generally takes the following form [90 6 3 1 0]. |
In the Distributed Voting, given an honest vote with this distribution of points [50 30 15 5 0], a tactical vote generally takes the following form [90 6 3 1 0]. |
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In the Distributed Vote it's valid that, during the counting, the more points are redistributed after the elimination of the worst candidate, the more the votes become honest. |
In the Distributed Vote it's valid that, during the counting, the more points are redistributed after the elimination of the worst candidate, the more the votes become honest. |
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===Equality=== |
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⚫ | If the seats had fractional value |
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⚫ | Eg: a streamer wants to talk about 3 topics in a 4-hour live, chosen by his supporters through a poll. With Distributed Voting the 3 winning arguments A,B,C would also have associated the % of victory: A[50%] B[26%] C[24%]. These % indicate to the streamer that he must devote 2 hours to topic A, and 1 hour to topics B and C. Without these %, the streamer would have mistakenly spent 1 hour and 20 min for each of the topics. |
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===[[Free Riding]]=== |
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Given an honest vote of this type A[50] B[30] C[15] D[5], [[Free Riding]] can have the following consequences: |
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#increase the points given to the most preferred candidates who probably lose. The vote becomes similar to A[90] B[6] C[3] D[1]. |
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#decrease the points given to candidates who probably win. The vote, with a decreasing probability of candidates' victory from left to right, becomes similar to A[25] B[25] C[35] D[15]. |
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#the candidates' chances of winning aren't known enough. In this case, [[Free Riding]] doesn't occur and the voter tends to vote honestly. |
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Using the [[Surplus Handling]], in addition to increasing the complexity of the counting, reduces the tactic number 2 and greatly increases the tactic number 1, to the point that this would be used even when the voters don't know enough the chances of victory of the candidates. The [[Surplus Handling]] in the Distributed Voting would also cancel the [[Distributed Voting#Equality|Equality]] in some steps of the count. |
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For these reasons it's better to avoid using Surplus Handling in Distributed Voting. |
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===[[Independence of Worst Alternatives|IWA]] example=== |
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35 A[0] B[1] C[99] |
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33 A[99] B[0] C[1] |
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32 A[1] B[99] C[0] |
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Sum A[3299] B[3203] C[3498] |
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Head-to-head: A beats C beats B beats A. Distributed Voting in the first step eliminates candidate B, considered the worst, and between A and C, wins A. |
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Distributed Voting satisfies the [[Independence of Worst Alternatives|IWA]], so if candidate B (the worst) is added to the AvsC context (with A winner), it makes sense that A continues to be the winner. |
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⚫ | Eg: a streamer wants to talk about 3 topics in a 4-hour live, chosen by his supporters through a poll. With Distributed Voting the 3 winning arguments A,B,C would also have associated the % of victory: A[50%] B[26%] C[24%]. These % indicate to the streamer that he must devote 2 hours to topic A, and 1 hour to topics B and C. Without these %, the streamer would have mistakenly spent 1 hour and 20 min for each of the topics. |
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===Vote writing=== |
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==Systems comparison== |
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===[[IRV]]=== |
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===[[Cardinal|Cardinal Voting]]=== |
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Given a [[Cardinal|Cardinal vote]] like A[10] B[4] C[2] (range [0,10]), candidate A is eliminated, because he is considered to be the worst candidate overall. |
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*If the vote takes the form B[4] C[2] (leaving the vote unchanged), then a voting system equivalent to the [[Score Voting]] is obtained in which the single winner is from the beginning the candidate with the highest sum. |
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*If the vote takes the form B[10] C[5] or B[8] C[4] or B[6] C[4] or B[2] C[1], then a different voting system will be obtained. |
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The problem is that all the forms of voting listed respect the relative interests of the voter, but at the same time, they can ultimately return a different single winner. The [[Cardinal voting systems]] solves this ambiguity by making an arbitrary choice, not decided by the voters. |
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The problem described is avoided by Distributed Voting, because by removing a candidate, there is only one and unique way to proportionally redistribute the 100 points of the voter, respecting his relative interests. |
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==Related Systems == |
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* [[Cumulative voting]] |
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* [[Baldwin's method]] |
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==Forum Debate== |
==Forum Debate== |