Distributed Voting: Difference between revisions
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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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==
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:
A[0] B[1] C[3] D[6] E[90]
A[0] B[100]▼
===Normalization formula===
▲A[0] B[10] C[30] D[60] : D is removed
▲A[0] B[25] C[75] : C is removed
▲A[0] B[100]
▲===Normalization of the vote===
▲e := value of the candidate eliminated from the vote.
v0 := old value of candidate X.
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\end{equation}</math>
<math>\begin{equation}
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\end{equation}</math>
▲===Managing votes without 0 points===
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.
===
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.
===
Cases of parity can occur during counting, as in the following example:
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==Other properties==
===
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.
===Equality===
===Fractional seats - Suitable for Web===▼
By "Equality" means "one person, one vote (100 points)".▼
If the seats had fractional value (instead of unitary), in addition to determining the winning candidates, the voting method should also determine the % of victory of the winning candidates. In the Distributed Voting the % of victory are already indicated by the sum of the points of the winning candidates, remaining at the end of the counting.▼
* In the Distributed Voting the voters at the beginning all have 100 points to distribute according to their preferences, therefore Equality is satisfied.▼
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.▼
* During all the counting steps, through the use of normalization, it ensures that all voters continue to have 100 points each, always distributed according to their interests, therefore Equality is satisfied.▼
* The result is one of the counting steps, in which Equality continues to be satisfied.▼
There is no passage in the Distributed Voting where Equality doesn’t met.▼
Eg: on a crowdfunding platform, fans can have a different weight in the vote, based on how much money they have donated. In Distributed Voting you can manage directly this difference in power by assigning fans different amounts of points to distribute.▼
===
Given an honest vote of this type A[50] B[30] C[15] D[5], [[Free Riding]] can have the following consequences:
To make the writing of the vote more comprehensible and simple, the voter can be left with almost complete freedom in the use of numerical values or only X.▼
#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].
Before the counting process, the grades will be normalized to 100-point grades, where the Xs are considered as equal weight values.▼
#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].
#the candidates' chances of winning aren't known enough. In this case, [[Free Riding]] doesn't occur and the voter tends to vote honestly.
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.
Examples of how a vote can be written by the voter and subsequently, in the counting, converted into 100 points:▼
For these reasons it's better to avoid using Surplus Handling in Distributed Voting.
===[[Independence of Worst Alternatives|IWA]] example===
X,0,0,0,0 → 100,0,0,0,0▼
35 A[0] B[1] C[99]
X,X,X,X,0 → 25,25,25,25,0▼
33 A[99] B[0] C[1]
32 A[1] B[99] C[0]
Sum A[3299] B[3203] C[3498]
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.
4,3,2,1,0 → 40,30,20,10,0▼
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.
40,6,3,1,0 → 80,12,6,2,0▼
101,0,0,0,0 → 100,0,0,0,0▼
▲If the seats had different fractional value
999,99,9,1 → 89.17, 8.83, 1, 1▼
▲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.
The complexity in writing the vote adapts to the voter, and it’s also noted that, if 101 or 99 points are mistakenly distributed, the vote will still be valid.▼
▲Eg: on a crowdfunding platform, fans can have a different weight in the vote, based on how much money they have donated. In Distributed Voting you can manage directly this difference in power by assigning fans different amounts of points/votes to distribute.
In the last example they are set to 1, the decimal values which should be less than 1, and the remaining points are divided proportionally among the other candidates (it serves to prevent Distributed Voting from becoming like [[IRV]]).▼
===
▲To make the writing of the vote more comprehensible and simple, the voter can be left with almost complete freedom in the use of numerical values or only X.
Examples where the 100 points are distributed exponentially:▼
▲Before the counting process, the grades will be normalized to 100-point grades, where the Xs are considered as equal weight values.
100 → it's like [[IRV]]▼
▲Examples of how a vote can be written by the voter and subsequently, in the counting, converted into 100 points:
99,1 → it's like [[IRV]]▼
90,9,1 → it's a bit different from [[IRV]]▼
▲The complexity in writing the vote adapts to the voter, and it’s also noted that, if 101 or 99 points are mistakenly distributed, the vote will still be valid.
70,24,5,1 → it's different from [[IRV]]▼
▲In the last example they are set to 1, the decimal values which should be less than 1, and the remaining points are divided proportionally among the other candidates (it serves to prevent Distributed Voting from becoming like [[IRV]]).
60,27,9,3,1 → it's very different from [[IRV]]▼
==Systems comparison==
By distributing points between 3 or more candidates, the Distributed Voting becomes increasingly different from the IRV, because of normalization in the counting.▼
===
▲Examples where the 100 points are distributed exponentially:
▲By "Equality" means "one person, one vote (100 points)".
▲ 100 → it's like [[IRV]]
▲* In the Distributed Voting the voters at the beginning all have 100 points to distribute according to their preferences, therefore Equality is satisfied.
▲ 99,1 → it's like [[IRV]]
▲* During all the counting steps, through the use of normalization, it ensures that all voters continue to have 100 points each, always distributed according to their interests, therefore Equality is satisfied.
▲ 90,9,1 → it's a bit different from [[IRV]]
▲* The result is one of the counting steps, in which Equality continues to be satisfied.
▲ 70,24,5,1 → it's different from [[IRV]]
▲ 60,27,9,3,1 → it's very different from [[IRV]]
▲By distributing points between 3 or more candidates, the Distributed Voting becomes increasingly different from the [[IRV]], because of normalization in the counting.
▲There is no passage in the Distributed Voting where Equality doesn’t met.
===[[Cardinal|Cardinal Voting]]===
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.
*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.
*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.
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.
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.
==Forum Debate==
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