Distributed Voting: Difference between revisions

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v1 := new value of candidate X.
v1 := new value of candidate X.


P := 100 (total points used in a vote)
<math>\begin{equation}
v1=\frac{v0}{1-\frac{e}{100}}
\end{equation}</math>

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:


<math>\begin{equation}
<math>\begin{equation}
v1=\frac{v0}{1-e}
v1=\frac{v0}{1-\frac{e}{P}}
\end{equation}</math>
\end{equation}</math>


===Vote without 0 points===
===Vote 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:
If the only candidate C with 0 points is eliminated from a vote like this A[80] B[20] C[0], there are 2 procedures you can use:


# A[100] B[0] : set the candidate with the least points to 0.
# honest form: A[80] B[20]
# A[80] B[20] : having eliminated C (0 points), there aren't points to redistribute.
# tactical form: A[100] B[0]


Eg. given the following 2 votes to count: V1-A[55] B[45] C[0] and V2-A[0] B[100] C[0] then:
It's recommended to use the honest form, also because the vote from the beginning may not have candidates with 0 points.

*using procedure 1, a tie is obtained between A and B.
*using procedure 2, B would win.

V1 likes A and B almost in the same way, so the victory of B would make both V1 and V2 happy. For this reason it's recommended to use procedure 2, which keeps the voter's honest interests even in the counting.


===Vote with only 0 points===
===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:


# The vote is excluded from the count: A[0] B[0].
# A[0] B[0] : the vote is excluded from the count.
# The points are divided equally between the remaining candidates with 0 points: A[50] B[50].
# A[50] B[50] : the points are divided equally between the remaining candidates with 0 points.


Using procedure 2 you get a vote that:
Using procedure 2 you get a vote that:
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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:


* Vote 1: A[55] B[25] C[10] D[10]
Vote 1: A[55] B[25] C[10] D[10]
* Vote 2: A[50] B[30] C[10] D[10]
Vote 2: A[50] B[30] C[10] D[10]
* Sum of votes: A[105] B[55] C[20] D[20]
Sum of votes: A[105] B[55] C[20] D[20]


The tie can be managed in various ways:
In this case, the worst candidate is both C and D so you have to eliminate them simultaneously. The amount of points to be redistributed will be the sum of the points that had C and D (40 in the example).

*delete C first, obtaining a result. Delete D first, getting another result. Check that the two results return the same winners.
*delete C and D at the same time.
*randomly delete C or D.

This situation is extremely rare, and even when it occurs it's further rare that the order in which the candidates in the tie are eliminated affects the result. Random deletion is the easiest to use.

===Procedure variant (discouraged)===

* When the worst is eliminated, the candidates with the lowest score among those left in the vote must be set to 0, and then normalizes.

* Surplus Handling is used in the case of [[Multi-Member System|Multi-Winner]].


==Other properties==
==Other properties==
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===Equality===
===Equality===


By "Equality" means "one person, one vote (100 points)".
By "Equality" means "equal power (100 points) to each person".


* In the Distributed Voting the voters at the beginning all have 100 points to distribute according to their preferences, therefore Equality is satisfied.
* In the Distributed Voting the voters at the beginning all have 100 points to distribute according to their preferences, therefore Equality is satisfied.
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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.
#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]]:
⚫
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.

⚫
* 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.
* cancel the [[Distributed Voting#Equality|Equality]] in some steps of the count.
* increase the complexity of the counting.
* if a voter votes A[99] B[1] C[0] ..., in case A wins by getting double the threshold, the voter would be very satisfied with A's victory, then move half the points from A to B would mean giving the voter extra unjustified power.

For these reasons it's better to avoid using Surplus Handling in Distributed Voting.
For these reasons it's better to avoid using Surplus Handling in Distributed Voting.


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If the seats had different fractional value, in addition to determining the winning candidates, Distributed Voting also determine their % of victory, which are already indicated by the sum of the points of the winning candidates, remaining at the end of the counting.
If the seats had different fractional value, in addition to determining the winning candidates, Distributed Voting also determine their % of victory, which are already indicated by the sum of the points of the winning candidates, remaining at the end of the counting.


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.
Eg 1: 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.

⚫
Eg 2: 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.


Eg 3: in an image contest, there is a cash prize to be awarded to the 3 best images. The prize will be divided appropriately according to the % of victory and not in a pre-established way before the contest.
⚫
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.


===Vote writing===
===Vote writing===
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