electowiki

Distributed Voting: Difference between revisions

Page Discussion

Distributed Voting (view source)

Revision as of 17:53, 30 March 2021

2,724 bytes added ,  3 years ago
Added Distributed Equal-Vote
VisualWikitext
mNo edit summary
(Added Distributed Equal-Vote)
 
(30 intermediate revisions by 3 users not shown)
Line 1:
[[File:DV Procedure.svg|alt=DV procedure|351px|thumb|DV procedure]]
Distributed Voting (DV) is a [[Single Member system|Single-Winner]] and [[Multi-Member System|Multi-Winner]] [[Cumulative voting|Cumulative voting system]].
Distributed Voting (DV) is a [[Single Member system|Single-Winner]] and [[Multi-Member System|Multi-Winner]], [[Cardinal voting systems]] proposed by [[User:Aldo Tragni|Aldo Tragni]].
 
==Procedure==
[[File:DV Procedure.svg|alt=DV procedure|350px|thumb|DV procedure]]
 
Voter score candidates with range [0,9]. The vote is then converted to 100 points (normalization).
Each voter has 100 points to distribute among the candidates according to his preferences.
 
# The point for eachworst candidate are summed and the one, with the lowest sum of points, is eliminated.
# In each individual vote, theThe points of the eliminated candidate are removedproportionally andredistributed thein each vote is normalized, so that it has 100 points again(normalization).
 
By repeating theprocesses process1 fromand the beginning2, athe worst candidate is eliminateeliminated each time, and the remaining candidates are the winners.
 
==Extended procedure (single winner)==
The remaining candidates are the winners.
 
It's the procedure indicated above in which:
* the votes are reversed and made negative before counting ''(subtracting 9 from the original ratings)''.
 
Original vote: A[9] B[7] C[5] D[3] E[1] F[0]
Reversed vote, made negative: A[0] B[-2] C[-4] D[-6] E[-8] F[-9]
 
''Reversing and making negative means that the voter's 100 points are used to disadvantage the worst from winning (points will be always negative in the counting). This procedure reduces the failure of monotony, for the single-winner case, and increases resistance to min-maxing strategies.''
 
==Ballot==
 
===Paper ballot===
 
Some examples of normalization:
 
Range [0,9] → Normalized in 100 points
9,0,0,0     →   100,0,0,0
9,9,0,0  →   50,50,0,0
9,6,4,1     →   45,30,20,5 (note: there isn't 0 in the lowest score)
 
[[File:Digital ballot DV.gif|320px|thumb|DV digital ballot (cumulative 100 points)]]
===Digital ballot===
 
By using self-resizing sliders it's possible to obtain a simple ballot that use the cumulative vote, with 100 points to distribute. However, it's better to use range [0,9] also in digital ballot.
 
==Procedure specification==
 
===Normalization formula===
 
P = 100 (can also be set to 1).
S = points sum of the candidates remaining in the vote, after an elimination.
V = old points value of candidate X.
newV = new points value of candidate X.
<math>\begin{equation}
newV=\frac{V}{S} \cdot P
\end{equation}</math>
 
If S=0 then all candidates remain at 0 points.
 
===Normalization example===
Line 24 ⟶ 61:
A[0] B[100]
 
===Tie during counting===
===Normalization formula===
 
Cases of parity can occur during counting, as in the following example:
e := value of the candidate eliminated from a vote.
 
Vote 1: A[55] B[25] C[10] D[10]
v0 := old value of candidate X.
Vote 2: A[50] B[30] C[10] D[10]
Sum of votes: A[105] B[55] C[20] D[20]
 
The tie can be managed in various ways:
v1 := new value of candidate X.
 
*delete C first, getting a result. Delete D first, getting another result. Check that the two results return the same winners.
<math>\begin{equation}
*delete C and D at the same time.
v1=\frac{v0}{1-\frac{e}{100}}
*randomly delete C or D.
\end{equation}</math>
 
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.
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:
 
===Procedure variant (discouraged)===
<math>\begin{equation}
v1=\frac{v0}{1-e}
\end{equation}</math>
 
One or more of the following steps are used:
===Vote without 0 points===
 
* 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.
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:
* [[Surplus Handling]] (in Distributed Voting it's not used for [[Multi-Member System|multi-winner]] context).
* If the remaining candidates are contained in a [[Smith set]], then the candidates with the highest sum wins.
 
==Seats allocation==
# honest form: A[80] B[20]
# tactical form: A[100] B[0]
 
The Distributed Voting indicates the method for obtaining single or multiple winners. The Distributed Voting System also describes how seats should be handled.
It's recommended to use the honest form, also because the vote from the beginning may not have candidates with 0 points.
 
===Vote with only 0 pointsParliament===
 
Procedure for electing parliamentarians:
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 state is divided into districts (at least 2, and possibly of similar size).
# The vote is excluded from the count: A[0] B[0].
* Each district must have at least 2 seats (at least 3, for a good representation). To satisfy this constraint you can increase the number of total seats or join the districts into groups.
# The points are divided equally between the remaining candidates with 0 points: A[50] B[50].
* In each district, the DV is used to obtain a number of winners equal to the number of seats in the district. The sum of the points for each winning candidate will indicate the % of victory of the candidates.
* If P is the power assigned to the district, then the weight of each seat will be: P • "% of victory of the candidate".
 
Example - 2 districts, 6 seats
Using procedure 2 you get a vote that:
Districts: d1{70%} d2{30%}
Seats: d1{3} d2{3}
Result: d1{ A1[40%] B1[35%] C1[25%] } d2{ B2[40%] C2[35%] D2[25%] }
Seat weights: d1{ A1[0.28] B1[0.245] C1[0.175] } d2{ B2[0.12] C2[0.105] D2[0.075] }
Total power: A[28%] B[36.5%] C[25%] D[6%]
 
If I had unit seats:
* cannot affect the victory of candidates who received the same points.
Seats: d1{4} d2{2}
* reduces the distance between the candidates present in it, and this can affect a possible process of assigning seats.
Result: d1{ A1[2] B1[1] C1[1] } d2{ B2[1] C2[1] }
* it can be considered not in accordance with the interests of the voter who, to those remaining candidates, had not awarded points.
Total power: A[33.3%] B[33.3%] C[33.3%] D[0]
 
Total difference: 5.3% + 3.2% + 8.3% + 6% = 22.8%
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.
An average error of 5.7% each candidate.
 
===Tie during countingGovernment===
 
Cases of parity can occur during counting, as in the following example:
 
Procedure for choosing the prime minister (PM) and the leader of the opposition (LO):
* Vote 1: A[55] B[25] 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]
 
* Parliamentarians elect, through Distributed Voting, the PM. Instead of being normalized to 100 points, the votes in this election are normalized to the weight that each individual parliamentary has (P = weight, in the normalization formula).
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).
* Once the PM is elected, only the votes that have assigned 0 points to the PM are taken and used to elect the LO, again through the Distributed Voting. Parliamentarians need to know in advance that giving 0 points to a candidate means being against them (opposites).
* Parliamentarians who gave 0 points to both the PM and the LO, can be considered neutral.
 
==Other properties==
Line 80 ⟶ 125:
===Tactical vote resistance===
 
'''Hypotheses'''
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].
 
Each voter, based on his own interests, creates the following 2 sets of candidates:
* If the first candidate to be eliminated were the first (the one with the most points), the two votes would both become like this [60 30 10 0], so the tactical vote would disappear.
 
* Winner Set = set containing a number of favorite candidates equal to or less than the number of winners.
* If instead the second and third candidates were eliminated, the two votes would become [91 9 0] (honest) and [99 1 0] (tactical). They are different but they are very similar, comparing them to their initial state.
* Loser Set = set containing the candidates who aren't part of the Winner Set.
 
InGiven thean Distributedhonest Votevote, it'sthe validtactical that,vote duringis theobtained counting,by minimizing the more points areof redistributedthe afterLoser Set, maximizing the eliminationpoints of the worstWinner candidateSet, theand moremaintaining the votesproportions becomeof honest interests within the two sets.
 
Example
===Equality===
Candidates: [A B C D E]
Honest vote: [50 30 15 5 0]
Tactical vote (1 winner): [90 6 3 1 0]
Tactical vote (2 winners): [60 36 3 1 0]
 
'''Single winner'''
By "Equality" means "one person, one vote (100 points)".
 
Meets the [[Honesty criterion]] (on hypotheses) because:
* In the Distributed Voting the voters at the beginning all have 100 points to distribute according to their preferences, therefore Equality is satisfied.
* 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.
 
* at each [[Honesty criterion|Update Steps]] of the count, in which a candidate with points is removed, the tactical vote decreases the deviation from the honest one (the deviation is the sum of the absolute differences of the points for each candidate, between tactical and honest vote).
There is no passage in the Distributed Voting where Equality doesn’t met.
* the [[Honesty criterion|Honesty Step]] occurs when the candidate in the Winner Set is removed or when all the candidates in the Loser Set are removed. In the best case, the [[Honesty criterion|Honesty Step]] can occur in the first [[Honesty criterion|Update Steps]].
* the [[Honesty criterion|Honesty Step]] is always present because in the single winner, during the counting, all candidates are always removed from at least one of the two Sets.
 
Example - 1 winner
===[[Free Riding]]===
Honest vote: [50 30 15 5 0]
Tactical vote: [90 6 3 1 0]
A is removed and the tactical vote becomes equal to the honest one, that is:
Vote: [60 30 10 0]
 
'''Multiple winner'''
Given an honest vote of this type A[50] B[30] C[15] D[5], [[Free Riding]] can have the following consequences:
 
Satisfy the [[Honesty criterion]] (on hypotheses) only if, in a vote, are removed first all the candidates of the Winner Set or first all those of the Loser Set.
#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].
#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.
 
===[[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.
For these reasons it's better to avoid using Surplus Handling in Distributed Voting.
 
Equality: Distributed Voting ensures that the power of the voters is always equal (100 points distributed) in all the counting steps, including the result.
===[[Independence of Worst Alternatives|IWA]] example===
 
The [[Surplus Handling]]:
35 A[0] B[1] C[99]
33 A[99] B[0] C[1]
32 A[1] B[99] C[0]
Sum A[3299] B[3203] C[3498]
 
* cancel the Equality in some steps of the count.
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.
* increase the complexity of the counting.
* isn't appropriate to manage seats with different weights.
 
For these reasons, it's better to avoid using Surplus Handling in Distributed Voting System.
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.
 
===Suitable for Web===
Line 124 ⟶ 174:
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* Ex.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.
 
* Ex.2: 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.
 
===VoteSystems writing=Variations==
 
===Distributed Equal-Vote (DEV)===
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.
 
Voter score candidates with range [-5,+5]. Each ballot is normalized by distributing -100 points between negative ratings, and 100 points between positive ratings (distribution of points uses the normalization of [[Distributed Voting]]).
Before the counting process, the grades will be normalized to 100-point grades, where the Xs are considered as equal weight values.
 
The candidate with the lowest sum of points is eliminated, and ballots normalized.
Examples of how a vote can be written by the voter and subsequently, in the counting, converted into 100 points:
 
By repeating the elimination process, the worst candidate is eliminated each time, and the remaining candidates are the winners.
X,0,0,0,0     →   100,0,0,0,0
X,X,X,X,0     →   25,25,25,25,0
4,3,2,1,0     →   40,30,20,10,0
40,6,3,1,0    →   80,12,6,2,0
101,0,0,0,0   →   100,0,0,0,0
999,99,9,1    →   89.17, 8.83, 1, 1
 
''Equal-Vote because given a vote, there can always be an opposite one that cancels it.''
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.
 
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]]).
 
==Systems comparison==
Line 153 ⟶ 196:
Examples where the 100 points are distributed exponentially:
 
100 99,1 → it's like [[IRV]]
99 90,9,1 → it's likea bit different from [[IRV]]
90 70,924,5,1 → it's a bit different from [[IRV]]
70 60,2427,59,3,1 → it's very different from [[IRV]]
 
60,27,9,3,1 → it's very different from [[IRV]]
Using range [0,9] completely eliminates the similarity:
 
range[0,9] → 100 points
9,1 → 90,10 → it's a bit different from [[IRV]]
9,5,1 → 60,33,7 → it's very different from [[IRV]]
 
Range [0,9] was chosen to better balance the simplicity of writing, the representation of interests, and the correctness of the count. Normalization applied to a range too small as [0,5], alters the voter's interests too much in the count.
 
===[[IRNR]]===
 
[[IRNR]] (L1 norm) is applied also on ranges with negative values such as [-5,+5] but this makes it subject to ambiguity.
 
Range [0,10] with IRNR
61: A[10] B[6] C[0]
39: A[0] B[6] C[10]
Eliminated in order C,A.
B wins.
 
Range [-5,+5] with IRNR
61: A[+5] B[+1] C[-5]
39: A[-5] B[+1] C[+5]
Eliminated in order C,B.
A wins.
 
In IRNR only by moving the range in negative value (leaving the interests of the voters and the size of the range unchanged), the winner changes. Distributed Voting instead avoid this ambiguity by imposing 0 as the minimum value in the range.
 
IRNR is a [[Single Member system|Single-Winner system]] which also, unlike Distributed Voting, doesn't reverse and make negative the vote before the count.
 
 
==Related Systems ==
By distributing points between 3 or more candidates, the Distributed Voting becomes increasingly different from the [[IRV]], because of normalization in the counting.
* [[Instant Runoff Normalized Ratings]] (ratings also negative, and it doesn't reverse and make negative the vote)
* [[Baldwin's method]] (Borda, and variant with different normalization)
 
==Forum Debate==
Aldo Tragni
206

edits

Retrieved from "https://electowiki.org/wiki/Special:MobileDiff/11402...13759"