electowiki

Distributed Voting: Difference between revisions

Page Discussion

Distributed Voting (view source)

Revision as of 17:53, 30 March 2021

495 bytes removed ,  3 years ago
Added Distributed Equal-Vote
VisualWikitext
(Added section about IRNR)
(Added Distributed Equal-Vote)
 
(8 intermediate revisions by the same user not shown)
Line 1:
[[File:DV Procedure.svg|alt=DV procedure|350px351px|thumb|DV procedure]]▼
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]].
 
This system, in the [[Single Member system|Single-Winner]] context, avoids the ambiguity of the [[IRNR]] (L1 norm). More information in the dedicated [[Distributed Voting#IRNR|section]].
 
==Procedure==
▲[[File:DV Procedure.svg|alt=DV procedure|350px|thumb|DV procedure]]
[[File:DV paper ballot.svg|320px|thumb|DV paper ballot (range [0,10])]]▼
[[File:Digital ballot DV.gif|320px|thumb|DV digital ballot (cumulative 100 points)]]
 
Voter score candidates with range [0,109]. The vote is then converted to 100 points (normalization).
 
# The worst candidate, with the lowest sum of points, is eliminated.
# The points of the eliminated candidate are proportionally redistributed in each vote (normalization).
 
By repeating processes 1 and 2, athe worst candidate is eliminateeliminated each time, and the remaining candidates are the winners.
 
==Extended procedure (single winner)==
The remaining candidates are the best (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==
Line 23 ⟶ 27:
Some examples of normalization:
 
Range [0,109] → Normalized in 100 points
109,0,0,0     →   100,0,0,0
109,109,0,0  →   50,50,0,0
109,56,54,01     →   5045,2530,2520,5 (note: there isn't 0 in the lowest score)
10,6,3,1     →   50,30,15,5 (note: there isn't 0 in the lowest score)
 
▲[[File:DV paperDigital ballot DV.svggif|320px|thumb|DV paperdigital ballot (rangecumulative 100 [0,10]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 [0,109] also in digital ballot.
 
==Procedure specification==
Line 38 ⟶ 42:
 
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 54 ⟶ 60:
A[0] B[25] C[75]
A[0] B[100]
 
===All 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:
 
# A[0] B[0] : the vote is excluded from the count.
# A[50] B[50] : the points are divided equally between the remaining candidates with 0 points.
 
Using procedure 2 you get a vote that:
 
* cannot affect the victory of candidates who received the same points.
* reduces the distance between the candidates present in it, and this can affect a possible process of assigning seats.
* it can be considered not in accordance with the interests of the voter who, to those remaining candidates, had not awarded points.
 
The two procedures return the same winners, but in the [[Multi-Member System|multi-winner]] procedure 2 generates more similar % of victory.
 
===Tie during counting===
Line 91 ⟶ 82:
 
* 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]] (in Distributed Voting it's not used in thefor [[Multi-Member System|multi-winner]] context).
* If the remaining candidates are contained in a [[Smith set]], then the candidates with the highest sum wins.
 
Line 138 ⟶ 129:
Each voter, based on his own interests, creates the following 2 sets of candidates:
 
* Winner Set = set containing a quantitynumber of favorite candidates equal to or less than the number of winners.
* Loser Set = set containing the candidates who aren't part of the Winner Set.
 
Line 175 ⟶ 166:
* cancel the 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 satisfaction (he's already 99% satisfied with the victory of A).
* isn't appropriate to manage seats with different weights.
 
For these reasons, it's better to avoid using Surplus Handling in Distributed Voting System.
 
===Suitable for Web===
Line 186 ⟶ 176:
* 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.32: 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.▼
* Ex.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, through the cumulative vote.
 
==Systems Variations==
▲* Ex.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.
 
===Distributed Equal-Vote (DEV)===
 
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]]).
 
The candidate with the lowest sum of points is eliminated, and ballots normalized.
 
By repeating the elimination process, the worst candidate is eliminated each time, and the remaining candidates are the winners.
 
''Equal-Vote because given a vote, there can always be an opposite one that cancels it.''
 
==Systems comparison==
Line 201:
60,27,9,3,1 → it's very different from [[IRV]]
 
Using range [0,109] completely eliminates the similarity:
 
range[0,109] → 100 points
109,1 → 9190,9 10 → it's a bit different from [[IRV]]
109,5,1 → 6360,3133,67 → it's very different from [[IRV]]
 
Range [0,109] 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 on rating ballots, also on ranges with negative values such as [-5,+5]. Distributedbut Voting,this inmakes theit [[Single Member system|Single-Winner]] context, is a subcategory of IRNR, which binds the minimum value of the rating ballotssubject to 0 (doesn't accept ratings with negative values)ambiguity. This constraint is important because it avoids the ambiguity of the IRNR:
 
Range [0,10] with IRNR and Distributed Voting
61: A[10] B[6] C[0]
39: A[0] B[6] C[10]
Eliminated in order C,A.
B wins.
IRNR and Distributed Voting are equivalent in this case.
 
Range [-5,+5] with IRNR
Line 226 ⟶ 225:
A wins.
 
In IRNR only by changingmoving 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 ratingrange.
 
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 ==
* [[Instant Runoff Normalized Ratings]] (ratings also negative, and it doesn't reverse and make negative the vote)▼
* [[Distributed Multi-Voting]] (particular vote conversion)
▲* [[Instant Runoff Normalized Ratings]] (ratings also negative)
* [[Baldwin's method]] (Borda, and variant with different normalization)
 
Aldo Tragni
206

edits

Retrieved from "https://electowiki.org/wiki/Special:MobileDiff/12172...13759"