Distributed Voting (DV) vs Range Voting (RV) - Extended

Distributed Voting vs Range Voting (Score Voting)
In the end there is a list of the downsides of the RV and DV.
If you want to comment on the topic, refer to the numbers next to the titles.
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(1) Philosophy of interests (introduction)
E.g. using foods (instead of candidates):

  1. there are foods that you are willing to eat (make you happy, satisfied), foods that you are not willing to eat (make you sad, unsatisfied) and unknown foods → Categories: Positive, Negative, Unknown
  2. Among the positive and negative foods, however, there may be some more positive than others → Sorting .
  3. In addition to sorting, it’s also important how much better or worse one food is → Distance .
  4. Unknown foods are (statistically) better than negative ones and worse than positive ones.

The real interests of a voter will take a numerical form similar to this, with range [-10,10]:
10 7 6 5 1 0 -2 -4 -8 -9 -10
0: for unknown candidates.
(0,10]: for positive candidates.
[-10,0): for negative candidates.
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(2) Form of the vote
Hypothesis of voter real interests: 10 8 6 4 2 0 -2 -4 -6 -8 -10

RV
Honest voting can take 4 forms:

  • 10 9 8 7 6 5 4 3 2 1 0 (sort)
  • 10 10 10 10 10 5 0 0 0 0 0 (cat)
  • 10 8 6 4 2 0 0 0 0 0 0 (sort-cat)
  • 10 10 10 10 10 8 6 4 2 1 0 (cat-sort)

Ambiguous vote: voters with the same interests may have different votes depending on whether they give greater importance to the category or the sorting.
Unknown favorites: in some types of vote, unknown candidates can even receive 5-8 points (type of vote 1,2,4).

DV
The honest vote of the voter takes only one form:
34 27 20 13 6 0 0 0 0 0 0

  • even in an honest vote, it makes no sense to waste limited points on unknown or negative candidates, when they could instead be given to positive candidates.
  • the fact of being an honest vote avoids the accumulation of points, which will be treated in the tactical votes.

Conclusion
Honest votes in the DV have no ambiguity and don’t favor unknown candidates (unlike the RV).
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(3) Writing a vote
RV
Simple on paper: you only need to blacken the score box to be assigned.
Simple digital: using slider or click on the value to be assigned.

DV
A little more complex in paper: it requires you to write the amount of points in number (which in any case doesn’t have to be 100, given that you can normalize the vote automatically before counting).
Simple digital: using sliders that automatically resize.

Conclusion
DV is a bit more complex to write in paper format.
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(4) Counting of votes
RV
Single winner

  1. sum of points for each candidate.
  2. the candidate with the highest sum wins.

Multiple winners (most famous)

  1. the winning candidate is removed, and the weight of the votes is changed.
  2. the points are added again to find a new winner, until the desired number of winners is reached.

Ambiguity / Complexity (multiple winners): there are different formulas used to change the weight of a vote. This ambiguity makes it complex to make a voter accept why a certain formula is used rather than another.
No % of victory (multiple winners): RV returns a certain number of winners but in its standard form it doesn’t indicate how much better a candidate is than the others who have won; only the order in which they win is indicated.

DV
Single and multiple winners

  1. The points are added for each candidate.
  2. The candidate with the smallest sum loses and is removed.
  3. The votes are normalized (the points assigned to the eliminated candidate are redistributed in the vote proportionally to the interests of the voter).
  4. Add the votes again to find a new loser to be eliminated, until reaching the desired number of winners, who are the remaining candidates.

No Ambiguity: there is only one way to normalize a score to 100 points.
Ex: [50 30 15 5 0] removing the first candidate, there would be 50 points to be redistributed proportionally, and the way to do this is only one, that is: [60 30 10 0]

Understanding (single winner): DV is a little more complex than RV because it also uses the normalization of the vote. If normalization is considered simple to understand then DV will also be simple.
Understanding (multiple winners): DV is simpler than the respective RV, because it doesn’t have the ambiguity of the RV.

% of victory: the % of victory is indicated by the sum of the points for each winning candidate left at the end.

Conclusion
Single winner: RV is a little easier to understand.
Multiple winners: RV has ambiguity (resulting complexity), and in the “standard form” it doesn’t return the % of victory, but only the order of victory of the candidates.
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(5) Tactical Votes - Unknown Results
RV - Single winner
The tactics that a voter can use are:

  1. increase the points given to its positive candidates, to make them win more likely.
  2. decrease the points of some candidates, to decrease the probability of victory or to increase the probability of victory of others.
  3. increase the points given to unknown candidates, to decrease the probability of victory of negative candidates.

High influence of the tactical vote: given a set of honest voters who vote with intermediate scores: [10 9 8 7 6 5 4 3 2 1 0] a group of tactical voters (also relatively small) who vote instead only with high or low scores: [10 10 10 10 10 0 0 0 0 0 0] would be highly favored over the others.

DV - Single winner
The tactics that a voter can use are:

  1. accumulate points on a more preferred candidate, to favor him over the others.

In this context there are no other types of tactical voting that can be used.

Little impact of the tactical vote: eg if the honest vote of a voter is like this: [50 30 15 5 0] then his tactical vote will look like this: [90 6 3 1 0]. The example shows that if the preferred candidate is eliminated (because it is a minority), the tactical vote becomes the same as the honest one, in fact in both cases, the 100 points would be distributed proportionally as follows: [60 30 10 0].
More in general, the more points are redistributed in a tactical vote, the more the tactical vote will become equal to the honest one. During the count, tactical votes tend to become more and more similar to honest voting.

RV - Multiple winners
All the tactics listed in the single winner apply.

DV - Multiple winners
The more the number of winners increases, the more the tactical votes are reduced (they are canceled when everyone wins).
Eg honest vote: A[50] B[30] C[15] D[5] E[0] F[0]
This honest vote means that the voter in question wants to give: half of his power to A, one third of his power to B, one sixth of his power to C, etc. therefore for this voter the best way to represent these interests is just to vote honestly. Accumulating points on candidate A would make him go against his true interests, in this case.

Conclusion
RV is subject has many tactics, and the tactical vote greatly affects the result.
DV has only one tactic that during the counting (for single winner), makes the tactical vote more and more honest. Also, as the winners increase, the need to use tactical votes decreases.
All this is valid only if before voting there is no information on the possible results of the vote.
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(6) Tactical Votes - Known Overall Preferences
RV
The use of tactics in RV is expanded, based on overall preferences.

Disadvantaged minorities (single winner): if the 2 favorite candidates of the vote are known, a voter tends to assign 10 points to the preferred candidate between the two favorites and 0 points to the other, so that his vote is as influential as possible in the probable final clash between the 2 favorites.
If all the voters, who support minorities, were to reason in this way, then it would be impossible for a minority to overcome one of the two favorite candidates because both the minority and the favorite receive 10 points in the votes.

DV
Normalization in the DV depends on how the points are distributed in the individual marks.
Knowing broadly the overall preferences of the voters doesn’t mean knowing the exact way in which a voter distributes his points in the single vote; this makes it difficult to predict how normalization will affect DV counting.
In the case of a single winner, normalization is often used so it’s difficult to create tactical votes despite knowing the overall preferences of the voters (this, compared to RV).

Doesn’t disadvantage minorities (single winner): if the 2 candidates preferred in the vote don’t like the voter, then the voter will simply have to give only 1 point out of 100 to that favorite candidate of the two, in this way:
(1) in the vote the preferred candidates (minorities) will have many more points than the candidate they don’t like (but who is favored).
(2) if the preferred candidates of the voter are actually minorities, they will all be eliminated and the 100 points will end up in the preferred candidate of the two remaining at the end, making the vote influential in the final clash (without the need to use tactical votes).

Conclusion
RV disadvantages minorities, unlike DV.
Normalization is difficult to exploit to create tactical votes.
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(7) Monotony vs IWA
RV satisfies Monotony, but not IWA.
DV satisfies IWA, but not Monotony.
Monotony and IWA are both important but both cannot be met, so you need to understand which of the two criteria is the best to meet.
We focus on the individual winner, since it’s the context in which these criteria fail more easily.

Monotony Failure (DV)
Monotony fails when:

  • by increasing the points given to a candidate, he loses
  • by reducing the points given to a candidate, he wins

(1) The two tactics indicated above are likely to backfire on those who use them.
(2) If there are many people to vote, it’s also necessary that the tactics indicated above are used by a large group of specific people (not trivial).
(3) First of all, we must also make sure that we are in a vote where Monotony can actually fail. To know this, in the DV it’s necessary to know well how the voters distribute their points in the votes (since the count is based on the normalization of the votes).
Summing up:
Exploiting the failure of Monotony to your advantage is extremely difficult, and extremely risky.

Failure of the IWA (in RV)

  • IWA fails when a new candidate is added, similar to the best (current winner) but worst of all.

Ex: R (right candidate), L (left candidate).
Those who support the right, far-right and center-right vote: R[10], L[0], and vice versa those who support the Left. In this context R wins.
Next, a far-right candidate eR is added. Far-right voters, who previously voted like this: R[10], L[0] could now vote e.g. like this: eR1[10], R[6], L[0], removing points to R.
This behavior reduces the points of R and makes L win.
Political factions, who know the general interests of voters well, can easily create candidates to play the role of eR (spoiler), to condition the election to their advantage.

Conclusion
The failure of IWA can be exploited very easily when compared to the failure of Monotony, so satisfying IWA is more important.
The example also shows a huge spoiler effect problem present in the RV, but not in the DV.
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(8) Downsides summary
RV

  • (2) ambiguity in honest voting (not in DV).
  • (2) favors unknown candidates (not in DV).
  • (4) in multiple winners it’s hard to understand and accept (because of ambiguity) and missing % victory (not in DV).
  • (5) tactics: increase points to positive candidates, to increase the probability of victory.
  • (5) tactics: I decrease points to the negative candidates, to decrease their probability of victory.
  • (5) tactics: increase points to unknown candidates, to decrease the probability of victory of the negative candidates.
  • (5) the tactical vote has a great impact on the result, in the single winner case (not in DV).
  • (6) disadvantages minorities (not in DV).
  • (6) easy to create tactical votes knowing the overall interests of the voters (less in DV).
  • (7) the IWA fails with a consequent increase in the spoiler effect (which is worse than the failure of the Monotony).

DV

  • (3) it’s a little more complicated to write in paper form (you need to write numbers).
  • (4) in the case of single winner is a bit more complicated to understand (because of normalization).

Partial defects with respect to the RV:

  • (5) tactic in single winner: accumulation of points on a more preferred candidate, to favor him over the others (the tactical vote has little effect on the result, so this tactic becomes less effective).
  • (7) Monotony fails (which, however, is better than the failure of the IWA).

But why does it make sense to give the same score to both a middle-satisfaction candidate and one you absolutely hate? If your first 5 candidates are eliminated your vote would be exhausted.

Really? I think the single-winner case of RV is most familiar (rating products on Amazon, etc). There has been a lot of discussion here about multi-winner RV but most people are not aware of that.

At every stage of all of the proportional RV systems I have seen, there is some number of total vote power left. A candidate’s score divided by that vote power is their % of victory.

This one contains all three of RV’s tactics within itself. RV just allows you to do the three independently.

False in practice, because as the number of winners increases, the number of candidates generally increases linearly.

If all voters are in 2 factions and everyone assigns 10 points to their candidate and 0 points to the opposing faction, there is still a chance for a mutually respected 3rd candidate to win in RV.

Your system does have the advantage that if I don’t really like my “favorite” of the 2 big rivals then I do not have to score them high… unless I think Best will lose to Worst head-to-head while Middle will beat Worst. In that case (just like with IRV and STAR) I might want to give more points to Middle to protect Middle against elimination.

This would be stupid for the far-right voters because they know their candidate is a long shot. Anyone who actually cares would vote eR[10], R[10], L[0]. Only if eR is actually a serious contender (e.g. passes L in points) should their base consider dropping the backup.

Political factions, who know the general interests of voters well, can easily convince their voters to vote for backup candidates, to condition the election to their advantage.

If your first 5 candidates are eliminated your vote would be exhausted

The logic of the DV is to redo the elections (through the normalization of votes) every time the worst is eliminated.
Given a rating like this: A[50], B[40], C[9], D[0], E[1]
If A,B,C are eliminated because they are the worst, the voter in question would have voted like this: D[0], E[100] so this is inevitably the vote that I must consider in the final clash between D and E.
If the candidates had been only D and E from the beginning, it would not make sense to say that the voter would have given only 1 point (out of 100) to E.

Multiple winners (most famous)

I mean that the RV, in the case of multiple winners, is much discussed and has different forms so I have considered the most common and general procedure that is: the weight of the votes is reduced on the basis of which candidate wins. In the case of a single winner instead, I speak of the classic RV (the biggest sum wins, and stop).

% of victory

In the proportional RV systems that I have seen, if a candidate receives more points than the threshold, these additional points are given to other candidates (based on the preferences of the marks).
In the end you get N winners who have all reached the threshold, but who are equal.

This one contains all three of RV’s tactics within itself. RV just allows you to do the three independently.

The tactic of giving points to unknown candidates to disadvantage negative ones is much rarer in DV because it would be a bit of a waste of points (better to give them to positive candidates).
For the other 2 tactics, it’s true but they have different consequences on the vote.
Real interests: A[80], B[50], C[10], D[-20], E[-100]
DV (accumulation of points): A[94], B[5], C[1], D[0], E[0]
The proportionality of A with respect to the others is falsified, but the others are respected.
RV (increase points to positives): A[10], B[9], C[8], D[0], E[0]
RV (decrease points to favor the favorite): A[10], B[2], C[1], D[0], E[0]
Proportionality falsified in all candidates (exaggerating in giving or removing points, order would also be lost).
Also remember that if A is eliminated as a minority, the vote in the DV becomes honest.

False in practice, because as the number of winners increases, the number of candidates generally increases linearly.

In practice, it can also increase but the candidates that appear are smaller and smaller minorities that can be eliminated by leaving honest all the votes not given to the minorities (and the votes that preferred a minority at most, become honest thanks to normalization).

If all voters are in 2 factions and everyone assigns 10 points to their candidate and 0 points to the opposing faction, there is still a chance for a mutually respected 3rd candidate to win in RV.

The possibility is there but it’s very reduced if 10 points are given to both the 3rd and 1 of the two favorites.

unless I think Best will lose to Worst head-to-head while Middle will beat Worst. In that case (just like with IRV and STAR) I might want to give more points to Middle to protect Middle against elimination.

No.
Eg. Favorites A and B; C is middle.
My favorite is C; in second place is A.
RV: since C probably loses, I assign 10 points to both A and C (the vote disadvantages the minority C who should have had more points than A in the vote).
DV: it’s irrelevant if he loses C or A first because anyway the 100 points will all end up on what remains (and all against B) so I can easily give more points to C and a little less to A (in the vote, C rightly has more points of A, therefore C is not disadvantaged as in RV).

Anyone who actually cares would vote eR [10], R [10], L [0]. Only if eR is actually a serious contender (e.g. passes L in points) should their base consider dropping the backup.

You are solving the problem by saying that voters should vote tactically (which is not a real solution)

Final consideration
if you want to get the result that is as correct as possible, then you should try to minimize the tactical votes of the voters (which badly represent the real interests of the voters).
Vote: A[10], B[10], C[0] instead of honest A[10], B[5], C[0] because A could lose, it’s something very problematic because it causes the voter doesn’t express his true interests in the vote.
Not to mention that a political faction could publish more or less false predictions of the results precisely to condition the voters to make certain tactical votes.
Not to mention the ambiguity of the honest vote in RV; honestly i wouldn’t know how to vote honestly in RV (single winner).

I’m used to voting tactically because otherwise my minority preferences would end up being an ineffective vote. That’s why intuitively as a voter I really like Distributed Voting (DV), this could be naive though since I’m not that good in understanding the deeper workings and unexpected and unintended consequences of voting methods. Would it be a good idea to adapt DV in order to reduce tactical voting to reward honest voters using the surprisingly popular method ( https://en.wikipedia.org/wiki/Surprisingly_popular method) ? It would require voters to somehow express something about their expectations and use that somehow in the DV method (yeah yeah, it might sound or be too complex).

I take this opportunity to say that the basic problem is that, there is no way to know a person’s absolute interests; the interests are always relative to the set of candidates proposed.
Given these two votes:
V1: A[0], B[1], C[99]
V2: A[99], B[0], C[1]
if C had not been there, to say that the votes would have had this form:
V1: A[0], B[1]
V2: A[99], B[0]
it should be true that V1 likes B 99 times less than V2 likes A, but this is impossible to know.
Since only the relative interests are known, the points can be correctly distributed only considering these relative interests, therefore like this:
V1: A[0], B[100]
V2: A[100], B[0]
If absolute interests could be used, most of the problems would not exist, but the (human) reality is relative (about interests), and if this generates errors, there is little to be done. The best you can do is minimize tactical votes (aware that there will still be errors, but less).

Would it be a good idea to adapt DV in order to reduce tactical voting to reward honest voters using the surprisingly popular method?

It might make sense to include the surprisingly popular method if you find a way to get people to answer questions honestly. If they have no interest in answering honestly, then they will find a way to tactically exploit the surprisingly popular method.
At the moment I can’t think of a way to make them honest in that method.

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Your example was more like A[50] B[40] C[10] D[0] E[0], except you had 5 candidates that got points and 5 that did not.

Doesn’t DV do that as well? In either case you could consider their “% of victory” to be the score they had before their excess is redistributed.

If the voter is voting tactically, why not give a point to D, because D may be the only candidate who can stop E from winning?

No, what would happen in a 5-winner district is the Democrats would run 5-7 candidates, the Republicans would run 5-7 candidates, and a strong third party would run maybe 2 or 3 candidates, and there would be a lot more. Most of, say, the Democrats are automatically “strong” and which one wins depends mostly on the preferences of Democratic voters.

If the factions are in a close split (e.g. less than 60-40) then the third party only needs to get an average of 6 points (which can come from a 10-vote from 60%, or 6-votes from everyone, or some other combination). If the third party cannot accomplish that, then it is too weak to deserve to win.

What if polls are saying that more people prefer B (your worst) over C (your fave), but also more people prefer A (your second place) over B? Then you do not want A to be eliminated first, because there will be more votes stretched to B[100] C[0] than vice versa, and B wins.

The difference here is that DV incentivizes you to take points away from your favorite, while RV does not.

Except you yourself  seem to suggest that DV encourages all voters to vote tactically. Since when is a vote of A[90] B[6] C[3] D[1] E[0] (preferences: A=+40 B=+30 C=+15 D=+5 E=0) anything but “tactical”?

If everyone exaggerates in this way, the system basically degenerates into Instant Runoff Voting, and well-liked consensus candidates that are few people’s first choices cannot win.

With RV, maximum tactical voting degenerates it into Approval Voting, which is better than IRV.


Let’s assume V2 is a minority (33%) and V1 a majority (67%). Part of the whole idea of RV is to sometimes allow the passionate minority to win – BUT ONLY IF THE MAJORITY ALLOWS IT TO HAPPEN. Of course, this would happen far more often if there were more than 2 candidates.

You might have an easier time indicating honest rated preferences when looking at individual head-to-head matchups, rather than constraining your preferences to a single scale.

RV
If for a voter A is worth half of B, then he has 5 ways to vote:
[1,2], [2,4], [3,6], [4,8], [5,10]
The voter will obviously choose the most influential representation [5,10], but this ambiguity generates problems.
DV
If for a voter A is worth half of B, then there is only one way to cast the vote: [33, 67]
therefore, no ambiguity (in honest contexts).

RATED PAIRWISE
The voting form of the Rated pairwise preference ballot is overly ambiguous in practice (perhaps the worst).

  • The winners in the first head-to-head are favored:

A or B: A is the best, and at the beginning the voter would tend to give 5 points to A.
B or C: B is much better than C, and the voter has two possibilities:
(1) He realizes that he had given A too many points previously, so he changes the points from 5 to 3.
(2) He doesn’t realize this thing (or doesn’t want to review all the previous head-to-head) and therefore A is more favored than necessary.
Theoretically, at each new head-to-head the voter should double check the consistency with all previous head-to-head.

  • Paradoxes of Condorcet.

A or B: A wins with 4 points.
B or C: B wins with 3 points.
C or A: C wins with 2 points.
Forcing the voter to vote by creating an order among the candidates (RV and DV) serves to ensure that the paradoxes of Condorcent are compulsorily resolved by the voter himself, at least in his single vote (and not by an arbitrary process, decided by other people).

  • Logical errors 1)

“A - - B” means that “in a head-to-head between A and B, B wins with 2 points”
Voter (3 candidates A, B, C):
“A - - - - - B”
“B - - - C”
“A - - C”
Combining 2nd and 3rd rules (head-to-head) I get:
“B - A - - C” in this context, however, 1st rule doesn’t make sense (it’s contradictory).
This contradiction can only be resolved by assuming that the points have different weight depending on the head-to-head and this generates a huge ambiguity.

  • Logical errors 2)

Voter (3 candidates A, B, C):
“A - - - - - B”
“B - - - C”
By combining the two rules we obtain: “A - - - - - B - - - C”
3rd rule should look like this:
“A - - - - - - - - C” (8 points away)
but it’s impossible to create a similar rule if the maximum range is 5.

  • Impossible to distinguish positive from negative candidates

The maximum distance that can be between a negative and positive candidate are 5 points, but the same distance can be between two positive candidates.
Eg in all head-to-head the distance is 5 points, obtaining the Condorcet ranking: A,B,C,D.
How do I know which candidates are positive among A,B,C,D?
All this seems to me exaggeratedly ambiguous.

If the voter “fixes the vote” solves the problems indicated above, this “arrangement” also remains subject to ambiguities (those of the RV).

  • Unknown candidates / Little known (problem present in any case)

In a head-to-head relationship between an unknown candidate and a negative candidate, the voter is very likely to win the negative (even a lot) of the unknown one.

Or, if A is a candidate only heard of by friends or relatives (therefore, if only the name is known, but not the actual ideologies) in a clash between A and an unknown candidate, A would emerge as the winner. This favors candidates who know how to advertise themselves.

Even if only a political faction is known about a candidate (and not specific ideologies), he will win (or lose) all clashes with other unknown candidates.

  • All the problems listed are amplified in tactical contexts (here I assumed that the voter was always honest).

P.S.
I admit that I haven’t thoroughly analyzed the counting of votes, also because all my criticisms relate only to the form of the rated pairwise.

Doesn’t DV do that as well? In either case you could consider their “% of victory” to be the score they had before their excess is redistributed.

This would be wrong because the voters would not have the same weight. In deciding how to assign power to the winners, the voters must all be worth 100 points.
With the procedure indicated by you, the voters tactically would give more points to the likely winners (in their starting votes) instead of minorities, disadvantaging them.

If the voter is voting tactically, why not give a point to D, because D may be the only candidate who can stop E from winning?

It depends how far D is from E; when this distance is high, it makes sense to give 1 point to D (in the example D[-20], E[-100] therefore it would actually make sense to give 1 point to D for safety).
It could be said that E is so far from the others, to make D look positive (Es. with foods: pizza, sandwitch, insects, shit. Shit makes insects look positive, while without shit, insects would be negative).
Often, however, you know roughly who the favorites will be, so only one of these candidates will make sense to put 1 point.

what would happen in a 5-winner district… and which one wins depends mostly on the preferences of Democratic voters.

No, if the Democratic voters (40% of the total) had their power divided into 8% out of 5 democratic candidates, then 8% can be defeated (and 40% out of 4 candidates becomes 10%, which can still be defeated).
Voters only need to: freely distribute their 96 points among the candidates of their faction, and reserve 1 point for the majority candidates they consider best (equivalent to saying “if my faction loses, then give my vote to another majority”) .

IF the factions are in a close split…

In RV, if you mistakenly think that they are NOT in close split, then you will also give 10 points to one of the two favorites. This disadvantages the minority, and above all, it’s a mechanism that can be easily exploited by opposing factions (they spread false predictions where the third seems to be a minority).

What if polls are saying that more people prefer B (your worst) over C (your fave), but also more people prefer A (your second place) over B? Then you do not want A to be eliminated first, because there will be more votes stretched to B[100] C[0] than vice versa, and B wins.

This seems to me the failure of Monotony, of which I have already said what I think in the post (section (7) ).

DV encourages all voters to vote tactically

I said that DV has a tactic and if you use it the vote obviously becomes tactical, but with an important observation:
Honest: A[50] B[30] C[15] D[5] E[0]
Tactic: A[90] B[6] C[3] D[1] E[0]
If A is eliminated in the count, because it’s one of the worst, the tactical vote becomes completely honest, that is:
B[60] C[30] D[10] E[0]
Specifically, what matters in the DV is only the proportion between the candidates so the tactical vote actually has only A false. If I consider the proportion between B and C, it’s equal to that of the honest vote.

DV doesn’t become IRV (or rather SNTV) because giving 100 points to a single candidate is extremely risky. In the example, if I vote like this:
A[100] B[0] C[0] D[0] E[0]
and A loses, vote becomes irrelevant (null). It makes much more sense to use a small part of the vote (about 10 points - 10%) by distributing it proportionally among the other candidates.
A tactic used in RV instead, remains definitely and completely present until the end of the count.

V1: A[0], B[1]
V2: A[9], B[0]
Let’s assume V2 is a minority (33%) and V1 a majority (67%)…

“Let’s assume”… you can’t! (i.e. you can’t assume how passionate voters are).
In the example, you should assume that “V2 loves A 9 times more than V2 loves B” but, you cannot know if this is true (they are different voters).
You could only assume a similar thing if all the voters used an absolute range to evaluate the candidates, but this absolute range doesn’t exist, even if the voters were honest.

Of a vote you can only consider the relative preferences that the individual voter has regarding the set of candidates (generally indicated as proportions among the candidates); so if the set of candidates is only A and B of the example, and the voters all have the same weight, then I can only say that V1 and V2 support the same way (same weight) respectively B and A, so:
V1: A[0], B[1]
V2: A[1], B[0]
or
V1: A[0], B[9]
V2: A[9], B[0]
or
V1: A[0], B[10]
V2: A[10], B[0]
DV solves these “or” by saying “100 points are always used, distributed proportionally”.
If a worst candidate is eliminated, the set of candidates changes and the 100 points must be redistributed proportionally (to the relative interests of each voter).

In the single-winner context, Range Voting (a. k. a. Score Voting) respects and implements each voter’s right to an equal vote. Distributed voting on the other hand violates that right, in that context.

DV is “1 person, 100 points” and this always applies thanks to normalization, so why do you say that the “equal vote” isn’t worth it? Can you give an example where RV (Score voting) works while DV doesn’t?

I also point out that SV is very subject to the spoiler effect more than the DV (section (7) of the post).

The proof of balance for RV is trivial, but I have not seen it for DV. Maybe I am not smart enough to find a counterexample, but the money interests are able to find and exploit it. A proof would provide comfort.

Wait a second… but, why stop there? Why not tactically vote A[87] B[10] C[2] D[1]? Then if A is eliminated you have more power on B. I cannot understand why it is only tactical to exaggerate your first choice but remain honest for everything else.

IRV only counts first choices, eliminates the candidate with the fewest votes, and redistributes. The only advantage your system has over IRV is that you can support multiple candidates at the same time (albeit by dividing your vote). If voters exaggerate, then it almost looks like IRV because your vote of A[90] B[9] C[1] D[0] does not help B very much at all until A drops, and does not help C very much until A and B both drop.

3 candidates. A promises to steal all the money from blue-eyed people (minority) and put it into public infrastructure. B promises a just taxation and to defend the rights of blue-eyes, but will raise less money. C, the incumbent governor, has been accused of corruption and has big money groups funding his campaign, but has some supporters.

If we assume most brown-eyes don’t care about blues but also don’t really hate hate them, then they might vote something like (in 0-10 RV)
A[10] B[7] C[0]

Meanwhile, the blue-eyes might vote
A[0] B[10] C[??] (?? = they may tactically vote for C to push A down)

Depending on the numbers, this could allow B to win. Of course, again, the majority has to agree to allow for the possibility of B.

I believe you are trying to imply that in RV, given any vote I can cast, there is an equal and opposite vote you can cast that cancels out our two votes.

Whether that criterion should rise to the level of “equal vote” is disputed. Personally, I think there are other problems with FPTP and IRV that make them “unequal”.

On what grounds? What good is “one person, one vote” if some voters have a stronger vote than others by their finding a bandwagon to join?

I did not say I disagreed, I just said it was disputed.

But I do think you making the claims need to provide evidence as opposed to saying others need to disprove you.
https://yourlogicalfallacyis.com/burden-of-proof

Thanks for the analysis of rated pairwise. I’d emphasize that one of the implementations in the article should be used, because you’re right, giving voters an actual rated pairwise ballot would be too much work. That resolves the following concern:

This wouldn’t be possible if using, say, the “preference threshold” implementation, since you’d have to score the candidates in order, and then you’d only be able to say whether you want certain pairwise matchups that are all next to each other in the order exaggerated.

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If voters exaggerate, then it almost looks like IRV

DV would become IRV if adequate exponential distribution could be used.

  • A[99], B[1] --> can be considered IRV.
  • A[90], B[9], C[1] --> is already starting to be a little different from IRV (ex. 50% of voters like this, means about 5% going to B and 45% to A, so you do a vote like this only if in any case it’s good for you to risk giving 5% to B from the beginning).
  • A[69] B[25] C[5] D[1] --> an exponential distribution with 4 candidates already becomes very different from the IRV.
  • Your example: A[87] B[10] C[2] D[1] is not IRV because if I eliminate A I get:
    B[77] C[15] D[8] which is not exponential enough to be considered IRV.

From 4 candidates up, DV is different from IRV.
From 4 candidates up, RV can still be AV.

the majority has to agree to allow for the possibility of B

Ok, but you yourself said that the score given to C (if the hypothesis holds) can be managed tactically to make B win. This in itself is always a bad thing; you have only constructed an example where this tactic is used to win “good”, but in another case it can be used to win “evil”.

In the DV I think that this tactic exists in the form of a failure of Monotony, which could be exploited by changing the points in C (but in a complicated way).

In the single-winner context, Range Voting (a. k. a. Score Voting) respects and implements each voter’s right to an equal vote. Distributed voting on the other hand violates that right, in that context.

DV doesn’t meet the Equality Criterion, but you have to prove that this is something negative for DV.

I said almost looks like IRV. It is an improvement over IRV because of this type of situation:
Relative utilities of the final three candidates
40x B=50 C=30 D=0
25x B<10 C=50 D<10
35x B=0 C=30 D=50

In 0-5 score voting C gets 120+125+105 = 350 while B gets 200-225 and D gets 175-200. (Note: If D voters try to be “strategic” and dump C, they risk the other side doing so as well, causing their worst candidate B to win.)
In IRV, C gets eliminated and has no chance at all.
In DV, if we assume a “strategic” vote where the B and D voters give C 1/5 (and C-voters give almost nothing to B/D):
40x B[80] C[20] D[0]
25x B[0/10] C[90] D[10/0] (read this as a random split between 0/90/10 and 10/90/0)
35x B[0] C[20] D[80]

B gets 3200 + 125 = 3325.
C gets 800 + 2250 + 700 = 3750.
D gets 2800 + 125 = 2925.

So the moderate C wins after all.

I guess this means DV is not entirely bad. I still would prefer RV, though.

I made some inaccuracies on the RV regarding:

  • missing % of victory (which can also be easily obtained in RV)
  • disadvantages minorities (which I continue to think is present, except when tactical votes based on good knowledge of the likely results can be used).

but the biggest problems remain.

Until now the only major criticisms of the DV that I have received, all concerned the failure of Monotony, which however remains something rare and difficult to exploit (unlike e.g. the failure of IWA).

Thanks for the discussion, it also served me to understand what are the points to be clarified more about “DV vs RV”.

Even CES basically agrees this will happen; see the image at the top of https://www.electionscience.org/approval-voting-101/.