Best single-winner Voting System (in full honest context)

Let’s assume we have voters with the following honest interests:
G1: “I love A almost double B, I love B triple C and D, E is the worst candidate”.
G2: “I love B to the max, all the others are the worst in the same way”
I could represent these interests in an honest and simple way in the form of proportions (the values ​​are assigned to the candidates in this way A,B,C,D,E):
G1: 5,3,1,1,0
G2: 0,1,0,0,0

In the example I want to propose you have 3 voters for G1 (75%) and 1 voter for G2 (25%).
For convenience, I represent the real interests by using 100 points for both, so that they can be compared a little better:
G1-3: 50,30,10,10,0
G2-1: 0,100,0,0,0
Excluding any tactical vote, who is the single winner in this context?

SNTV - Single non-transferable vote
The votes will take the following form:
G1-3: X,-,-,-,-
G2-1: -,X,-,-,-
A wins.

IRV - Instant-runoff voting
The votes will take the following form:
G1-3: 1st,2nd,3rd,4th,-
G2-1: -,1st,-,-,-
They are eliminated in order E,D,C, and finally A wins.

Borda
The grades take this form (I use the scores immediately, not the ranking):
G1-3: 4,3,2,1,0
G2-1: 0,4,0,0,0
A wins.

DV - Distributed Voting (definition)
Votes take this form:
G1-3: 50,30,10,10,0
G2-1: 0,100,0,0,0
They are eliminated in order E,D,C, redistributing the points, and finally B wins.
Note that: G1<4 wins B, G1-4 draw of A and B, G1>4 wins A.
Intuitively it makes sense that by increasing the voters of G1, A gets to win.

AV - Approval Voting
Votes take this form:
G1-3: X,X,-,-,-
G2-1: -,X,-,-,-
B wins.
Note that: G1>0 always wins B.
Observing the real interests, G1 voters prefer A more than B, therefore by increasing a lot G1, A should win sooner or later, instead in AV he continues to lose.
The incorrect representation of the interests of the AV is clearly a problem, making it wrong (compared to the DV).

SV - Score Voting (range 0-100)
Votes take this form:
G1-3: 100,60,20,20,0
G2-1: 0,100,0,0,0
A wins.
Note that: G1<3 wins B, G1≥3 wins A.

To deal with this case we need to make 3 observations:

  1. Same interests: G1’s interests regarding A and B, which are “A is almost double better than B” are perfectly respected (at the same identical proportion) from DV and SV.
  2. Same weight: in democracy it’s necessary that the voters (and the votes) have the same weight.
    The fact that in DV, A wins when G1≥5, while in SV, A wins when G1≥3, means that either DV or SV are poorly representing the weight of the voters G1.
  3. The vote of the DV, after eliminating C,D,E, takes this form:
    G1: 62.5 , 37.5 (worth 100 points, exactly as G2’s points is 100 points).
    The SV vote instead, excluding C,D,E, who are losers in any case, takes this form:
    G1: 100, 60 (uses 160 points while G2 uses only 100 points).

The SV turns out to be wrong because it badly represents the weight of the voters (giving more weight to G1 than G2, risking to cancel democracy itself). This doesn’t happen in the DV where it’s guaranteed that the votes are always worth 100 points.
This thing in AV is masked by the bad representation of interests (which always makes B win, for G1>0).

All that has been said, applies both to the sum and the average of the points (therefore, it also applies to the Range Voting, STAR Voting and similar).

Conclusion
In this context, the DV is the only one that correctly wins B (if G1<4, otherwise with G1≥5 obviously wins A). The only other method that makes B win is the AV, which however would make B win with G1>0 (also with G1-1000), so it’s wrong.

In contexts, without tactical votes and single-winner, DV can be the best.
I could also say that: if the DV returns the wrong candidate because of tactical votes, then the other methods will return a wrong candidate because of the same type of tactical votes, or bad representation of interests. Try to disprove this with a counterexample.

And why do you assume that B is the best candidate in this example? I think A should win.

I’ll have to go even more specifically.

I focus only on candidates A and B, since the others don’t count in this case.
The original interests were:
G1: “I love A almost double B”
G2: “I love B to the max, and A is the worst ever”
I decided to represent the interests of G1 e G2 as a proportion like this:
G1: A[1.67], B[1] (where A is almost double B).
G2: A[0], B[1] (where A is the worst ever, and B the best)

Now, how do I combine these proportional forms to understand how they relate to each other? I have 2 ways:
SV
G1: A [100], B [60]
G2: A [0], B [100]
DV
G1: A [62.5], B [37.5]
G2: A [0], B [100]

SV problem
SV assumes that G1 loves A as much as G2 loves B, but this is not known! G1 and G2 are two separate people, they don’t have a common (absolute) range that can be used as a reference point.
The conversion of the SV is therefore very ambiguous and unrealistic.
That is, the reality could be that the grade G1 should have this form in SV: A[50], B[30] because the way G1 loves A is half as strong as the way G2 loves B, but we can’t know this because people are separated, and they don’t have a common absolute range.
In fact, let us remember that we are trying to represent the voters in the best possible (real) way, excluding any type of tactical vote or deviation from the true interests of the voter.

The DV instead gives 100 points to both (democracy forces voters to all have the same weight), and in the way in which these 100 points are distributed there is no ambiguity (each candidate respects his proportions independently of the others).

Returning to the example:

  • If I have 1 G2 person and 1 G1 person, the winner is clearly B and I think we agree on this.
  • If the people of G1 increase to 10, the winner becomes A instead, and also on this I think we agree.
  • The problem is: what is the value of G1 that makes the winner change from B to A?
    To find the answer it’s necessary to represent the interests in the smallest details and the only methods that allow it are the SV and the DV, with the difference that the DV doesn’t derive from ambiguities and in it the 100 fixed points guarantee that the weight of the vote is always the same for everyone.

Using DV I get:
G1-3: A[62.5], B[37.5] --> A[187,5], B[112,5]
G2-1: A[0], B[100] --> A[0], B[100]
Sum: A[187,5], B[212,5] --> B wins.

These are my arguments that B wins until G1<4.
What are your arguments for saying that the winner should be A? And how do you understand exactly what is the maximum value of people G1 for which B wins?

One observation I have is that DV is basically equivalent to SV but where G1 voters have a weight of 0.625 because they also supported candidates that are irreverent to the comparison between A and B.

You’re right, it isn’t known. But neither is it known that G1 loves A 0.625 times as much as G2 loves B.

It is less ambiguous then saying that G1 loves A 0.625 times as much as G2 loves B.

This is the false assumption that you are making that is leading you to assume that calculating the results as if G1 loves A 0.625 times as much as G2 loves B is somehow less arbitrary then calculating the results as if these two factors were equal: that the two votes have the same weight if the total score given to each candidate on each ballot is the same. This is a very FPTP way of viewing how much voting power each voter has in an election.

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I don’t fully understand what you mean and maybe you also don’t fully understand what I mean.
I try another way:

You have 10 songs and a person (P1) you don’t know.
How do you know the real interests that individual person has towards those songs? (I really care about your answer)
My answer is:

  • If you use SV and that person gives the value 10 to a song, you still don’t really know what it means because you don’t know exactly what 10 means for that person.
  • Then use my method (different from the SV) and decide to give 100 min to that person, in which she will be able to listen to the songs she wants, among the 10 proposals.
    The songs he chooses to listen to and the time he devotes to listening to them, will describe his actual interests.

Now I add another person (P2) and make him do the same thing.

If in the end P1 used 10min for song A, while P2 used 10min for song B, in DV it doesn’t mean that P1 and P2 love A and B respectively in the same way!

In DV the philosophy is:
in complete freedom (10 songs) P1 chose to give his power (10 min) to A and P2 to B; I don’t really know how much A and B like them (I can’t know) but I know the amount of time (power) people have been willing to give them, respect to other songs, and that’s enough for me.

If in the set of 10 songs, the dedicated time is this:
A[90], B[6], C[4], D[0] … (all 0 the others)
I may know that if D had not been there, time would have been used in the same way.
If instead A had not been there, I would know that time would have been used like this:
B[60], C[40], D[0]…
This isn’t ambiguity, I’m just respecting the proportions expressed by the voter in full freedom (10 songs).
What if I add a new song? In this case it would be impossible for me to predict how time would be used, because I don’t know the amount of time the new song will take from the others, for this reason the DV-type vote should be made on the largest group of candidates.

In short: the DV doesn’t absolutely indicate how much the voter likes a candidate (which the SV wants to do instead), the DV indicates how much power a voter is willing to give to a candidate despite having other alternatives to choose from (and the power he is willing to give him must be the same for everyone, so 100 for everyone, because this is democracy).

If you say rate them on a 0 to 10 scale then you know they really, really like that song and it is probably either their favorite or tied for favorite.

No, the person will probably listen to their favorite song for all 100 minutes. After all, why spend any time on something inferior?

In an election I fear this will cause voters to want to vote IRV-style (e.g. 90, 9, 1, 0).

I guess I see where you are coming from. One advantage this has over IRV is that later preferences are counted, admittedly at the perhaps temporary expense of your favorite. I would like to see this system simulated.

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Before I get started, I would just like to point out that the scale from 0 to 100 where 0 is bad and 100 is good is arbitrary. You could easily imagine a weird parallel universe where 0 meant good and 100 meant bad so instead of expressing how much you like an option when rating it, you were expressing how much you don’t like it.

You don’t. Nor do you know what 3 means for that person. Or even 0 to that person. (Do they enjoy that song as much as not listening to anything in the first place, do they get negative satisfaction from listening to that song, or do they get some satisfaction from that song but they still rated it 0 because it is just their least favorite song?)

But, if they rated song A a 10, song B a 3, and and song C a 0, there are three things you know: how many times stronger their preference for A over C is then their preference for A over B, how many times stronger their preference for A over C is then their preference for B over C, and how many times stronger their preference for A over B is then their preference for B over C.

Or you could do the reverse. Suppose that the person is a highly respected song critic with a blog where she elaborates in great detail what each song does wrong. She wants to point out each of the song’s flaws that week but only wants to spend 100 hours total blogging about songs that week. How many hours does she spend on each song?

The anti-DV philosophy then would be:
in complete freedom (10 songs) P1 chose to give her power (10 hours) against A and B; I don’t really know how much she likes A and B ( I can’t know ) but I know the amount of time (power) people have been willing to give against them, respect to other songs, and that’s enough for me.

Based on this the scores this voter must of given to each candidate (if she gave a 100 to her favorite) must have been 100, 6 and 2/3rds, 4 and 4/9ths, and 0. If 100 meant worst instead of best and 0 meant best instead of worst, then these scores would instead be 0, 93 and 1/3rd, 95 and 5/9ths, 100 (which when you divide that by the total score against each candidate: 288 and 8/9ths, that becomes 34.62, ). Thus if we continue with the anti-DV philosophy, it would be:

If in the set of 10 songs, the dedicated time is this:
A[0], B[32.31], C[33.08], D[34.62] … (all 0 the others)
I may know that if A had not been there, time would have been used in the same way.
If instead D had not been there, I would know that time would have been used like this:
A[0], B[49.41], C[50.59]…

Since these philosophies are so similar (they are just mirror images of one another) what I want to know is what makes the DV philosophy any more correct then the anti-DV philosophy.

The thing is, ratings are not portions of support, or portions of non-support. If you increase or decrease a voter’s rating by a constant, that shouldn’t change anything since that doesn’t affect the relative strengths of preferences between pairs of candidates I talked about earlier, yet adding a constant to a voter’s rating does affect their rating in both the DV and anti-DV philosophies.

Before I get started, I would just like to point out that the scale from 0 to 100 where 0 is bad and 100 is good is arbitrary. You could easily imagine a weird parallel universe where 0 meant good and 100 meant bad so instead of expressing how much you like an option when rating it, you were expressing how much you don’t like it.

I know only with certainty this information from the voter: “A is the triple better than B”.
This information, using ranges, can take various forms:
[A | B]
[100 | 33], [75 | 25], [60 | 20], [30 | 10], [3 | 1], …
SV chooses to use representation [100 | 33].
This choice, however intuitively correct it may seem, is in fact a subjective choice imposed by the method among different possibilities, therefore there is ambiguity.
it’s Imposted because a voter who can vote like this [100 | 33], would never choose to vote like this [30 | 10] by making his vote 1/3 count.
This ambiguity also affects the result (see example of this post).

If, instead of the ranges, I gave voters limited points (the same for everyone) to represent their interests then, starting from the only initial information I have, the representation I get is always and only one:
[75 | 25] or better [75% | 25%]
Ambiguity is gone, and that’s a fact.

New ex, with candidates Z,P,V:
SV
V1-1: 100, 5, 0
V2-2: 50, 100, 0
P wins (2nd column).
DV
V1-1: 95, 5, 0
V2-2: 33, 64, 0
Z wins.

Since there are only 3 people in the example, I can also write the fight in words:

  • A is 20 times B
  • A is 1/2 of B
  • A is 1/2 of B
  • B is 1/20 of A
  • B is 2 times A
  • B is 2 times A

Considering this information together, do you think B should win?

DV and SV are different (they generate different results starting from the same information) and since SV has ambiguities, DV is better for me.
It doesn’t seem to me that you have denied this (“anti-DV philosophy” doesn’t deny it).

Extra
What determines a person’s happiness or sadness in an election?
The candidates who win, but also those who lose.
If I have to choose between 2 foods, sandwich ( P ) and vegetables ( V ), and the group wins P, I’m very happy.
But if among the foods there was also pizza (Z), even if there were the same people to choose, he could have won P again but in this case I would have been very (really very) sad for the defeat of Z.

But, if they rated song A a 10, song B a 3, and and song C a 0, there are three things you know: how many times stronger their preference for A over C is then their preference for A over B, how many times stronger their preference for A over C is then their preference for B over C, and how many times stronger their preference for A over B is then their preference for B over C.

Of course, SV contains all the information of the proportions between candidates; the problem is that it also contains more ambiguous information (the choice of the range among the various possible).

Or you could do the reverse. Suppose that the person is a highly respected song critic with a blog where she elaborates in great detail what each song does wrong. She wants to point out each of the song’s flaws that week but only wants to spend 100 hours total blogging about songs that week. How many hours does she spend on each song?

In my metaphor the songs were candidates that the person already knew. Those he didn’t know, “would not have listened to them” in that limited “hour” (100 points) that I gave him.
Then the fact that a song lasts about 3min makes my metaphor not very suitable, sorry.
It would have been better to say that the voter is given time to listen to 100 individual songs and see which ones he would have listened to and how many times the same.

“anti-DV philosophy”

or “anti-SV philosophy” I thought they were jokes (parallel universes) but you talk a lot about it so I’ll have to answer.
To avoid them, simply tell the voter: “if you want a candidate to go to the government, give more points otherwise give less”, this has no ambiguity.
Parallel universe or not, if they want to win A, he should give him 100 instead of 0.
If the proportion says “A is worth double B”, then the voter wants A to be winner over B, double.
Inverting the meaning of “better” with that of “worse” makes no sense, no voter would make a similar mistake (it would be like saying in SNTV that X makes candidates lose).
P.S.
I didn’t say that in the SV, a vote like this:
V1: A[100], B[50], C[0]
it could mean that for V1, A is worse than B.
I said that for 2 different voters, V1, V2:
V2: A[10], B[100], C[0]
V1 doesn’t actually like A as much as V2 likes B, but it’s still certain that V1 likes A more than B and V2 likes B more than A.
I haven’t used any “anti philosophy”.

If you say rate them on a 0 to 10 scale then you know they really, really like that song and it is probably either their favorite or tied for favorite.

Read the first piece of this Reply, especially the “extra” part.

No, the person will probably listen to their favorite song for all 100 minutes. After all, why spend any time on something inferior?
In an election I fear this will cause voters to want to vote IRV-style (e.g. 90, 9, 1, 0).

I changed the metaphor saying “you are given time to listen to 100 songs” instead of “you are given 100 min” which was too vague.
However, surely if you like a song to the fullest, you will only listen to that song 95 times and only 5 times some of the others (and this is right, real).
If instead you have several favorite songs, then you could listen 32 times once, 30 times another, and 38 times another; in this case it wouldn’t make much sense to rate the 3 songs like this: 90,9,1.

One advantage this has over IRV is that later preferences are counted, admittedly at the perhaps temporary expense of your favorite.

One, but it’s that difference that makes DV exaggeratedly better than IRV (especially in honest contexts).
In contexts with tactical votes, practically any method ends up favoring only one candidate, disadvantaging the others if possible (also by removing points from the others, in the case of Borda, AV, SV, etc).

Not really. If a voter who rates A as 100, B as 33, and C as 0 is indifferent to a candidate rated as 50 and has negative satisfaction for C, then for this voter to like A tipple the amount by which she likes B, B would have to be rated a 67, not 33. This voter actually likes A negative 3 times as much as she likes B.

They both have ambiguities. SV assumes that two voters who give a candidate the same score each like that candidate the same amount. DV assumes that

  1. A voter who gives one candidate double the score then another likes that candidate double as much as the other.
  2. In a head to head match-up between two candidates, the amount of weight a voter has is equal to the sum of score that voter has given to the two candidates. In reality, score that you give to A and score that you give to B cancel out so the absolute voting power actually have in that runoff is (A_score_used_by_voting_method - B_score_used_by_voting_method)*(+1 if this voter prefers A, -1 if this voter prefers B) and your actual weight (voting power relative to the actual strength of the preference you expressed) is (A_score_used_by_voting_method - B_score_used_by_voting_method)/(score_given_to_A - score_given_to_B).

Also, are you concerned with DV’s lack of monotonicity, consistency, reversal symmetry (I suspect it fails this as well), IIA, and other criteria that demonstrate that many of the results DV picks don’t make sense? What about DV’s failure of many strategy resistance criteria too like favorite betrayal, monotonicity, and participation?

I haven’t understood the two previous criticisms, sorry.

In a head to head match-up between two candidates, the amount of weight a voter has is equal to the sum of score that voter has given to the two candidates.

Wait, if you do a head-to-head between A and B, it means that you are eliminating all the other candidates so the 100 points will be distributed proportionally between A and B.
A rating like this: A [1], B [3], C [6], D [90], E [0] if I do a head-to-head between A and B, first I make it like this: A [25], B [75] then I add it to all the other vows converted in this way.

Speaking more concretely, with the metaphor of the songs, that is:
there are 4 songs and you have to represent the interests that a voter has regarding those songs.
SV: I give it a range [0-100] and I tell it to score each song.
The result will be his interests but as already said the range is ambiguous (2 voters who give 10 to A, may not like it in the same way, but in the counting the score 10 is considered equal).
From this representation the proportions are extracted (how much one candidate likes compared to another).

DV: I know that voters have the same power in democracy, so I divide that power into 100 “parts”.
That voter will be able to listen to 100 songs at will, and which and how many songs he will choose to listen to, will determine his interests.
From the vote that I will get (which will be 100 points distributed) I will extract the proportions among the candidates.
Note that this is the method used in life to really establish a person’s true interests (i.e., observe what he does and how long he does it, if it is free time).
Here too, if 2 voters gave 10 points to A, A might not like it the same way, but there is one thing I know for sure (more than SV): these voters decided to give those 10 points to A rather than to the other candidates.
In this form, I also know with certainty that the various marks all have the same weight, at least as long as they all contain 100 points within them.

If the voter will be honest in both the SV and the DV, then will the same proportions be extracted from both votes?
Until now I thought so, but I start to think that it is not certain, so I struggle to continue this clash between SV and DV regarding ambiguity.

One thing I know for sure is that in a pure proportional system (everyone wins), adding the points for each candidate in the DV, I get a practically perfect result (the number of points obtained by a candidate equals the number of times that the voters have chosen to listen to him compared to others).
The difficulty appears when I want to reduce the number of winners (up to 1).

  • I could say that the winner is the one who received the most points, but this would have the spoiler effect, as in the SV, and I hate the spoiler effect.
  • I could eliminate the worst candidate of all, and redo the elections on the small number of candidates (which is what DV is currently doing), but there are rare cases with very particular results.
    And here I stop.

As far as mathematics is concerned, I still don’t have any actual proofs; I want to focus more on the philosophical discourse because given that there are criteria that are in any case inconsistent with each other, the important thing is not to satisfy as much as possible but to satisfy the right ones.
Many criteria do not imply that the voting method is right or wrong; it also depends on how they combine.
Eg monotony fails in the DV but in all cases where it has failed, stupid tactical votes were used (which had a form much more consistent with the real interests of the voter and with which the monotony would not have failed, allowing at the same time to achieve the objective of the tactical vote).
If stupid tactical votes are excluded, perhaps monotony is respected, but precisely I have no demonstrations.

If you want to give both voters the same power in a head to head match between A and B then just dividing a voter’s power between A and B won’t work because their A parts will cancel out with their B parts. Thus voters will have different numbers of parts. If you want each voter to have the same power then assign all of their parts to the candidate that they like more.

However if you don’t care about how much power each voter expresses in a head to head match between A and B and instead care about preserving how much power each voter has in this head to head match relative to the strength of their preference between the two, then just do what SV does.

By breaking a voter’s vote into 100 FPTP votes and splitting it between both candidates, you are not making how much power each voter has equal. Doing it this way is not any more democratic. It just makes it so that the influence voters have in a head to head election between A and B is no longer proportional to the difference in score a voter gave between the two candidates because voters who give a non zero score to their less preferred candidate between the two now have much less influence in the election then they should have.

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In any given example of monotonicity, whether the voter changes their vote for tactical reasons or for honest reasons is subjective: In the same non-monotonic example where you say that the voters changed their vote for tactical reasons, you could of also said that they changed their vote for honest reasons and it would not change the non-monotonicity example. There is no “passing monotonicity only when you exclude certain types of votes”, either you pass it or you fail it, and in any voting method that fails monotonicity, we know with mathematical certainty that it picks the wrong result at-least once.

If you want to give both voters the same power in a head to head match between A and B then just dividing a voter’s power between A and B won’t work because their A parts will cancel out with their B parts. Thus voters will have different numbers of parts. If you want each voter to have the same power then assign all of their parts to the candidate that they like more.

If I give: A [10], B [30]
while another gives: A [40], B [0]
The result would be: A [50], B [30]
I know that my vote is equivalent to A [0], B [20] in deciding only 1 winner here, but if I had given my points (power) so A [10], B [30], they will still be given like this .
I (method) do not have the right to change the way a person has distributed his points. I can only redistribute them proportionally when I remove a candidate from the vote.
I think any voter would tactically make the vote become A [0], B [40] but I don’t want to make it tactical.

A voter is like a set of wills that want different things; if 10 wills want A and 30 B, that’s the way I have to represent them honestly.
Yes, it is as if the voter made an FPTP in his head and the result is his vote (so for all voters, like a big mind).

There is no “passing monotonicity only when you exclude certain types of votes”, either you pass it or you fail it, and in any voting method that fails monotonicity, we know with mathematical certainty that it picks the wrong result at-least once.

When it fails, are honest or tactical grades used?
If it happens with honest votes then maybe I know what it is that time, but it’s a case where the SV would generate a spoiler effect.

I haven’t read through all of this in detail, but I think when it comes to utility, it’s not the best way to say that you like this choice x times that choice, because I think any zero point is arbitrary. What does make sense is the size of the gaps between each candidate.

It’s often said that the best way to look at it is in terms of a lottery. If you give A a score of 10, B 7 and C 0, then it means that you should be indifferent between choosing B or choosing a lottery where you have a 7/10 chance of getting A and a 3/10 chance of getting C. But note that this would also be the same if the scores were 11, 8, 1 or 9, 6, -1.

The utility equations for each example go like this:

0.7 * 10 + 0.3 * 0 = 1 * 7
0.7 * 11 + 0.3 * 1 = 1 * 8
0.7 * 9 + 0.3 * -1 = 1 * 6.

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I haven’t read through all of this in detail, but I think when it comes to utility, it’s not the best way to say that you like this choice x times that choice, because I think any zero point is arbitrary.

I think so too.
Summarizing, with candidates A,B,C,D in this order (definition DV):
SV: 100, 50, 50, 0
DV: 50, 25, 25, 0
If I eliminate D I get:
SV: 100, 0, 0 - (change)
DV: 50, 25, 25 - (doesn’t change)
If instead I eliminate B, I get:
SV: 100, 50, 0 - (doesn’t change)
DV: 64, 33, 0 - (change)
If instead I eliminate A, I get:
SV: 100, 100, 0 - (change)
DV: 50, 50, 0 - (change)

SV Philosophy: I take candidates A,B,C,D; I put my favorite at 100, and the worst at 0; the others I place them in the center in relation to the range.

  • The 0 in the SV is equivalent to a hated candidate (the worst), who has a certain relationship with the others, therefore eliminating all the 0 from the SV vote, the scores assigned change, because the worst changes, that is, the reference range changes.
  • By removing internal candidates instead, the scores of the other candidates do not change.

Philosophy DV: each voter has many “wills” (even contradictory, difficult to evaluate) so I give him 100 points (100 votes) which he can distribute among the candidates as he prefers (that is, based on his “will”).

  • The 0 in the DV is equivalent to a candidate to whom the voter decides not to give any support, therefore it includes both a candidate who sucks him completely or even unknown ones.
    If I take away candidates to whom he has not supported (0 points), this rightly does not alter the (honest) support assigned to the other candidates. In DV by eliminating all 0s, the (honest) way in which support is distributed does not change.
  • Instead, if I remove a candidate who received support (points), these points will simply be given to the other supported candidates (based on how much they were supported in the vote itself); this applies not only to the candidate with the most points (as happens instead in the SV).

This is the substantial difference between DV and SV in the representation of interests.

Unknown candidates
One thing is noticeable in the DV: candidates unknown to the voter correctly do not receive support.
In the SV instead, what happens to the unknown candidates?
Inevitably they must have a score (when counting the votes) but at the same time they cannot be correctly evaluated by the voter in the range (“do not evaluate them” is a different way of saying “we give him 0 points” that is “they are the worst of all” , which is wrong because you don’t really know how they are compared to others).
Typically in the SV such candidates receive 0 points, but the statistically correct thing to do for someone unknown, would be to give him 50 points, and the problem with this is evident (a lot of “free point” given to unknown candidates).
It’s not strange to think that in the SV, some voters can give points (up to 50) to unknown candidates, to disadvantage the hated ones, because it’s the philosophy of the method that leads you to do it (it’s a risk but statistically acceptable).

Another thing I would say is that instead of IRV-style elimination, couldn’t you put all the candidates against each other head-to-head to make it more like a Condorcet type method?

I had thought of using Condorcent and in majority rule cycle cases simply use the initial sum to choose who wins; it can work but I don’t have time to test it.

If your method truly is related to IRV, I’d recommend any Condorcet version you create ought to be similar to the Smith-efficient Condorcet-IRV hybrids. One problem I’ll note with those is that with a 1-winner example

26 A>B
25 B
49 C

they don’t elect B, despite a majority preferring B>C.

26 A>B
25 B
49 C

Ex 1
In DV it could be:
26: A [51], B [49] (vote that favors at most B, with A> B)
25: B [100]
49: C [100]
Sums points: A [1326], B [3774], C [4900]
I eliminate A, and redistribute the points in the votes (A [51] B [49] becomes B [100])
B and C remain, with B winning.

Ex 2
In DV it could be:
26: A [99], B [1]
25: B [100]
49: C [100]
Sums points: A [2574], B [2526], C [4900]
I eliminate B, and redistribute the points in the votes.
A and C remain, with A winning.
Note that A wins little, but it makes sense by observing the interests of the voter.

However, the DV at the moment doesn’t satisfy the monotony so I will have to change the vote count to satisfy it. I think I’ve already found a way to do it.

Sorry for the title of the post, there had to be a “?” but I could no longer edit it.