Now I don’t remember it well, I did it some time ago in the Distributed Score Voting (point 3 of counting) which I then put aside because to complex; it should be like this:

Rating: [3,5,7] -> to the range [0,10]

W = 10 points (if I want to normalize to MAX = 10; 100 points if I want to normalize in DSV to 100).

max = maximum mark value = 7.

Vold = old value of a candidate

Vnew = new value of the candidate.

Vnew = (Vold / max) * W

The mark becomes: [4.3, 7.14, 10]

So only the highest and lowest get pushed to MAX and MIN? What if more than one is at the highest/lowest value?

The precedence is this:

- I put all the values = a min (of the vote) to MIN.
- I put all the values = a max (of the vote) to MAX.

If the initial values were all the same, I will all have MAX at the end; if it was half and half, I will only have MIN or MAX at the end. The difference from other normalizations can be seen when there are many candidates.

They are not caveats; simply if the range were ex. [1,7] then the range of proportions will be [1/7, 7] (ie, a candidate could be at least 7 times better than another or 7 times worse).

Handling 0 simply uses those values to manage the range caused by the 0 that is [0,+inf] --> [1/7, 7].

And it is generally accepted that it’s the difference between utility scores, not the ratios that are important.

In SV if I vote like this: A[10] B[5]… then how many more votes will it take to make B reach A? 1 other vote having B[5] therefore for 1 A[10] you need 2 votes B[5] to equal A and B.

The sum of the points also hides the concept of proportion.

So that is to say that if you score candidates A, B and C 1, 2 and 3 respectively then the difference between A and B is the same as the difference between B and C.

In SV no, because in SV if I have 1: C[3], then 3: A[1] are needed to make C be equal to A.

If what really matters to you is only the difference (distance), then you could create a “Cardinal Copeland” voting system in which in head-to-head you only consider the distance between two candidates.

In this case with A vs B, a vote like A[3] B[2], would earn A 1 point (and lose B 1 point); end immediately found the best, or find the worst to delete, normalize, etc … @Keith_Edmonds also done a type of “Cardinal Copeland”.

Using utility (and therefore scores) properly, 99, 98 is the same difference as 1, 0.

This is what you don’t understand. In my normalization only the scores [1, MAX] can be compared to a range with sum.

The 0 is equivalent to the absence of an AV cross.

See it like this: DV and TM is as if they were AVs, but in which the candidates to whom from the X you can evaluate them more precisely (with a range).

This your example:

1 voter: A = 99, B = 1

1 voter: A = 0, B = 1

equivalent to:

1 voter: A = X, B = X

1 voter: A = 0, B = X

The candidates who receive points are as if they had the X of the AV, and those who do not receive the X are the 0.

This is said to the voters so that they take it into consideration: “choose which approved (as in AV) and then evaluate them precisely, (not caring about those without X, who you know will not be favored in any way, regardless of how do you rate your favorites)”.

All this makes the voter be more honest about favorites candidates.

P.S.

In your example, B would not have received X in TM (A win), and in DV would have won A because B is the worst.

well it depends on what you mean by fails

Any DV problem that other cardinal methods have not.