Brian Olson--
You probably have written a better method than IRV.
You wrote:
Instant Runoff Normalized Ratings (IRNR)
Every voter casts a rating of each choice on a scale of -1.0 to 1.0 or some equivalent scale. Each voter's voting power is normalized, each rating is divided by the sum of the absolute values of the ratings
I reply:
The sum f the absolute values of his own ratings, or of all the ratings of him and the other voters?
The rest of the definition seems clear.
You continued:
Condorcet: yes-ish.
I believe that IRNR is more powerful than Condorcet because it also addresses the degree of preference and not just the order.
I reply:
That's how a method loses Condorcet's strategy advantages. If how far above Y you rank X is counted, then the only way you can fully vote X over Y is if you vote X in 1st place and Y in last place. That gives Borda its big strategy problems.
People would like to be able to fully vote Compromise over Worst, while still fully voting Favorite over Compromise. That's impossible unless we count only the fact that you vote X over Y, disregarding how far over Y you've voted X.
That's why CR doesn't have Condorcet's strategy advantages. But CR is still very good, because it has its own strategy advantages. Personally I like the advantages of Condorcet best, but I'd gladly settle for CR or Approval as the official public voting system.
"Strategy Free": maybe not. A 51% majority could rate candidate A at 0.02 and B at 0.01, 49% could vote B 1.0 and A -1.0 . B would win. Does this violate SFC?
I reply:
A point system isn't likely to meet SFC. IRNR probably doesn't meet SFC. Your example that you give above, with the 51% and the 49% addresses a reason why IRNR is unlikely to meet CC or SFC.
But it isn't a complete failure example. Can an example be written in which no one falsifies a preference, and a majority of all the voters prefer the CW to candidate B, and vote sincerely, but B wins anyway in IRNR? If so, then IRNR fails SFC.
I can almost guarantee that such an example can be written. And your 51% &: 49% kind of situation could likely be part of that example. The majority sincerely rating the CW over B, by a small ratings margin, while the B voters rate B over the CW, voting them at opposite extremes of the range.
For simplicity, let's consider an example with just 2 candidates. A majority prefer A to B. Therefore A is the CW in that 2-candidate election. No one falsifies a preference. And the A & B voters vote as you described, with the majority voting A .001 points above B, and with the B voters giving B the maximum points rating and A the minimum.
So, no one has falsified, and a majority prefer the CW to B, and vote sincerely (because they haven't falsified a preference or failed to vote a preference the method in use would have allowed them to vote in addition to the preferences that they actually did vote--because, with 2 candidates, they only have one pairwise preference, and they voted it), and B wins.
B wins with IRNR in that 2-candidate example, doesn't it?
You continued:
Is it a just system anyway?
I reply:
Maybe. Failing SFC doesn't make a method unjust. Approval and CR fail SFC, and they're among the best methods. But I still like SFC compliance, which is why Condorcet wv is my favorite.
You continued:
If IRNR were modified to expand votes out to a 1.0 to -1.0 scale before normalizing them the 51% vote would translate to A=1.0 and B=-1.0; A would win.
I reply:
If all the negative ratings becames -1, and all the posiive ratings became 1, wouldn't that change the method to Approval? Sure, then the majority would win in the 2-candidate example. That shows an advantage of Approval over CR: Approval doesn't give people a chance for sincere voters to be had by strategizers as can happen in CR.
But that doesn't mean that the modified IRNR woiuld then meet SFC. It would no longer fail SFC in that particular example that I used before. But with more candidates it would. Say there are 3 candidates, and the majority prefer B to C. Some of that majority have A as favorite. They give 1 to A and -1 to B & C. That's sincere, because they aren't falsifying a preference, voting a preference that they don't have. And they aren't failing to vote a preference that the balloting system in use would allow them to vote in addition to the preferences that they actually did vote. That's because if they gave 1 to B, they'd no longer be voting their preference for A over B. So they're voting sincerely when they give -1 instead of 1 to B.
The C voters, let's say, give 1 to C and -1 to B & A. Though they're a little short of a majority, the C voters have no trouble thereby making C get more points than B or A. Because, let's say, the B voters have given -1 to A, which is sincere for the same reasons described above.
So C wins even though a majority prefer B to C and vote sincerely. All that remains is to make B be the CW in the example. Sincere preferences:
40: CBA 25: BCA 35: ABC
B is CW, and a majoritly prefer B to C, as SFC's premise requires. In my example, the voting is as follows:
40: 1C, -1B, -1A 25: 1B, -1A, -1C 35: 1A, -1B, -1C
Those ballots are sincere for the reasons that I described, though all SFC requires is that the B & A voters vote sincerely.
Point totals:
A: -30 B: -50 C: -20
So no one is falsifying a preference, and a majority prefer the CW, B, to C, and vote sincerely, and C wins.
C wins, even though the premise conditions of SFC are met. -1,1 CR, which is the really the same as Approval, fails SFC.
You continued:
GSFC: no comment at this time. See Strategy Free.
I reply:
Anything that fails SFC fails GSFC.
You continued:
Strong Defense Strategy: Yes. A majority casting votes can win without mis-ordering any votes.
I reply:
But SDSC requires more than that. A majority preferring X to Y has to be able to make Y lose without voting a less-liked candidate _equal to_ or over a more-liked one.
(Where someone votes X equal to Y iff s/.he doesn't vote either over the other, but votes each over someone).
Say there's a bare majority for X over Y. Say the Y voters give maximum to Y and minimum to everyone else. The majority must give nearly the maximum to X (and the minimum to Y) to make Y lose. Even if the X favorite voters give maximum to X, the members of the X>Y majority to whom X isn't favorite still have to give some nearly maximum amount to X, to make him beat Y. Sure, ideally they could give barely enough to X to put him over Y, and give maximum to their favorite. And, if they can give as finely-graded point ratings as they want to, they could still avoid voting less-liked candidates equal to more-liked candidates. So, it looks as if infinitely-finely-graded CR could meet SDSC.
Your method isn't CR, and I don't know if it meets SDSC, but it might, if it allows infinitely-finely-graded ratings.
You continued:
Does SDS actually mean that the winner should be picked by the largest majority?
I reply:
No. SDSC requires that if a majority prefer X to Y, then they should have a way of voting that ensures that Y won't win, without voting a less-liked candidate equal to or over a more-liked one.
(A voter votes A equal to B iff s/he doesn't vote either over the other, but votes each over someone).
Approval and CR meet FBC and WDSC. And, as I was saying, maybe CR can meet SDSC if it allows infinitely fine gradation of points ratings.
So maybe your point system can meet those criteria too.
The eliminations complicate the compliance determinations, and I can't say at first glance if IRNR meets those criteria.
As someone already pointed out, the eliminataion process prevents you from saying that IRNR meets Participation based only on initial point scores.
Mike Ossipoff
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