Trivia Question: Is it possible to pass both Favorite Betrayal AND Later No Harm citeria?

[Aaron Hamlin]

Question: Is it possible for a voting system to pass both Favorite Betrayal AND Later No Harm criteria?

I think this is an important question for purposes of rhetoric.

[Dale Sheldon-Hess]

Minimax (Pairwise Opposition) passes both (but unlike most minimax
methods, fails Condorcet).

--
Dale Sheldon-Hess

[Clay Shentrup]

IRV with rank equalities would suffice I believe.

[Clay Shentrup]

On Friday, May 4, 2012 9:54:27 AM UTC-7, Dale Sheldon-Hess wrote:

Minimax (Pairwise Opposition) passes both

But only with rank equalities permitted. See Wikipedia:

When the pairwise opposition variant is used, Minimax also does not satisfy the Condorcet criterion. However, when equal-ranking is permitted, there is never an incentive to put one's first-choice candidate below another one on one's ranking. It also satisfies the Later-no-harm criterion, which means that by listing additional, lower preferences in one's ranking, one cannot cause a preferred candidate to lose.

[Clay Shentrup]

On Friday, May 4, 2012 12:25:49 AM UTC-7, Aaron Hamlin wrote:

I think this is an important question for purposes of rhetoric.

I know where you were headed with this, but you can still point out that basically every sensible voting method fails one or the other.

But I go even further and argue that satisfying Later-no-harm is actually a bad thing, because it forces a system to ignore an arbitrarily large increase in support for Y vs. X, among an arbitrarily large number of voters — so long as those voters still prefer X to Y (even by the tiniest amount). 

[Toby Pereira]

Would other methods originally designed to be Condorcet (e.g. Schulze)
pass these if pairwise opposition was used intstead of e.g. winning
votes (or margins in other cases)?

On May 4, 5:54 pm, Dale Sheldon-Hess <d...@sheldon-hess.org> wrote:

[Jameson Quinn]

No. Say you support A>B>C and the honest pairwise matrix is: (WV for row over column)

    A   B   C

A       5   2

B   2       4

C   5   3

C wins. But if you and a friend betray A for B, then B will win. There's no other way for you to do it.

Jameson

2012/5/18 Toby Pereira <tdp...@yahoo.co.uk>

[Toby Pereira]

So minimax with pairwise opposition is the only system that satisfies
both criteria? What strategy would be optimal with this system?

On May 18, 11:49 pm, Jameson Quinn <jameson.qu...@gmail.com> wrote:
> No. Say you support A>B>C and the honest pairwise matrix is: (WV for row
> over column)
>
>     A   B   C
> A       5   2
> B   2       4
> C   5   3
>
> C wins. But if you and a friend betray A for B, then B will win. There's no
> other way for you to do it.
>
> Jameson
>

> 2012/5/18 Toby Pereira <tdp2...@yahoo.co.uk>

[Dale Sheldon-Hess]

On Sun, May 20, 2012 at 7:31 AM, Toby Pereira <tdp...@yahoo.co.uk> wrote:
> So minimax with pairwise opposition is the only system that satisfies
> both criteria? What strategy would be optimal with this system?

That's a good question, but not one with an easy answer.

I think this whole discussion has only served to convince me that, as
nice as FBC is from a voter's perspective, passing IIA is where it's
really at.

--
Dale Sheldon-Hess

[Toby Pereira]

I'm just trying to work out what passing favourite betrayal and later
no harm allows a voter to do. I think it only passes if equal ranks
are allowed. So if A is your favourite and B your favoured likely-to-
win candidates, does ranking A=B instead of A>B never causes A to
lose?

On May 21, 6:40 pm, Dale Sheldon-Hess <d...@sheldon-hess.org> wrote:

[Dale Sheldon-Hess]

On Fri, May 25, 2012 at 11:15 AM, Toby Pereira <tdp...@yahoo.co.uk> wrote:
> I'm just trying to work out what passing favourite betrayal and later
> no harm allows a voter to do. I think it only passes if equal ranks
> are allowed. So if A is your favourite and B your favoured likely-to-
> win candidates, does ranking A=B instead of A>B never causes A to
> lose?

I think yes, but also ranking A=B>C instead of A=B will never cause A
or B to lose.

--
Dale Sheldon-Hess

[Toby Pereira]

Yes, certainly ranking A=B>C instead of A=B should never cause A or B
to lose in a system that passes later-no-harm. I think this system
only passes favourite betrayal if equal ranks are permitted, which
suggests to me that the optimum strategy is likely to be to top rank
your favourite along with your favourite among the likely winners (in
fact it's beginning to sound like approval strategy).

By ranking A (your favourite) and B (a likely winner) equal, then if
it did cause B to win over A, then this system could still be said to
pass later-no-harm in some technical sense because you aren't actually
ranking B later than A. But then approval voting would also pass and
as far as I understand it's generally regarded as not passing -
http://en.wikipedia.org/wiki/Later-no-harm#Approval_voting.

On May 25, 8:22 pm, Dale Sheldon-Hess <d...@sheldon-hess.org> wrote:

[Toby Pereira]

I don't know if I'm missing something, but I'm struggling to see how Minimax with pairwise opposition passes later no harm.

 

Let's say my preference is A>C>B and this is the how people vote (including my ballot):

 

1: A>C>B

9: A>B>C

10: B>C>A

10: C>A>B

 

The highest pairwise opposition scores for each candidate are:

 

A: 20 (against C)

B: 20 (against A)

C: 19 (against B)

 

So C wins.

 

But I could have voted A>B>C to force a three-way tie. So isn't this a failure of later no harm? I thought later no harm was that anything I rank below a candidate shouldn't harm that candidate's chances. But I have harmed my favourite (A) by honestly voting C above A.

 

If there were two of us with the same views, the honest ballots would be:

 

2: A>C>B

9: A>B>C

10: B>C>A

10: C>A>B

 

The highest pairwise opposition scores for each candidate are:

 

A: 20 (against C)

B: 21 (against A)

C: 19 (against B)

 

C still wins.

 

But if we both strategically raise B above C:

 

11: A>B>C

10: B>C>A

10: C>A>B

 

The highest pairwise opposition scores for each candidate are:

 

A: 20 (against C)

B: 21 (against A)

C: 21 (against B)

 

So A wins. The conclusion is that we can't safely rank C as our second favourite without is harming A's chances of winning.

 

Also, according to the Wikipedia article http://en.wikipedia.org/wiki/Later-no-harm later no harm is incompatible with Condorcet but that all three Minimax variants (winning votes, margins and pairwise opposition) are equivalent when ties aren't allowed. It says "Since all the variants are identical if equal ranks are not allowed, there can be no example for Minimax's violation of the later-no-harm criterion without using equal ranks." But Minimax is supposed to be a Condorcet method, equal ranks or not (except with pairwise opposition), and Condorcet is supposed to be incompatible with later no harm, so there seems to be a contradiction in here somewhere.

[Jameson Quinn]

This has do do with why later no harm is a worthless characteristic. The idea in your scenario is that your honest A>C>B is no worse than a truncated A>C=B. The fact that A>B>C is better than either is, for this criterion, irrelevant. But of course it's hard to argue that such a narrowly-defined criterion means anything in this real-life situation. Similarly, in situations where IRV passes LNH but not FBC, I don't think that LNH is worth much.

Jameson

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[Toby Pereira]

It does sound like a very weak criterion under that definition. However, doesn't IRV pass the stronger criterion that anything that happens after A on your ballot can't hinder A's chances? In this case A>C>B, A>C=B and A>B>C would be the same for A's chances. Anything behind A on your ballot only gets looked at if A is eliminated.

 

(I'm not advocating IRV.)