[EM] MinMax Opposition

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[EM] MinMax Opposition

John Karr
I've seen very little written about the MinMax Pairwise Opposition
Method. Which is surprising, given that it is the only Later Harm Safe
RCV method other than IRV (that I'm aware of).

It counts the votes against each choice and elects the choice that had
the lowest opposition in its worst pairing.

It appears to agree with Condorcet more often than IRV does and handle
Clones much better than IRV. Its' weakness is that it fails the
Plurality and Condorcet Loser Criterion.

The obvious fixes involve pairing it with other methods such as
restricting it to Smith Set when there is no Condorcet Winner (only
helpful when there is no Condorcet Winner) or having a Runoff of the IRV
Winner vs the MMPO winner, both of which introduce some later harm
potential. Or alternately Dropping all choices lower in approval than
the first choice votes for the plurality leader (while fixing Plurality
it does not guarantee to eliminate the Condorcet loser) also introduces
a later harm concern.



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Re: [EM] MinMax Opposition

Kristofer Munsterhjelm-3
On 02/11/2020 06.51, John Karr wrote:

> I've seen very little written about the MinMax Pairwise Opposition
> Method. Which is surprising, given that it is the only Later Harm Safe
> RCV method other than IRV (that I'm aware of).
>
> It counts the votes against each choice and elects the choice that had
> the lowest opposition in its worst pairing.
>
> It appears to agree with Condorcet more often than IRV does and handle
> Clones much better than IRV. Its' weakness is that it fails the
> Plurality and Condorcet Loser Criterion.
>
> The obvious fixes involve pairing it with other methods such as
> restricting it to Smith Set when there is no Condorcet Winner (only
> helpful when there is no Condorcet Winner) or having a Runoff of the IRV
> Winner vs the MMPO winner, both of which introduce some later harm
> potential. Or alternately Dropping all choices lower in approval than
> the first choice votes for the plurality leader (while fixing Plurality
> it does not guarantee to eliminate the Condorcet loser) also introduces
> a later harm concern.

About the only thing MMPO has going for it is that it, indeed, meets
LNHarm and Participation. The cost is a very strong Plurality failure.
But if you try to fix the Plurality failure by modifying MMPO, then
it'll no longer meet either LNHarm or Participation. In that case, why
not use another method?
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Re: [EM] MinMax Opposition

John Karr
The other Later Harm (IRV/Hare) safe method is also highly flawed.

Ultimately I think the best method is gong to have to be a compromise
between Later Harm and better results. Extending Arrows Theorem: to get
sincere ballots the voters must not be concerned by Later Harm Risk, the
Condorcet and Smith criteria cannot be met while guaranteeing Later Harm
protection.

My query was hoping to find more discussion of this problem. Since MMPO
appears to produce outcomes closer to Condorcet than IRV, is there a fix
to MMPO that protects against its two flaws with only a minimal amount
of Later Harm impact.

On 11/2/20 5:38 AM, Kristofer Munsterhjelm wrote:

> On 02/11/2020 06.51, John Karr wrote:
>> I've seen very little written about the MinMax Pairwise Opposition
>> Method. Which is surprising, given that it is the only Later Harm Safe
>> RCV method other than IRV (that I'm aware of).
>>
>> It counts the votes against each choice and elects the choice that had
>> the lowest opposition in its worst pairing.
>>
>> It appears to agree with Condorcet more often than IRV does and handle
>> Clones much better than IRV. Its' weakness is that it fails the
>> Plurality and Condorcet Loser Criterion.
>>
>> The obvious fixes involve pairing it with other methods such as
>> restricting it to Smith Set when there is no Condorcet Winner (only
>> helpful when there is no Condorcet Winner) or having a Runoff of the IRV
>> Winner vs the MMPO winner, both of which introduce some later harm
>> potential. Or alternately Dropping all choices lower in approval than
>> the first choice votes for the plurality leader (while fixing Plurality
>> it does not guarantee to eliminate the Condorcet loser) also introduces
>> a later harm concern.
> About the only thing MMPO has going for it is that it, indeed, meets
> LNHarm and Participation. The cost is a very strong Plurality failure.
> But if you try to fix the Plurality failure by modifying MMPO, then
> it'll no longer meet either LNHarm or Participation. In that case, why
> not use another method?
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Re: [EM] MinMax Opposition

robert bristow-johnson


> On 11/02/2020 2:56 PM John Karr <[hidden email]> wrote:
>
>  
> The other Later Harm (IRV/Hare) safe method is also highly flawed.
>

so maybe LNH is a little bit overrated.  i don't think it's an issue with a Condorcet method except in the thin possibility that a cycle occurs.

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Re: [EM] MinMax Opposition

Kevin Venzke
In reply to this post by John Karr
Hi John,

We've discussed MMPO a lot in past years. Its main advantage is not just LNHarm,
but also FBC (favorite betrayal). (Kristofer mentions Participation, but I think
he may have DSC in mind there.)

I think I agree with Kristofer at least in that, if you modify the method such
that you break compliance with the criteria, you'll have the burden of showing
that the method still performs better than average according to your metric. And
you have to keep people's attention long enough to make the case.

I can't think of too many efforts I made to "fix" MMPO while salvaging LNHarm.
The closest I can think of is my idea to use MMPO to choose the winner from
Woodall's CDTT, which is the Schwartz set defined using only the majority-strength
pairwise contests. This set is more LNHarm-friendly (basically because it is less
responsive to changes in the matrix), but remains incompatible with LNHarm given
4+ candidates. The combined method also doesn't satisfy Plurality. Off the top of
my head all it really does is fix the standard MinMax Clone-Winner failure
scenario.

There is tension between Plurality, LNHarm, and respecting pairwise majorities.
If you secure the first two and weaken the third, you'll probably end up with
something that isn't quite satisfying from a Condorcet perspective.

I'll mention a couple other ranked LNHarm methods. There's Woodall's Descending
Solid Coalitions (DSC) which satisfies Participation and also clone independence.
Your ranked ballot is basically translated into votes for each set of candidates
you prefer over every candidate ranked lower. Then there's a Tideman-like
procedure to lock results. You can easily make your vote useless if you have an
unusual preference order. This gives it a strange burial strategy (technically)
that resembles responding to the incentives of a chicken dilemma criterion.

I made a LNHarm method that I called Quick Runoff (QR) or Chain Runoff. I think
Chain Runoff is a more evocative name now. Sort the candidates by first
preference count. (You can't equal rank.) You examine the pairwise contest
between each adjacent pair of candidates, starting at the top and going down. But
you stop as soon as the lower-ranked (i.e. fewer first preferences) candidate
does not have a full majority (i.e. of all voters) win over his opponent. That
opponent is elected.

(Equivalently, elect the candidate with the most first preferences who both has a
majority-strength win over the candidate ranked above him (or has no such
candidate), and also does not have a majority-strength loss to the candidate
ranked beneath him (or has no such candidate).)

This satisfies LNHarm because adding a new lower preference A>B can only have an
effect if B is currently the winner. It satisfies Plurality since the winner of
the method is either the first preference winner, or else has a majority-strength
pairwise win over somebody (meaning only a majority favorite could disqualify
them). On the negative side, there is a monotonicity issue in that a losing
candidate can wish they had received fewer first preferences, as it would have
given them more advantageous match-ups.

Just a few comments on the topic.

Kevin



Le dimanche 1 novembre 2020 à 23:51:13 UTC−6, John Karr <[hidden email]> a écrit :


I've seen very little written about the MinMax Pairwise Opposition
Method. Which is surprising, given that it is the only Later Harm Safe
RCV method other than IRV (that I'm aware of).

It counts the votes against each choice and elects the choice that had
the lowest opposition in its worst pairing.

It appears to agree with Condorcet more often than IRV does and handle
Clones much better than IRV. Its' weakness is that it fails the
Plurality and Condorcet Loser Criterion.

The obvious fixes involve pairing it with other methods such as
restricting it to Smith Set when there is no Condorcet Winner (only
helpful when there is no Condorcet Winner) or having a Runoff of the IRV
Winner vs the MMPO winner, both of which introduce some later harm
potential. Or alternately Dropping all choices lower in approval than
the first choice votes for the plurality leader (while fixing Plurality
it does not guarantee to eliminate the Condorcet loser) also introduces
a later harm concern.



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Re: [EM] MinMax Opposition

John Karr

Thanks for your reply!

If MMPO could be fixed or fixed with a trivial LNH violation, then it would be a very attractive option. It sounds like others have looked at this before. I think it warrants more coverage in the main electowiki, but I don't have the background to add it.

Digression:

Given sincere ballots I consider any method that meets the Smith Criteria superior. Opposing that for the Voters to cast sincere ballots LNH is a juggernaut. I currently support Smith-IRV as it is simple and has the least LNH possible for a Smith compliant method. Smith-MMPO is probably still worth further investigation, but would require extra steps to exclude plurality violation.

As an advocate I'm searching for a compromise option with less LNH effect than Smith-IRV (or Smith-MMPO) that produces better results than IRV. To have sincere ballots the voter must perceive dropping a supported choice for LNH concern to be far outweighed by the increased chance an unsupported choice will win.

For Vote::Count I spent some effort exploring Redacting Condorcet vs IRV Methods, one of the approaches can be used to measure the later harm effect (by determining how many second choice votes the Condorcet winner needed from the IRV winner), and also to use it to set a Later Harm Tolerance threshold against the Margin of the Condorcet Winner over the IRV Winner. With no tolerance it almost never overturned IRV. A simpler variant which only redacts the first choice votes of the IRV winner produced better results, and is likely to fall within the Later Harm tolerance I expressed earlier, but is moderately complex, which detracts from its viability when we're in the phase of trying to get RCV adapted.

The documentation is here: https://metacpan.org/pod/Vote::Count::Method::CondorcetVsIRV

On 11/2/20 10:11 PM, Kevin Venzke wrote:

Hi John,

We've discussed MMPO a lot in past years. Its main advantage is not just LNHarm,
but also FBC (favorite betrayal). (Kristofer mentions Participation, but I think
he may have DSC in mind there.)

I think I agree with Kristofer at least in that, if you modify the method such
that you break compliance with the criteria, you'll have the burden of showing
that the method still performs better than average according to your metric. And
you have to keep people's attention long enough to make the case.

I can't think of too many efforts I made to "fix" MMPO while salvaging LNHarm.
The closest I can think of is my idea to use MMPO to choose the winner from
Woodall's CDTT, which is the Schwartz set defined using only the majority-strength
pairwise contests. This set is more LNHarm-friendly (basically because it is less
responsive to changes in the matrix), but remains incompatible with LNHarm given
4+ candidates. The combined method also doesn't satisfy Plurality. Off the top of
my head all it really does is fix the standard MinMax Clone-Winner failure
scenario.

There is tension between Plurality, LNHarm, and respecting pairwise majorities.
If you secure the first two and weaken the third, you'll probably end up with
something that isn't quite satisfying from a Condorcet perspective.

I'll mention a couple other ranked LNHarm methods. There's Woodall's Descending
Solid Coalitions (DSC) which satisfies Participation and also clone independence.
Your ranked ballot is basically translated into votes for each set of candidates
you prefer over every candidate ranked lower. Then there's a Tideman-like
procedure to lock results. You can easily make your vote useless if you have an
unusual preference order. This gives it a strange burial strategy (technically)
that resembles responding to the incentives of a chicken dilemma criterion.

I made a LNHarm method that I called Quick Runoff (QR) or Chain Runoff. I think
Chain Runoff is a more evocative name now. Sort the candidates by first
preference count. (You can't equal rank.) You examine the pairwise contest
between each adjacent pair of candidates, starting at the top and going down. But
you stop as soon as the lower-ranked (i.e. fewer first preferences) candidate
does not have a full majority (i.e. of all voters) win over his opponent. That
opponent is elected.

(Equivalently, elect the candidate with the most first preferences who both has a
majority-strength win over the candidate ranked above him (or has no such
candidate), and also does not have a majority-strength loss to the candidate
ranked beneath him (or has no such candidate).)

This satisfies LNHarm because adding a new lower preference A>B can only have an
effect if B is currently the winner. It satisfies Plurality since the winner of
the method is either the first preference winner, or else has a majority-strength
pairwise win over somebody (meaning only a majority favorite could disqualify
them). On the negative side, there is a monotonicity issue in that a losing
candidate can wish they had received fewer first preferences, as it would have
given them more advantageous match-ups.

Just a few comments on the topic.

Kevin



Le dimanche 1 novembre 2020 à 23:51:13 UTC−6, John Karr [hidden email] a écrit :


I've seen very little written about the MinMax Pairwise Opposition
Method. Which is surprising, given that it is the only Later Harm Safe
RCV method other than IRV (that I'm aware of).

It counts the votes against each choice and elects the choice that had
the lowest opposition in its worst pairing.

It appears to agree with Condorcet more often than IRV does and handle
Clones much better than IRV. Its' weakness is that it fails the
Plurality and Condorcet Loser Criterion.

The obvious fixes involve pairing it with other methods such as
restricting it to Smith Set when there is no Condorcet Winner (only
helpful when there is no Condorcet Winner) or having a Runoff of the IRV
Winner vs the MMPO winner, both of which introduce some later harm
potential. Or alternately Dropping all choices lower in approval than
the first choice votes for the plurality leader (while fixing Plurality
it does not guarantee to eliminate the Condorcet loser) also introduces
a later harm concern.



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