[EM] Fwd: Ranked Pairs
Colin Champion
colin.champion at routemaster.app
Wed Sep 20 07:30:28 PDT 2023
Well, I coded up Minimax(WV) for my own evaluation. Rather to my disgust
(and contrary to Darlington) I find that it does indeed outperform
Margins for truncated sincere ballots. I ran a large number of trials
with 10001 voters under a spatial model, 8 candidates being truncated to
4. Minimax (margins)=83.35% correct, minimax(wv)=84.09%. Other methods
which outperformed standard minimax in the simulation include Approval
Sorted Margins (in an ordinal version suggested by Ted Stern): 84.14%;
Black: 84.22%; Smith,Borda: 84.22%.
Hastily written and unreliable code, not to be trusted.
CJC
On 18/09/2023 22:30, Michael Ossipoff wrote:
> Hi Colin—
>
> Yes, margins beats wv for social-utility under sincere voting when
> there’s that vanishingly rare natural top-cycle.
>
> But Darlington & Tideman evidently aren’t considering resistance to
> offensive strategy, which is a much bigger threat than natural top-cycles.
>
> Protecting the CW from offensive strategy is more important than SU in
> natural top-cycles.
>
> …& is better for SU.
>
> On Mon, Sep 18, 2023 at 07:03 Colin Champion
> <colin.champion at routemaster.app
> <mailto:colin.champion at routemaster.app>> wrote:
>
> Thanks to Kevin and Michael for pointing out a feature of minimax
> I was unaware of. I had however seen Richard Darlington's paper
> [1] in which he referred to 'several studies' comparing margins
> with winning votes. He reports that margins 'was the big winner in
> all of them'. I suppose I'll have to look deeper.
> Colin
> [1]. https://arxiv.org/abs/1807.01366
> <https://arxiv.org/abs/1807.01366>
>
> On 18/09/2023 07:57, Michael Ossipoff wrote:
>>
>>
>> ---------- Forwarded message ---------
>> From: *Michael Ossipoff* <email9648742 at gmail.com
>> <mailto:email9648742 at gmail.com>>
>> Date: Sun, Sep 17, 2023 at 22:54
>> Subject: Re: [EM] Ranked Pairs
>> To: Forest Simmons <forest.simmons21 at gmail.com
>> <mailto:forest.simmons21 at gmail.com>>
>>
>> This was meant to be sent by “Reply All”, in order to post it. So
>> now I’m forwarding it to EM.
>>
>> Forest—
>>
>> But wv prevents truncation (strategic or otherwise) from taking
>> the win from a CW.
>>
>> …&, with, wv, refusing to rank anymore you don’t approve will
>> cause offensive order-reversal by their preferrers to backfire.
>>
>> I’d always take that precaution, & would advise others to.
>>
>> When we discussed these guarantees years ago they seemed
>> absolute, & we still have the guarantee-criteria based on
>> them…met by wv versions of MinMax, RP, CSSD, & Smith//MinMax.
>>
>> …&, with MinMax, whose winner can come from anywhere, not just
>> from the top-cycle, & so, offensive order-reversal, when there
>> are a fair number of candidates, is unpredictable & risky for its
>> perpetrators, even if the precaution of deterrent-truncation
>> isn’t taken.
>>
>> On Sun, Sep 17, 2023 at 21:17 Forest Simmons
>> <forest.simmons21 at gmail.com <mailto:forest.simmons21 at gmail.com>>
>> wrote:
>>
>>
>>
>> On Sat, Sep 16, 2023, 9:42 PM Michael Ossipoff
>> <email9648742 at gmail.com <mailto:email9648742 at gmail.com>> wrote:
>>
>> Is that RP(wv), or RP(margins) ?
>>
>> RP(wv) would thwart & deter offensive strategy, an
>> important property in public elections.
>>
>> …&, actually, it seems to me that MinMax(wv) would do
>> that better.
>>
>> That’s because, choosing only from the Smith Set RP,
>> limits it’s choice to the strategic top-cycle that
>> created by the offensive strategists.
>>
>> Suppose that the CW’s preferrers don’t do defensive
>> truncation (never rank anyone you wouldn’t approve in
>> Approval, or whose preferrers you regard as likely to
>> offensively order-reverse) ?
>>
>> Knowing that RP will limit its choice to their small
>> strategic top-cycle, it would be easier for the
>> strategists to be fairly sur that their candidate would
>> win in that top-cycle.
>>
>> But, with MinMax, the winner is chosen more broadly, &
>> could be anywhere in the candidate-set. …making it more
>> difficult & risky to confidently do offensive order/reversal.
>>
>> RP(margins) might the best choice for a completely honest
>> electorate, but MinMax(wv) seems better for public
>> elections, due to its better thwarting & deterrence of
>> offensive strategy.
>>
>> Yes, MinMax doesn’t meet the luxury cosmetic look-good
>> criteria that RP meets.
>>
>> But for one thing, I remind you that natural ( sincere)
>> top-cycles are vanishingly-rare.
>>
>>
>> This is the same conclusión I have come around to.
>>
>> And methods that break a three member top cycle at the
>> weakest link tend to reward the burier faction.
>>
>>
>> So do you want to have less strategy-protection, in order
>> for the result to maybe look better in a vanishingly rare
>> natural top/cycle?
>>
>> …& how bad is a violation of Condorcet-Loser anyway.
>> “Beaten by all the other alternatives” sounds like some
>> kind of unanimity, but of course it isn’t. It isn’t like
>> a Pareto-violation. I remind you that the MinMax winner
>> has fewer voters preferring some particular candidate
>> over him than anyone else does.
>>
>> Clone-Criterion violation? How bad that really in MinMax,
>> especially when we’re talking about a vanishingly rare
>> natural top-cycle?
>>
>> RP(margins) for a completely honest electorate.
>>
>> MinMax(wv) for public elections.
>>
>> ..& about a primary to reduce the candidates to 5: Forget
>> the primary. If you think people will have trouble
>> rank-ordering lots of candidates, I remind you that, to
>> vote among them in a primary, they’d still have to
>> examine & choose among the initial many candidates.
>>
>> …harder than ranking only the ones you know & regard as
>> deserving & definitely in your accepts& preferred set.
>>
>> On Wed, Sep 13, 2023 at 00:18 Colin Champion
>> <colin.champion at routemaster.app
>> <mailto:colin.champion at routemaster.app>> wrote:
>>
>> I notice that RP is the only election method
>> mentioned by name in the
>> Virginia agenda.
>>
>> A while ago I ran some simulations on elections with
>> truncated ballots.
>> Something I noticed was that the presence of RP in
>> the list of methods
>> made the software unacceptably slow. I didn't look
>> into the cause, but
>> there's a natural explanation, which is the fact that
>> RP is known to be
>> NP-complete when it deals correctly with tied
>> margins, i.e. by
>> exhausting over all their permutations. Presumably if
>> some candidates
>> are unpopular and ballots are extensively truncated,
>> then tied margins
>> are much likelier than with complete ballots.
>>
>> I gather that practical implementations of RP choose
>> a random
>> permutation rather than exhausting. This seems to me
>> to bring a danger.
>> The presence of a few vanity candidates (truncated
>> off almost all
>> ballots) may lead to ties, and this may lead to a
>> comfortable winner
>> looking as though he owes his victory to a coin-toss.
>> Obviously this
>> undermines the legitimacy of his win.
>>
>> CJC
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