[EM] Fwd: Ranked Pairs
Colin Champion
colin.champion at routemaster.app
Fri Sep 22 00:56:59 PDT 2023
A possible explanation for the discrepancy between my result and
Darlington's is that in my evaluation every ballot had the same number
of ties and in Darlington's the numbers differed.
On the face of it, WV doesn't treat voters equally. If we defined
"winning votes" as "the number of voters who prefer A to B plus half the
number who rank them equally", then every voter would contribute
m(m-1)/2 winning votes and WV would be equivalent (I think) to Margins.
But instead we define winning votes asymmetrically so that WV is *not*
equivalent to margins but voters contribute different numbers of winning
votes depending on the number of ties in their ballots. I can imagine
this leading to artefacts which Darlington's evaluation would pick up
and mine would miss. If this is what happened, then even Darlington's
evaluation must be too lenient to WV since he doesn't include effects
which would in fact arise, such as voters truncating differentially
according to their political viewpoint.
Maybe these things have been taken into account; I have no idea,
having never seen the thinking behind WV.
CJC
On 21/09/2023 03:35, Forest Simmons wrote:
> I think that if you were looking at the success rates of unilateral
> burial options along with the basic burial defense of truncation below
> sincere CW ... then the difference between Winning Votes and Margins
> would be more striking (still in favor of wv).
>
> On Wed, Sep 20, 2023, 2:12 PM Michael Ossipoff <email9648742 at gmail.com
> <mailto:email9648742 at gmail.com>> wrote:
>
> Thanks for the experiment. I hope that Tideman’s organization
> won’t be promoting the old margins version of RP. …unless just
> for maybe choosing between pizza-toppings or movies.
>
> On Wed, Sep 20, 2023 at 07:30 Colin Champion
> <colin.champion at routemaster.app
> <mailto:colin.champion at routemaster.app>> wrote:
>
> 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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