[EM] Fwd: Ranked Pairs

Colin Champion colin.champion at routemaster.app
Sun Sep 24 13:31:23 PDT 2023

Kevin – I'm not sure if you're right about IRV. If someone votes A=B>C, 
I'd attribute half a first-place preference to each of A and B. I don't 
know what other people would do.

On 24/09/2023 18:41, Kevin Venzke wrote:
> Hi Colin,
> Le dimanche 24 septembre 2023 à 07:41:45 UTC−5, Colin Champion <colin.champion at routemaster.app> a écrit :
>> Kevin – thanks for this helpful reply. I'm inclined to favour viewing a tie as two
>> half-voters with opposed preferences. I admit that this can only be a rule of thumb,
>> but I find it quite persuasive. After all, the whole point of ranked voting is that
>> voters start out, I assume, with nebulous cardinal judgements in their heads, and
>> that turning these judgements into rankings puts them onto a common basis (albeit
>> with loss of information) which allows them to be meaningfully combined. The WV rule
>> could easily undermine the premise of this procedure.
> I understand this as an abstract ideal. Something jarring to me is that the practical
> consequence of converting equal preferences into half-votes would vary a lot based
> on what the base method is. Under IRV it wouldn't do anything. (But maybe you don't
> find that IRV conforms to "the whole point of ranked voting.")
>> I believe that asymmetric treatment of ties in the Borda count leads quite directly
>> to errors of the sort I described, but I don't know if this is widely accepted.
> Isn't it pretty clear that symmetric treatment of ties under Borda results in a
> practically unusable method? In terms of strategic dilemmas it's like margins on
> steroids.
> I wonder if the errors you mean are defined precisely enough to say.
>> It's true that Darlington models ties as genuine expressions of indifference. In
>> practice ties can mean almost anything; indifference, laziness, ignorance... Quite
>> possibly voting methods which work well for one sort of tie will work less well for
>> another. The result I produced myself is probably genuine, and indicates that WV is
>> more accurate than margins for mandatory truncation; but I was wrong to suppose that
>> it could be interpreted more generally since it omits the effect which is most
>> likely to work against WV.
>> As for the positive arguments you put forward, well they might justify a rule of
>> thumb but I wouldn't find them compelling.
> Yes, I offered a rule of thumb that leads to a heuristic called WV. There can be
> other rules of thumb and other heuristics, and if they test in simulations as having
> low strategic incentives (especially low compromise incentive) then I will advocate
> those methods, too.
> I left out talk of my own simulations, but compromise incentive is a focus of mine.
>> I don't find the Condorcet principle
>> persuasive on its own merits (and do not believe it generally sound), but I accept
>> it as a working principle because I don't know any other way of obtaining simple
>> accurate voting methods under a spatial model.
> I would agree that Condorcet itself shouldn't be taken as a first principle.
> It sounds like you would advocate Condorcet as the best heuristic available to
> identify the best outcome when voters are sincere under a spatial model.
> I would advocate Condorcet because it makes the ballot a more effective agent to
> represent the voter's interests.
> Kevin
> votingmethods.net
> On 23/09/2023 02:47, Kevin Venzke wrote:
>>    Hi Colin,
>> Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion <colin.champion at routemaster.app> a écrit :
>>>    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.
>> I am not sure what to make of Darlington's defeat strength comparison. It sounds like
>> it was basically a simulation of sincere voters who vote equality because they actually
>> consider the candidates equal. That premise is fine but somewhat far removed from how
>> this topic is usually discussed, i.e. with some consideration of comparative strategy.
>> I notice incidentally that Darlington says incorrectly on page 22 that MinMax(PO) is a
>> Condorcet method. I wonder whether he implemented it as one to get his numbers on that.
>> In any case:
>> To find the motivation for WV I would start with first principles. How should we design
>> a Condorcet completion method to minimize strategic incentives? A motivation behind
>> Condorcet itself is that voters should not vote sincerely only to find that they
>> should've voted another way.
>> What could this mean here? Well, a full majority can always get what they want by
>> changing their votes. Therefore if a majority votes A>B yet B is elected, we have
>> *probably* done something wrong, because the majority certainly did have the power to
>> make A win instead. The election of B gives the A>B voters an incentive to vote
>> differently to change the outcome. The voters obtain a "complaint," I will call it.
>> Since majorities will most predictably obtain such complaints when we override their
>> preference, we should prioritize locking majorities.
>> With WV, there is no special heed paid to majorities, it just goes down the list of
>> contests starting with the largest winning blocs. But this achieves the goal. It
>> applies its principle to sub-majority contests as well, and maybe this is good bad or
>> neutral, but maybe we can believe that if it was helpful (for our end goal) to favor
>> majorities over sub-majorities then it could also be helpful to favor larger
>> sub-majorities over smaller sub-majorities. It certainly stands to reason that the more
>> voters you have sharing some stance, the more likely it is that a vote change on their
>> part could change the outcome.
>> (On my website I describe a different approach focused on compromise incentive, and
>> measuring the potential for this more directly, and one can take that as me suggesting
>> that WV actually leaves some room for improvement.)
>> You notice that adding half-votes to equal rankings under WV will turn it into margins.
>> This would give every contest a full majority on the winning side, and seemingly we can
>> trivialize this requirement of mine to prioritize majorities.
>> But I think it's clear, in the context of this analysis, that adding half-votes for
>> equal rankings doesn't make sense. The voter who says A=B doesn't turn into a pair of
>> opposing "half-complaints," where one of the complaints has the potential to be voiced
>> when *either* of A or B is elected. The A=B voter has no possible complaint either way,
>> as neither result can incentivize them to change their vote.
>> Additionally, I think that voters expect and want it to be the case that abstaining
>> from a pairwise contest does not mean the same thing as saying they rate both
>> candidates equal. I touched on this in my previous post.
>> Consider this election:
>> 7 A>B
>> 5 B
>> 8 C
>> Margins elects A, which is very unusual across election methods, and I think most
>> people would find this result surprising due to a sense of what truncation ought to
>> mean.
>> (Consider copying it into votingmethods.net/calc to see margins and MMPO stand alone
>> here.)
>> Perhaps with enough education people can *understand* that the method takes seriously
>> the apparent equality of the truncated preferences. But I don't think voters will find
>> it comfortable to vote under those circumstances. I think voters want to be able to
>> identify the set of candidates that they believe they are trying to defeat, leave them
>> out of their ranking, and not have to think any further about it.
>> Kevin
>> votingmethods.net

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