[EM] Fwd: Ranked Pairs

[Kevin Venzke]

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