[EM] Fwd: Ranked Pairs

[Kevin Venzke]

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