[EM] Quick and Clean Burial Resistant Smith, compromise

[Kristofer Munsterhjelm]

On 17.01.2022 09:48, Colin Champion wrote:
> A bit of a side question, but is strategy resistance a good metric to
> quote?

It's a good metric "all other things equal". I agree that it's not a
good metric by itself since, as you point out, the strategy-proof
methods (random ballot, random pair) are not particularly good in
practice as you end up giving up too much to resist strategy.

We could get a better image by considering both the resistance to
strategy and the honest voting performance (in the form of VSE for the
particular distribution that was chosen). We'd then get a Pareto front
that shows just how bad a method has to get under honesty to resist this
much strategy.

Some methods would simply be Pareto-dominated: I think IRV would be
dominated by the Condorcet-IRV hybrids because the latter both have
better honest performance when there is a CW, and better strategy
resistance (due to Condorcet fixing much of IRV's compromise incentive).

It's true that some methods work better under strategy than with
honesty. While I think the strategy measure may be somewhat misleading
in such a case, I think that it still indicates that the method isn't
optimal.

The reason is related to the revelation principle. Suppose that method X
does poorly with honest results but pretty good with strategy. Then we
can construct another method, DSV-X, that executes this strategy on
behalf of the honest voters. DSV-X will be better on honest than X by
our initial assumption. In addition, the algorithm inside DSV-X will
have full information of the ballots and so can potentially execute even
better strategies than the voters can do with imperfect information.
Thus the failure of X to itself do so (and the voters to have to do it
instead) is a flaw of the method X, and DSV-X (or some other method that
patches the problem) should be used instead.

(This is part of my beef with Range: it expects the voters to perform
some kind of strategy to cover for its shortcomings, and if the voters
misjudge the strategy things can go very wrong. And because there's no
unambiguous honest vote, its advocates tend to not consider this kind of
voting strategic in the first place.)

A true utilitarian might say that instead of recording the number of
elections where it's possible to strategize, we should separately record
the mean max loss (i.e. mean of worst loss that can come from
strategizing, over every election with strategy), mean expected loss,
mean maximum gain (as an indicator of when it might be better to replace
the method with a DSV one), and variance.

While I can see that point, there's something I like about just
recording the raw count: it's sort of a precautionary approach, that
strategy could be bad so we better avoid it. One could make a number of
arguments that utility calculations don't show the full picture: e.g.
suppose a method incentivizes two-party rule but has pretty good
(utility) performance once multiple parties are viable. Then the latter
is of less importance because you can't easily get there. Trying to
eliminate as many venues for strategy as possible should reduce the
chance of such problems happening.

-km