[EM] Poking about Heaviside methods, again

[Kevin Venzke]

Hi Kristofer,

> > If we compare to methods that people actually propose, it seems true that non-Condorcet
> > methods don't tend to have huge burial issues. Main exceptions would be Borda, MMPO, and
> > iterated DSV methods that are nearly Condorcet-efficient. Methods like DSC and Chain Runoff
> > do have burial incentive, but their compromise incentive is probably a much bigger concern.
> 
> Some LNHelp methods have burial problems, though it's usually easier to
> just truncate instead of bury.

Do you say this because you conceive of burial as simultaneously adding one candidate while
lowering another, or because you include altering relative order within the ranking and not
just at the bottom?

I can imagine saying that Bucklin for example has burial incentive, but it feels a bit
off.

> My general direction of thought was: it would be useful to identify just
> what contributes to low burial incentive because all the strategy
> resistant methods I know of have mainly low burial incentive.

I guess from my perspective I don't have a good way to merge different forms of strategic
incentive into a single resistance metric. Even if I could do exhaustive searches it seems
like different strategies are qualitatively different, for example in how intuitive they
are for a voter to apply.

> Then amending them with Condorcet, e.g. going from IRV to Benham, seems
> to turn some of the compromising incentive into burial instead. But it
> doesn't greatly increase the strategic susceptibility as a whole, and
> that seems like a good trade for avoiding center squeeze and the likes.
> 
> So if that's true, then we should find some method that has very little
> burial incentive and that is strategy resistant (e.g. not Plurality,
> whose compromise incentive goes to 100% very quickly).

Sure, I understand what you want to do.

> >> - An interesting pattern seems to be: nonmonotone CV generalizations
> >> work by "If A and B are at the top by first preferences, then credit A
> >> with A>B and B with B>A". Monotone ones are about absolute comparisons
> >> instead: "if A and B combined are above some quota, then...".
> >
> > That's interesting but I have to imagine the latter approach breaks at some point (i.e.
> > ceases to provide monotonicity), perhaps with more than four candidates.
> 
> As I mentioned in a private mail, it should retain monotonicity because
> A and B share the pool that's compared against the quota. A will get A>B
> from any B where A and B's first preferences combined exceed the quota,
> so raising A to top on a B ballot can't harm A.

After playing with the H(fpA + fpB - fpC - fpD) method (max or sum, no Condorcet check) I
find a problem:

Suppose that the first preference count order goes ABCD, and the proportions are such that
the majorities are AB, AC, and AD. Say that B wins. If B obtains new first preferences at
the expense of C, the proportions could change so that fpB + fpD is now a majority. This
could allow D to be elected on the basis of a strong D>B gross score which wasn't
admissible before.

> But if it's necessarily true that you can only have burial resistance
> with elimination, then a direct consequence is that we can't have burial
> resistance and summability.

I have recently found a couple of exceptions to the first part although not the second.
That's to say LNHarm+LNHelp methods that can't be explained in terms of eliminations. I'm
not sure it will be any use to you, but it's still interesting. I'm sort of checking my
work and looking for any "nearby" findings before posting.

Kevin
votingmethods.net