[EM] Approval-enhanced IRV

[Forest Simmons]

On Mon, Aug 7, 2023, 2:34 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 8/7/23 11:03, C.Benham wrote:
> > Kristofer,
> >
> >> So I wouldn't say that compromise incentive has gone entirely out of
> >> fashion :-)
> >
> > And neither would or did I.  In English, there is a big difference in
> > meaning between "a bit" and "entirely".
>
> I'll rephrase. What I'm saying is that there is, from a Condorcet
> perspective at least, a natural bound to how much the method can
> backslide on compromise incentive. Hence, even if it looks like it's
> going "a bit" out of fashion, it does not imply that the tendency can
> continue to the degree where everybody gets so focused on say, burial
> resistance, that they forget compromise entirely.
>
> And that this bound is fairly high; and the wiggle room is fairly narrow
> for strict ballots due to the observation about compromise incentive
> always existing with a majority-strength cycle.
>
> > But if you as Condorcet advocate over-emphasise "compromise
> > resistance", what is your argument when it is pointed out that
> > Condorcet is incompatible with Favorite Betrayal and suggested that
> > if it is all about compromise resistance why not get the maximum
> > possible with a method that meets Favorite Betrayal?
>
> In short: because FBC is very demanding and thus it may be too much to
> ask. But research is still possible, and we might be surprised.
>
> To expand on that:
>
> I would approach that in three ways. First, that strong FBC is too
> strong and that this is just the way the math goes (see Alex Small's
> paper); and second, that if cycles are rare, there's no problem (when
> there's a CW, we pass IIA etc).
>
> Third, that the Condorcification logic says nothing about what happens
> when there's no majority strength CW, such as when you equal-rank or
> truncate, which is the domain of the ordinary (weak) FBC. So it should
> be possible to find a range of methods all the way from something that
> doesn't pass Condorcet with equal-rank, say something like MMPO, and to
> classical Condorcet methods like Schulze, that don't pass the weak FBC.
>
> More investigation into these wouldd of course be welcome. Most of them
> seem to have other problems (e.g. MMPO's egregious Plurality failure, or
> the way at least some tied-at-the-top methods degrade to Approval
> because min-maxing is so beneficial).
>
> When we talked about Condorcification earlier, Kevin mentioned that
> these FBC methods don't necessarily have a lower general compromise
> incentive either. So what is and isn't possible in this domain is still
> pretty unclear.
>
> If one wants to get the maximum possible with a method that meets the
> FBC, then that's not necessarily incompatible with majority-strength
> Condorcet. But as it stands, FBC methods seem to go too far. At least
> the ones I know; either they have other problems (like MMPO) or they
> degrade into Approval,


In a way MMPO can be used to make Approval more meaningful ... by using the
MMPO candidate C as the approval cutoff candidate ... the approval of X
could be the number of ballots on which X is ranked above C plus the number
of ballots on which they are ranked equal top, plus half the number on
which they are ranked equal below top (but above bottom).

So C's approval would be its top (including equal top) count plus half of
the number of ballots where it is ranked strictly between top and bottom.

which has that manual DSV/Burr dilemma that I
> really don't like.
>
> -km
>
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