[EM] Approval-enhanced IRV

[Kristofer Munsterhjelm]

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, which has that manual DSV/Burr dilemma that I 
really don't like.

-km