[EM] Inclusion/Exclusion Counts

Kristofer Munsterhjelm km_elmet at t-online.de
Mon Oct 24 02:43:46 PDT 2022


On 10/23/22 04:55, Forest Simmons wrote:

> Critics have always maintained that this idea shows a lack of awareness 
> of clone dependence. But that judgment assumes that just because there 
> is a bad way of using those ballots, there can be no good way.

Here's a thought that occurred to me, that would explain why the 
(seemingly out of nowhere) implication that we can't have both reversal 
symmetry and DMTCBR.

First preferences are unaffected by burial, and last preferences are 
unaffected by compromising. Suppose we had a method that were DMTCBR and 
reversal symmetric. Then we could freely translate between a method 
that's very strong against burial and very strong against compromise by 
just reversing the ballots, since the reversed ballots' first 
preferences would be last preferences.

Thus a method that passes both DMTCBR and rev. sym. would be extremely 
resistant to both burial and to compromise. But since the favorite 
betrayal criterion is so hard to pass, we have reason to believe that 
this is impossible. So no such method can be rev. sym -- which is what 
we at least see with Condorcet methods!

It's thus quite that the implication is stronger: that we can't have all 
of DMTBR, majority, and reversal symmetry. But the proof is probably a 
lot harder to find, too.

So all of the above implies that when creating a resistant ranked 
method, we can't both have extreme resistance to burial and compromising 
- we have to pick one. Fortunately (as James Green-Armytage originally 
showed), we already get a great deal of compromising resistance from the 
Condorcet criterion itself (since, for instance, it does the right thing 
under center squeeze). Thus it's more sensible to choose further burial 
resistance over further compromise resistance if we can only have one.

(Unless we consider maximum compromise resistance absolutely 
non-negotiable, e.g. Mike O's insistence on the FBC.)

...

Finally, it might be useful to see just what the analog of the DMTCBR is 
for a reversed DMTCBR-compliant method. It's something like...

Suppose that more than 1/3 of the ranks some Condorcet loser last. Then 
nobody who prefers this loser to the current winner can make the loser 
win by upranking him.

-km


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