[EM] Why I Prefer IRV to Condorcet

[Kristofer Munsterhjelm]

Chris Benham wrote:
> Kristopher,
> All Condorcet methods are vulnerable to Burial. Smith,IRV has in
> common with IRV but not the other well-known Condorcet methods
> that a Mutual Dominant Third winner can't be buried. But like all other
> Condorcet methods it is not absolutely invulnerable to Burial like IRV.
>  
> 37: A>B
> 31: B>A
> 32: C>B
> 
> B is the CW, but if the A>B voters bury B by changing to A>C then
> the Smith,IRV winner changes from B to A.
> 
> For the advantage over IRV of the difference between Smith and
> Mutual Dominant Third (MDT), we lose Burial Invulnerability and
> Later-no-Harm and Later-no-Help and Mono-add-Top.
>  
> So I think the argument that Smith,IRV is really much better than the
> simpler plain IRV is weak. Likewise the case that Smith,IRV is the
> best Condorcet method.

I wouldn't say Smith,IRV is the best Condorcet method, either, but it 
may be the closest thing if people are very inclined towards burying 
candidates (and we want Condorcet).

> "Is it possible to make a monotonic method  that's resistant to burial?"
>  
> Yes, FPP fills that bill. Other methods have  incentives to "bury" only
> by truncating, not order-reversing. (According to a definition I'm not
> entirely happy with this qualifiies as "burying"). I have in mind the 
> methods
> that met Later-no-Help and not Later-no-Harm, such as Bucklin and
> Approval.

It would seem that in order for a method to be completely resistant to 
burial (including truncation), it must meet both LNHelp and LNHarm. That 
makes sense, because Burial involves altering the position of those 
lower down on your ranking to help the candidate that's higher up in 
your ranking. However, we know from Woodall that we can't have both 
LNHs, mutual majority, and monotonicity, nor can we have LNH* and 
Condorcet. Thus a method that's completely resistant would seem to need 
to be nonmonotonic or fail mutual majority, and in either case fail 
Condorcet.

There is one way out: consider a method that fails LNH* only in such 
ways that are not conducive to burial. For instance, it may be that if 
you vote A>B>C, then moving B last would cause C to win (instead of B). 
This is like Warren's claims about Black (Condorcet else Borda). You 
gave an example where burial works in Black, so Black is somewhat 
susceptible to burial, but it's theoretically possible there may be a 
method that works this way.

There's also another caveat in the other direction: consider a method 
with compulsory full ranking and a fixed number of candidates. It may be 
susceptible to burial (order reversal) even if LNH* no longer make any 
sense.

-

FPTP works, but really just because you can't bury. This can technically 
be "fixed" by treating FPTP as a ranked voting method where only your 
first preference matters. Still, it's a bit of a trick, so let me try 
something a bit more detailed. I wonder if there's a method that meets 
Condorcet and Dominant Mutual * burial resistance (the lesser the 
fraction the better), and is also monotonic. Both Smith,IRV and "first 
preference Copeland" meet Dominant Mutual Third burial resistance, but 
they're both nonmonotonic. While I'm wishing, having it summable would 
also be nice.

Or, for that matter, do we have a method that meets DMTBR, mutual 
majority, and monotonicity? Perhaps DAC (since it meets LNHelp), but it 
has other problems, and it doesn't meet plain DMT.