[Election-Methods] A Better Version of IRV?

[Kristofer Munsterhjelm]

> I don't see how IRV's failure to elect the Condorcet candidate is 
> necessarily linked to its "non-monotonicity".
> There are monotonic (meets mono-raise) methods that fail Condorcet, and 
> some Condorcet methods that fail mono-raise.

(For information: I think Bucklin would be an example of the former, and 
one of the Borda-elimination methods be an example of the latter.)

> I think Smith (or Shwartz),IRV is quite a good  Condorcet method. It 
> completely fixes the failure of Condorcet while being more complicated
 > (to explain and at least sometimes to count) than plain IRV, and a Mutual
 > Dominant Third candidate can't be successfully buried.
> But it fails Later-no-Harm and Later-no-Help, is vulnerable to Burying 
> strategy, fails mono-add-top, and keeps  IRV's failure of  mono-raise 
 > and (related) vulnerability to Pushover strategy.

At the risk of taking this thread away from its original topic, I wonder 
what you think of Smith,X or Schwartz,X where X is one of the methods 
Woodall says he prefers to IRV - namely QTLD, DAC, or DSC.

(Since QLTD is not an elimination method, it would go like this: first 
generate a social ordering. Then check if the ones ranked first to last 
have a Condorcet winner among themselves. If not, check if the ones 
ranked first to (last less one), and so on. As soon as there is a CW 
within the subset examined, he wins. Schwartz,QLTD would be the same but 
"has a Schwartz set of just one member" instead of "has a CW".)

DAC and DSC only satisfy one of LNHelp/LNHarm, but they're monotonic in 
return. According to Woodall, you can't have all of LNHelp, LNHarm, and 
monotonicity, so in that respect, it's as good as you're going to get. I 
don't know if those set methods are vulnerable to burying, though, or if 
they preserve Mutual Dominant Third.

Then again, satisfying one of the LNHs may not matter since combining it 
with Condorcet in that manner makes the combination fail both LNHs. 
Combining a method that satisfies LNHarm with CDTT gives something that 
still satisfies LNHarm, but the result fails Plurality, and that's not 
good either... and the Condorcet method of Simmons (what we might call 
"First preference Copeland") resists burial very well, but it isn't 
cloneproof.