[EM] IRV is best method meeting 'later no harm'?

[Kristofer Munsterhjelm]

seppley at alumni.caltech.edu wrote:
> Can it be said that Later No Harm (LNH) is satisfied by the variation of
> IRV that allows candidates to withdraw from contention after the votes are
> cast?

I'm not sure. In the wider picture, the candidates would use the ballot 
data in order to determine whether their withdrawal would cause a better 
result. One of the "IRV spoilers" might see that, because of later 
preferences, a median candidate would win if he were to withdraw, 
whereas the current case (with no withdrawals) is that an extreme 
candidate wins. If the voters had not provided later preferences, the 
candidate could not have made such an inference, or perhaps the median 
would not have won even if the spoiler had withdrawn.

If it's possible to construct such an example, then IRV+Withdrawal would 
fail LNH, since later preferences would inform spoilers that they were 
spoilers -- that is, unless there's an "ordinary" method out there 
somewhere that passes LNHarm *and* doesn't have IRV's kinda-spoiler problem.

Or, to get at it from another angle: consider each candidate a function, 
and that this function takes the election (set of ballots) as input and 
provides an output regarding whether to withdraw. Then it should be 
possible to make a function so that the combined system fails LNHarm, 
even if we limit ourselves to functions that will help the median 
candidate win.
Again, this is with the caveat of LNH methods that are centrist: for 
instance, it might be possible to construct a function for Withdrawal 
emulation so that the system acts like MMPO, which is LNHarm and kinda 
median-seeking, but MMPO has other problems.

> I'm not claiming median positions are necessarily best.  But I do believe
> there are significant advantages to voting methods that induce candidates
> who want to win to take median positions:  Less polarization and less
> demagoguery.  Stability & incrementalism, since issues (e.g., abortion)
> will tend to get settled until the median position changes significantly. 
> Accountability on more issues, since a candidate who takes a non-median
> position on some issue would be risking that another candidate will take
> the (majority-preferred) median position and match his/her positions on
> other issues, and also since many other issues would already be settled
> (in an accountable way: the median).  Increased competition, since such
> methods would by necessity have very little spoiling (unlike plain IRV). 
> Reduced corruption, since accountability on more issues and increased
> competition would allow voters to rank less corrupt candidates over more
> corrupt candidates.  Reduced cost of campaigning, since "big tent" parties
> (if they continue to exist) would no longer need to conduct primary
> elections to winnow their contenders to one per office.

While I agree with that, for the sake of completion, I'll note that 
IRV/FPP supporters would probably say something like: "yeah, and replace 
our current candidates with a bunch of weak-willed flipfloppers who are 
afraid of offending anyone". Or in the words of Rob Speer, on this list 
back in 2003:
"Weak centrist!"
"Condorcet winner!"
"Weak centrist!"
"Condorcet winner!"

> By the way, if my understanding is correct, IRV is not Single Transferable
> Vote (STV), the single-winner voting method used in Australia & Ireland. 
> IRV severely limits the number of candidates each voter can rank (to 3, if
> my understanding is correct) whereas STV allows (or requires) each voter
> to rank every candidate.  STV satisfies LNH, and many people may consider
> it to be somewhat better than IRV. (STV facilitates greater competition
> and less spoiling, especially if candidates are permitted to withdraw
> after the votes are cast.)

IRV is STV(1,n), i.e. single winner IRV. What you describe sounds like 
FairVote's RCV, which was limited to three ranks to make it work on SF's 
machinery.

> Since IRV is said to satisfy LNH, then one must say Plurality Rule
> satisfies LNH too, because Plurality Rule can be viewed as just a
> variation of IRV with a smaller limit (one candidate per voter).

Plurality does, if you want to be exact, satisfy LNHarm. It does that by 
simply ignoring everything after the first rank, so that no matter who 
you rank after your top choice, your top choice is never harmed.

> If Withdrawal//IRV and Plurality Rule satisfy LNH, then I think it's
> reasonable to say that so do some methods in the Voting for a%2

What is "Voting for a%2"?