[EM] Automatic Withdrawal of Losing Candidates

[MIKE OSSIPOFF]

When Tom Round first proposed the candidate withdrawal option for IRV, in 
'94 or '95, we all recognized that it really gets rid of IRV's defensive 
strategy problem. It also does gets rid of whatever negligible defensive 
strategy problem Condorcet wv has.

How is that possible, considering the Gibbard-Satterthwaite theorem? Gibbard 
& Satterthwaite were talking about elections whose only input was the 
ballots. What they said doesn't apply to elections with the candidate 
withdrawal option.

When Tom proposed that, I posted here a suggestion of automatic candidate 
withdrawal.

After each count, the method deletes from the rankings any losing candidate 
without whom another losing candidate would have won. Sure, there's a 
problem when 2 losing candidates would have each won without the other. In 
that case maybe go by which one has the most voter support by some 
measure--maybe which one pairbeats the other. Maybe by which is ranked first 
by the most. The former sounds better.

Repeat till there's only one candidate left.

Considering how good candidate withdrawal is, automatic candidate withdrawal 
sounded pretty good, and still  does.

But when I found that IRV with automatic candidate withdrawal ils subject to 
order-reversal, and that the same is true of ordered Buckliln with automatic 
candidate withdrawal, I abandoned automatic candidate withdrawal. At that 
time my standards for new methods were unrealistically high: I was lookling 
for one that wan't vulnerable to offensive order-reversal.

But, because all nonprobabilistic 1-balloting methods that don't have worse 
problems are vulnerable to order-reversal, maybe automatic candidate 
withdrawal deserves another look. Maybe ordinary ordered Bucklin deserves 
another look too (I likewise abandoned it when I found that it was 
vulnerable to order-reversal). But especiallly automatic candidate 
withdrawal should be checked-out.

When I abandoned it then, I probably didn't even check Condorcet with 
automatic candidate withdrawal. I still haven't. Since, other than with 
enhancements such as I've described, a method has no way of finding the CW 
or the order-reversers in a circular tie, all 1-balloting methods must be 
vulnerable to order-reversal. But it isn't immediately obvious how Condorcet 
wv with automatic candidate withdrawal would have that vulnerability. After 
all, since, unlike IRV, wv's only defensive strategy need is caused by 
offensive order-reversal, and since that is gotten rid of by the candidate 
withdrawal option, and presumably by automatic candidate withdrawal, it 
isn't obvious how order-reversal could remain a problem for wv with 
automatic candidate withdrawal. That should be checked out. That 
combination, wv and automatic candidate withdrawal might turn out to be a 
winning combination that will further improve wv's freedom from strategy 
need.

Mike Ossipoff

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