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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