[EM] "Serious stragtegy problem of Condorcet but not IRV"?

[MIKE OSSIPOFF]

There have been a few replies to a message with subject line something like 
this: Serious strategy problem that Condorcet has but IRV doesn't have.

I haven't been able to find the posting that the repiles are to. Could 
someone tell me what day the initial message was posted, or, better yet, 
what the serious strategy problem is?

Right now I'll tell you a strategy problem that Condorcet & Approval have 
but that IRV doesn't have. It's hardly surprising that there is one. Why 
should we expect all methods to have the same problems. And we know from 
Gibbard & Satterthwaite that there's no such thing as a completely 
stragtegy-free nonprobabilistic method.

IRV's shining example:

sincere preferences:

40: C
35: AB
25: BA

A is the CW, and is chosen by Condorcet and by IRV.

But now what if if the B voters refuse to rank A? Now, in Condorcet, we get 
a circular tie in which B wins.

I've often mentioned this before: the fact that SFC's protection only 
protects a majority-supported CW. If a majrority won't suport a CW, then 
there isn't much that the method can do.

The important thing about this is that it is _not_ a majorilty rule 
violation. IRV, in its bad-examples, frequently and easily violates majority 
rule, failing the majority defensive strategy criteria met by Condorcet and 
Approval. Those are WDSC, and, for Condorcet, SFC. And, for SSD, RP, and 
BeatpathWinner/CSSD, GSFC & SDSC. I might as well add here that Bucklin too 
meets WDSC and SDSC, and, with equal rankings, FBC, and, with AERLO, Strong 
FBC.

As I said, Approval and Condorcet both have this "problem". So does Bucklin. 
It's a co-operation/defection dilemma, in which the A voters can be had if 
they sincerely rank B. But if they refuse to, and if the B voters refuse to 
rank A, then C wins.

Of course, in the campaign, the A voters should be pointing out that A seems 
to have more support than B does, and that therefore A is the more rightful 
winner. If there's so much distrust that this co-operation/defection problem 
is known to exist, then the A voters will know that these pubilc statements 
about A being the rightful winner are just another way of telling the A 
voters to refuse to rank B. And the B voters will know that that's how the A 
voters will vote. No need for A advocates to actually say "We won't rank B", 
a statement that could offend B voters and emotionally obligate them to 
defect.

Not only is there no majority rule violation, but presumably A & B are 
similar, since both prefer eachother to C. So it doesn't make such a 
terribly great difference which wins. I merely point that out to show that 
it isn't the serious problem that it has been portrayed as.

James A. has mentioned this problem in connection with Approval.

Why doesn't IRV have this probem? Because you aren't allowed to help a 2nd 
choice unless your favorite is gone. Even the stingiest person can be very 
generous in his will.

But, as I've pointed out before, in these mutual majority situations, IRV 
demonstrates its failure of FBC & WDSC. Consider the C voters. Or don't we 
care about them? If they know that {A,B} is a mutual majlority, and if they 
had a preference between A & B, then they should rank A or B in 1st place 
instead of their favorite.  They have strategic need to bury their favorite.

So what, you say; why should they expect C to win if there's a majority 
against C? The problem is that we don't have perfectly reliable information. 
Therefore, the C voters, if they preferred A to B or B to A, might sometimes 
or often give the election away when C could have won, because they've 
misjudged. That's really the whole problem with all methods that have 
drastic defensive strategy need. For instance, it's the problem in 
Plurality. If we knew who is the best we can get, which we need as our 
compromise, Plurality wouldn't be nearly as bad.

So, for all these reasons, that example doesn't really seriously count for 
IRV against Condorcet, Approval, & Bucklin.

I've mentioned the automatic truncation line option (ATLO). ATLO would be a 
solution to this problem in Condorcet. The A voters could rank 1A, 2B, but 
draw an ATLO line just below A.

Approval could have the option of "reciprocal votes", counted only if 
they're reciprocated, or "equalling votes", counted only to bring B equal to 
A, but not over A. Condorcet could also have reciprocal or equalling votes; 
they could be defined in such a way as to be meaningful for Condorcet. But, 
as I said, in Condorcet ATLO would do the job too.

Though I mention a few possible solutions to the poroblem, by added voting 
options, I re-emphasize that the problem is nothing when compared to IRV's 
problems.

In ERIRV, the problem is avoided if the A voters merely rank 1A, 2B, without 
equal ranking or AERLO.

But though  ERIRV seems to avoid this problem more easily than Condorcet, 
which needs some kind of added voting option, remember that equal ranking 
itself is an added option to IRV. Without it, IRV is no good at all.

ERIRV, especially with AERLO, is a good improvement on IRV, if only the IRV 
promoters would accept a mitigation compromise. So far they refuse to, 
because apparently they seem determined to impose all of IRV's worst 
problems on the voting public.

In our communications with IRVists, let's offer ERIRV, preferably with 
AERLO, as a mitigation compromise.

IRVists: If you'll replace unmitigated IRV with ERIRV with AERLO in your 
proposals, I won't oppose your proposal or write or speak against it when 
the pubilc are going to vote on it.

ERIRV(fractional) meets WDSC. With AERLO it meets SDSC. That isn't nearly as 
good as Condorcet's SFC, GSFC, WDSC, & SDSC compliances, but it's a big 
improvement over IRV & Plurality.

So I suggest ERIRV with AERLO as a compromise. ERIRV(fractional) shouldn't 
be objectionable to IRVists. Why shouldn't someone be able to divide their 
vote? And why should you object to
AERLO? What's wrong with equal-ranking a preferred set in 1st place if none 
of them can win otherwise? Who wouldn't want to do that?

Another IRV mitigation compromise that has been offered, by Steve Eppley and 
by Tom Round, is the candidate withdrawal option:

When the count is done, and there's a winner, any candidate can withdraw if 
s/he wants to, and call for another count. This can be done again by another 
candidate after the next count,...etc.  It gets rid of IRV's worst problem. 
It's probably the best of the IRV mitigation compromises.

IRVists have objected to this because they say it takes control away from 
the voter and gives it to the candidate. What kind of control is that? The 
right to have your last choice win because you don't want you losing 1st 
choice to withdraw? Your wishes aren't violated if your favorite withdraws 
when it's established that he can't win, and if his withdrawal can elect 
your 2nd choice instead of your last choice.

So take your pick, IRVists--All these mitigation compromises have been 
offered to you. If you accept one of them, you'll avoid running a proposal 
(unmitigatged IRV) that's no good, with us telling people why it's no good.

Also, Don Davison once posted here a method that he called Runoffs Without 
Eliminations (RWE), a version of IRV that doesn't do eliminations. It's 
related to Bucklin, and meets SDSC. That too would be an acceptable 
mitigation compromise.

Mike Ossipoff

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