# Condorcet order-reversal problem? (was Re: First Debate

Steve Eppley seppley at alumni.caltech.edu
Wed Dec 11 09:24:04 PST 1996

```Hugh T wrote:
>>> The more difficult problem for Condorcet arises when B has more
>>> than 40% first place support in an otherwise similar scenario (20%
>>> middle), and B supporters thus could use order-reversal to create a
>>> circular tie that B could win.
-snip-
>Mike says the M voter will truncate to deter this strategy,

I think Mike said the M voter would truncate to deter this strategy
only under certain conditions: the electorate would have to be
massively sophisticated (devious, to use his term) for there to be a
likelihood of order reversal massive enough to change the result, and
the M voters would have to be confident that M would be the middle
"compromise" winner if people voted sincerely.

>even though that could elect A (whom the M voter despises) if B
>voters are not deterred by the M voter's stated intent to truncate

Is it reasonable to think the M voters will despise A more than B,
particularly when it's the B campaign which is organizing to steal
the election from M?

I think the B voters are well-deterred by the method itself.  Even
if most of the M voters don't truncate, order-reversal by the B
voters figures to backfire and elect their greater evil.

Sincere:
46:BMA                             46:BAM    <-- massive reversal
10:MBA                             10:MBA
10:MAB                             10:MAB
34:AMB                             34:AMB

B    M    A                        B    M    A
B       46   56L                   B       46   56L
M  54L       66L                   M  54L       20
A  44   34                         A  44   80L
---- ---- ----                     ---- ---- ----
LL 54    *   66                    LL 54   80   56

The amount of reversal necessary to create the circular tie and make
B the winner is massive, and could be deterred by just a few who find
the reversal abhorrent.

>I think the M voter is in a tough spot here,

46:BAM   <-- massive reversal
10:M     <-- truncation defense
10:MAB
34:AMB

B    M    A
B       46   46L
M  54L       20
A  44   80L
---- ---- ----
LL 54   80   46

I agree with Mike's opinion that this game of chicken is easily won
by the M voters.  Even if they despise A much more than they despise
B, realistically the B voters figure to despise A even more than the
M voters despise A.

>but agree with Mike that this rather special case is a minor problem
>compared to tactical opportunities in IRO.

I agree with you both.  But if you're referring to "offensive"
tactical opportunities in IRO, as I recall they're not a problem.
It's the routine need for defensive "lesser of evils" voting in IRO
which impeaches it.

>Examples have been discussed previously, but time permitting I'll
>post one again.

Now that I see which examples you had in mind, I withdraw my request
that you (re)post one.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

```