[EM] compromising strategy in Condorcet...

[Markus Schulze]

Dear James Green-Armytage,

you wrote (19 Sep 2004):
> Are there any situations in IRV where there is NO Condorcet
> winner, and yet compromising is NOT a useful strategy? That
> is, does the absence of a Condorcet winner mean that some
> group of voters can potentially benefit from compromising
> in IRV? If so, then we would have logical proof that
> compromising strategy incentive is more frequent in IRV
> than Condorcet. Or, is there any other easy way to prove
> that IRV has a more frequent compromising strategy? Does
> every example which produces a compromising incentive in
> Condorcet also produce a compromising incentive in IRV?
> I think that this is a key point of comparison between
> the two methods.

The majority criterion and invulnerability to compromising
are mutually incompatible. Proof:

    40 A > B > C.
    35 B > C > A.
    25 C > A > B.

    Suppose that the used election method meets the majority
    criterion.

    Suppose that A wins the elections. Then the 35 BCA
    voters can change the winner from A to C by voting CBA
    (i.e. by compromising).

    Suppose that B wins the elections. Then the 25 CAB
    voters can change the winner from B to A by voting ACB
    (i.e. by compromising).

    Suppose that C wins the elections. Then the 40 ABC
    voters can change the winner from C to B by voting BAC
    (i.e. by compromising).

The above example demonstrates that when there is no
Condorcet winner and the used election method satisfies
the majority criterion then there is always an incentive
to use a compromising strategy.

Markus Schulze