[EM] Compromise strategy?

[MIKE OSSIPOFF]

There's a website with an article that lists some strategies
that are possible with various single-winner voting systems.
It says that Condorcet is subject to "compromise strategy",
meaning that voters have an incentive to insincerely up-rate
a compromise.

If we ask that no one ever have strategic incentive to vote
a less-liked candidate equal to or over a more-like one
(meaning that no one can ever conceivably gain by doing that),
then no method meets that criterion.

Say we ask that no one ever have strategic incentive to vote
a less-liked candidate equal to or over _their favorite_. Still
no can do. No method meets that criterion.

Then what about asking that no one ever have strategic incentive
to vote a less-liked candidate over one's favorite? That we can
do. Approval meets that criterion. No other method does.

But let's loosen it up a bit, and, instead of talking about
what incentive some individual voter could have, let's talk
about what a majority has to do to get something that it all
agrees on. A majority has the power to elect anyone they want to,
or to prevent the election of anyone they want to (At least unless
the method is Borda). So it's of interest what they have to do
in order to achieve such a result.

With almost all of the methods that have been discussed here
a majority can elect anyone they all like best, without insincere
strategy. So let's ask that a majority have a way to ensure that
someone won't win, without any member of that majority having
to vote a less-liked candidate over a more-liked one.

That criterion is met by Condorcet, Approval, and Bucklin.
It's not met by Instant Runoff (IRV or IRO), or by
Schulze(Margins), or by any other method that measures pairwise
defeats according to margins of defeat.

Let's take it farther and ask that a majority have a way to ensure
that someone won't win without any member of that majority having
to vote a less-liked candidate _equal to_ or over their favorite.
That criterion is met by the best Condorcet versions, including
Schulze, SSD, SD, DCD, & Tideman. The methods that won't drop
a defeat unless that defeat is the weakest defeat in some particular
cycle. It's also met by Bucklin.

All of the genuine Condorcet version, including the abovementioned
ones, and Plain Condorcet & Smith Condorcet meet the criterion
that asks that if a majority of all the voters vote the
"Condorcet winner" (candidate who'd pairwise-beat everyone if
all the voters sincerely ranked all the candidates--abbreviated CW)
over candidate B, then B can't win unless people vote unfelt
preferences. If that criterion is generalized so that there's no
CW, but B, who isn't a member of the top cycle, is beaten by
someone who is in the top cycle, and we don't want B to win
if no one votes an unfelt preference, then now only the best
Condorcet versions meet it, the versions that only drop a defeat
if it's the weakest in some cycle--including the 5 methods I
named in the previous paragraph.

The 2 criteria described in the previous paragraph are about
compromise strategy, because they say that, under certain plausible
conditions, that majority can keep B from winning without doing
anything other than ranking over him the CW or a member of
the top cycle.

These criteria will be more precisely stated in a subsequent
message, in which I show why the best Condorcet versions
meet the defensive strategy criteria, the majority-based
criteria that include the ones that I listed here.

To summarize, then, freedom from compromise strategy could be
defined in a number of ways, some of which are met by no method;
one met only by Approval; one met by a number of good methods
including Approval, Bucklin & Condorcet (but not IRV or
Schulze(Margins); and one that is met only by what I'll call
the cycle Condorcet methods and Bucklin; and one met by all
Condorcet versions; and one met only by the cycle Condorcet
versions.

Mike Ossipoff

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