# [EM] Fluffy the Dog and group strategy

Bart Ingles bartman at netgate.net
Sun Sep 23 01:06:45 PDT 2001

```Sorry about the late replies, but my inbox got away from me again.

Craig Layton wrote:
>
> Let me leave fluffy aside.  I don't have my original example but I'll
> provide a simple one;
>
> 49.2% A>B>C (sincere utilities 100>30>0)
> 49.3% C>B>A (sincere utilities 100>30>0)
> 00.5% B>A>C (sincere utilities 100>10>0)
>
> When all of the voters have expressed their preferences honestly, and 99.5%
> would prefer a random dice throw between the three candidates over the
> actual result, then I think this indicates that there is a problem with the
> method.  The fact that this will happen in the best constrained preferential
> voting methods doesn't ameliorate the fact that it is still a significant
> problem.

This was my original reason for opposing Condorcet, but I now believe
the problem is to some extent self-healing.  If A and C each have a 50%
change of winning against each other, there is no way that sincerely
ranking B could improve the situation (and may worsen it).  In fact they
should both truncate whenever their utility for B is < 50.

Taking it farther, suppose the probabilities of a win in an A vs. C
contest is 70%/30%:

pw(AB)
--------------------------
70%     A>B>C  (100:69:0)
30%     C>B>A  (100:29:0)
N/A     B>A>C

In this case the A and C voters should still truncate, since sincerely
ranking B can only worsen the expected outcomes for each group.

In both cases, the best strategy for the B voters is to either rank
sincerely, or vote B=A>C (it makes no difference which, where the
outcome is concerned).

Note that these are exactly the same strategies that would be optimal
under approval voting.

Not sure if the opposite is true of a high-utility Condorcet candidate.
In the original case, if the 30 is changed to 70:

49.2% A>B>C (sincere utilities 100>70>0)
49.3% C>B>A (sincere utilities 100>70>0)
00.5% B>A>C (sincere utilities 100>10>0)

should the A and C voters rank B first along with their favorites?  It
looks as though it wouldn't harm the outcome (B would win either way),
but could improve it if it looked as though B might lose or become
involved in a cycle, possibly due to truncation or reversal strategy on
the part of some of the other voters.

Things get more complicated when you consider a possible range of
utilities within each faction:

05.0% A>B>C (sincere utilities 100>05>0)
44.2% A>B>C (sincere utilities 100>50>0)
49.3% C>B>A (sincere utilities 100>50>0)
00.5% B>A>C (sincere utilities 100>10>0)

If it appears that the election is on the edge, the sub-group of the ABC
voters who *really* don't like B may choose to "bury B" (i.e. vote
A>C>B) in order to cancel out some of the other votes.  This is
generally considered a dangerous strategy, but if you don't really have
much of a preference between B and C, what is there to lose?

So while I'm now less concerned about low-utility Condorcet winners than
I once was, I still prefer approval voting on the grounds that:

1)  I'm not convinced that the added complexity of ranked methods buys
any improvement.
2)  Ranking may mislead some voters into thinking that sincere voting is
the best strategy, and may make strategy unduly complicated for those
are sophisticated enough to try to use it.
3)  Ranking allows for more extreme strategies (i.e. order reversal)
which may give small factions undue power.

Bart

```