Strong FBC

[Rob LeGrand]

Adam wrote:
> It's not absolutely deterministic, although I admit it is close.  Alex came
> up with this example where Approval voting can settle in a rut:
>
> 25 A>B>C
> 49 B>A>C
> 26 C>A>B
>
> Now suppose the initial approval votes are
>
> 25 AB
> 49 B
> 26 C
>
> So B wins, 25-74-26, even though A is the Condorcet winner.  No voter has a
> clear incentive to change their vote; the vote combination is a Nash
> equilibrium, when factions are considered players.  Now this rut is very
> tenuous, and one could certainly imagine the voters breaking out of
> it.  But they will not certainly break out of it.

That depends on the strategies the proxy approval "voters" use at each
iteration.  My CRAB simulations currently offer a voter four strategies:

Strategy L: Approve all candidates I prefer to my least favorite of the current
CRAB first-placer and second-placer.

Strategy T: Approve all candidates I like at least as much as my favorite of
the current CRAB first-placer and second-placer.

Strategy M: Approve all candidates with a higher utility than the average of
the current CRAB first-placer and second-placer.

Strategy A: Approve all candidates I prefer to the current CRAB first-placer;
also approve the first-placer if I prefer him to the second-placer.

If the winning CRAB quota is calculated deterministically and the strategies
the voters use are deterministic (like the above), then CRAB is completely
deterministic.  As for getting stuck in ruts, that's a valid concern.  Of the
four strategies listed above, only strategy A always homes in on the Condorcet
winner when one exists and all voters use the same strategy.  Strategy M does
fairly well; it finds the CW about 96% of the time, but strategy T (by far the
one most often recommended on this list) finds the CW only about 77% of the
time.  That's a lot of ruts.  (Strategy L does even worse.)

In Adam's above rut example, strategies A and L would get out of the rut and
settle on

25 A
49 B
26 CA

giving the victory to A, the Condorcet winner.  Strategy M might get out of the
rut, depending on the voters' reported utilities, but strategy T would stay
stuck in the rut.

Of course, the voters don't all have to use the same strategy.  Presumably,
each would choose the strategy thought to be most likely to lead to the best
result for the individual voter.  I'm currently working on a simluation to find
how well each of the above strategies performs for its users in the long run.

> Has anyone tried to simulate a repeated approval balloting election where 
> some voters use insincere strategy - that is, they approve a candidate who 
> they like less than a candidate they do not approve?  Obviously, there is 
> no incentive to do so in a normal approval vote, but in a repeated approval 
> vote, such disinfestation may help you by convincing other voters to 
> approve your favorite as a compromise.

The problem is that the approval "voters" in CRAB don't know when the balloting
will stop, so insincere strategy almost always backfires in the end, even if
it's effective at first.  I've tried some tricky strategies in my simulations,
but they never help the voters using them in the long run.  If anyone has
specific strategies for me to try, I'm taking suggestions.

--
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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