Strong FBC

[Adam Tarr]

Rob LeGrand wrote

>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.

Well, my standard example seems to work here, if we allow a little 
order-reversal.  Once again, the sincere preferences are

49 Bush>Gore
12 Gore>Bush
12 Gore>Nader
27 Nader>Gore

Now, with all voters using the "A" strategy from your previous post, the 
voting reliably settles on

49 Bush
24 Gore
27 Nader, Gore

And Gore wins, 51 to 49 (Bush) to 27 (Nader).  But what if 17 Bush voters 
decide to lock in with (Bush, Nader) in stead?  If everyone else sticks to 
the "A" strategy, this insincere ranking sends the equilibrium to

17 Bush, Nader
33 Bush
12 Gore, Bush
39 Gore, Nader

And now Bush wins, 61 to 56 (Nader) to 51 (Gore).  Basically, the insincere 
ranking convinces the 12 Gore>Bush>Nader voters that they need to support 
Bush to prevent Nader from winning.

I'll grant that it is difficult to spoof the system like this.  If too many 
Bush voters insincerely rank, they will appear to hand the election to 
Nader, and they will quickly lose their resolve to vote insincerely.  In 
this case, I've shown just the right number of Bush voters playing the 
game, such that Nader slots evenly between Gore and Bush.

Getting back to the SVM, though... I'm beginning to believe it's 
possible.  The simulation aspect of things makes the election harder to 
corrupt.  The thing is that you can't "lock in" your vote to the SVM.  All 
you can do is give it a set of rankings.  If the 16 insincere voters gave 
the SVM a ranking of Bush>Nader>Gore, then the SVM would have them vote for 
only Bush, and Gore ends up emerging as the winner.  But if they force the 
issue by reversing all the way to Nader>Bush, then they will end up giving 
the election to Nader.

It may be that by limiting the voter to a certain set of strategies, we can 
prevent order-reversal and the like from being effective.  In this case, a 
sort of simulated repeated approval balloting (SRAB) could be a viable 
election method, even for public elections.

Rob, have you proven that universal use of the "A" strategy always settles 
on the Condorcet winner if one exists?  If so, this could be a great 
election method.  The thornier proof (but also very important) is to show 
that there is a unique equilibrium in all non-tied situations.  If this is 
the case, then I think we should seriously examine SRAB as a public 
election method.

-Adam

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