[EM] Buying Votes

[Raph Frank]

On Sat, Oct 25, 2008 at 8:02 PM, Greg Nisbet <gregory.nisbet at gmail.com> wrote:
> Ok now the actual criticism. I know that FAWRB is nondeterministic.
> Here is why that is bad.
>
> Factions (both unwilling to compromise):
>
> A 55%
> B 45%
>
> you view A as gaining a "55% chance of victory".
>
> This reasoning is flawed. Instead of viewing A as getting .55 victory
> units, think of it as a random choice between two possible worlds:
>
> A-world and B-world
>
> A-world is 10% more likely to occur, however they share remarkable similarities.
>
> In both worlds >=45% of the people had no say whatsoever.

The trick with his method is that neither A-world or B-world is likely
to actually occur.  It creates an incentive to find a compromise,
called say, AB-world.

If all voters vote reasonably, then the result is a high probability
that the AB option will be picked.

The utlities might be
..... A-AB-B
55: 100-70-0
45: 0-70-100

In effect, each A supporter agrees to switch his probability to AB in
exchange for a B supporter switching to AB.

So, the initial probabilities would be

A: 55%
AB: 0%
B: 45%

Expected utility
55: 55
45: 45
Total: 100

However, after the negotiation stage, the results might be

A: 10%
AB: 90%
B: 0%

Expected utility

55: 10% of 100 and 90% of 70 = 73
45: 90% of 70 = 63
Total: 136

I don't 100% remember the method (and it could do with a web
description :p ), but that is what it is attempting to do.

The idea is not that it is random.  The idea is that it says "OK, if
you can't all agree on a compromise, then we will pick a winner at
random".

The threat that a random winner will be picked is what allows the
negotiation.  If a majority can just impose its will, then there is no
point in compromising.