ACC strategy-free?

[MIKE OSSIPOFF]

Adam wrote:

The reason I also like the other equilibrium, however, is that it is more
free of concern about what the other camp does. This makes it more
stable. If the Gore>Bush voters are told to bullet vote Gore, but the Bush
voters announce that they plan to order-reverse anyway, then you get into a
game of strategic brinksmanship. Both camps would prefer each other to
Nader, but if they protect against Nader (by not truncating in the Gore
camp, or by not reversing in the Bush camp) they run the risk that the
other side will use the more aggressive strategy and win the election.

Looking at this as a two-player game sheds some light on the
situation. The players are the 49% Bush>Gore>Nader voters, and the 12%
Gore>Bush>Nader voters. Each has two strategies. The Bush camp's
strategies are Bush>Nader>Gore and Bush>Gore>Nader ("reverse" and "no
reverse"), while the Gore camp's strategies are Gore>Bush=Nader and
Gore>Bush>Nader ("truncate" and "no truncate"). The outcomes of the game 
are:

Truncate | No Truncate
|---------+-------------|
| | |
| Nader | Bush | Reverse
| | |
|---------+-------------|------------
| | |
| Gore | Gore | No Reverse
| | |
-------------------------

There are two Nash Equilibria here: (no-reverse, truncate) and (reverse, no
truncate). One gives the election to Gore, and the other to Bush. Hence,
the game of brinkmanship to see which camp will be able to bully the other
camp into letting them win to stay away from Nader.

That's not all the information we can garner from this table,
however. Game theorists refer to a strategy as a "dominated strategy" if,
for every response the other player gives, one strategy is as good or
better than another. In this case, truncation is a dominated strategy for
the Gore camp. If the Bush camp reverses, they do better by not
truncating, and if the Bush camp does not reverse, then they do just as
well by not truncating as by truncating. This suggests that the Bush camp
has an advantage over the Gore camp in the game of brinkmanship.

I fully recognize that this does not mean the Bush camp will succeed in
convincing the Gore camp to give in and rank Bush second. The leaders of
the Bush camp seem to have a much more difficult job, trying to convince
their supporters to uprank Nader, even though this runs the risk of handing
Nader the election. The leaders of the Gore camp just have to convince
their supporters to bullet vote, which seems to me a much easier job.

Furthermore, it seems that the Bush voters would be even more averse to
Nader than the Gore voters, which puts them at a disadvantage in the
brinkmanship/bullying contest. This won't necessarily be true in a more
general case, though.

I reply:

That does put the Gore voters in a stronger position: If both players
strategize, and Nader wins, that isn't as bad for the Gore voters
as for the Bush voters, and the Bush voters know that. We've all
seen on tv the strategist who says "Hey, I've got less to lose!"

Adam continued:

At any rate, back to my original point. This is why I like the other
equilibrium, where the Nader voters announce that they plan to equal-rank
Gore and Nader. This effectively nullifies all offensive strategy on the
part of the Bush camp. Of course, it requires insincere equal
first-ranking, so it has problems of its own. But it has none of the
stability issues of the other equilibrium.

I reply:

That's true, the equal-ranking is more self-contained, not depending
on influencing others, and it isn't dominated.

Both defenses have their advantages, and I'm not saying that one
is 100% better. But, as a Nader voter who doesn't value the
Democrats significantly higher than the Republicans in most elections,
I'd often hold out, and insist on voting N>D, and announce to the Democrats
that I won't strategize for them.

Another brinksmanship game is between the Nader voters & the
Gore voters, where they could both bluff that they won't strategize
to protect Gore. The difference between Gore & Bush is what
both sides stand to lose if Bush wins.

The Democrats are asking the
Nader voters to do more than the Nader voters are asking them to do.
Also, they'd be saying to the Nader voters, "You have to protect our
candidate", which sounds more difficult to say than "You have to
protect your candidate".

Two brinksmanship games, then, between Gore & Bush voters, and between
Gore & Nader voters, if the Nader voters do that bluff.

One other thing, about the truncation being dominated, dominated
deterrent strategies are common in the legal system and in the
animal kingdom. They must work, or they wouldn't continue in use.
I'm not saying that their disadvantage can be fully brushed-off
, though.

Also, since Gore is the CW, everyone knows that he's a more rightful
winner. That gives extra credibility to the Gore voters' threat,
because they're threatening to take a risk to protect the rightful
winner, whereas the Bush voters would be threatening to take a risk
to steal the election from the rightful winner.

All in all, I'm not saying that truncation is the better defensive
strategy, because there are too many  different considerations
pointing different ways.

I suggest that the Gore & Nader voters should have meetings to
decide who should strategize to protect Gore.

Mike Ossipoff


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