From: John Conover <john@email.johncon.com>
Subject: Re: CNET.com - News - E-Business - Latest dot-com bomb: TheMan.com
Date: 10 Nov 2000 22:58:35 -0000
BTW, for the record, I stand corrected. My statement:
"Its interesting because the popular and electoral votes may
differ for the first time in history, (a very small chance, but
not insignificant.) ..."
is not correct-the electoral and popular votes for President were not
the same on 3, (or 4, depending on which historian is telling the
story,) previous occasions. The last was 1888, (but other historians
are claiming W. Wilson's election was the last time.)
However, it is kind of interesting the way things turned out. Gore,
(et al, or whoever,) did sling mud, G. W. Bush did not, (at least not
as much and as bad,) and it looks like a reasonably high probability
that Gore will take the popular vote-coming from behind-and loose the
electorate, and the nomination for Presidency, to G. W. Bush, by
playing a nearly optimal game, under the circumstances.
John
BTW, you can arrive at the same conclusion from a game-theoretic
perspective, too. You will find the solution, (simplex tableu,)
identical to the well known non-iterated, zero-sum, prisoner's dilemma
game, where the optimal strategy is always to play a defection
strategy, (a la linear algebra/simplex.)
If the game is iterated, the resultant time series will have fractal
characteristics, and the last game will have a go-for-broke
optimization, (sling all the mud that can be slung.)
The trouble is that power is a zero-sum game, (winner takes all,)
which makes the defection strategy for the the only, or last,
iteration of the game the optimal solution.
If the game was positive-sum, (i.e., all candidates got some power for
running,) then a mixed mode solution would be best, i.e., sling mud
sometimes, but not always, and do so randomly, (at least where one's
opponents wouldn't be able to figure out when one is going to do it
next,) would be the optimal solution. (That's the theory of the
parliamentarian system-which has other zero-sum optimal defection
solutions.)
The game-theoretic solutions are interesting because it can be shown,
re: Kenneth Arrow/Impossibility Theorem, that there is no perfect
political system where cooperation is optimal. It is impossible to
remove the zero-sum nature of politics in a social system of more than
3 people. All one can hope to do is shuffle around the zero-sum
problem via structural implementation-but it can not be eliminated.
Slinging mud, (and other assorted political defection strategies,) are
completely rational-and have been around since the beginning of
civilization, (see the Gilgamesh, circa 3K BC, the Summarian God of
Wisdom's describing the gift to Holy Ianna of Uruk.)
John Conover writes:
>
> And what should Gore do with a 22% chance of winning? What is his
> optimal strategy?
>
> He should use a Greedy algorithm, (which has characteristics of what
> the mathematicians call a "Devils Stair Case",) over the next four
> days, which means he bets half of 47 - 43 = 6 / 2, or 3% of his
> tracking poll, every day, until he is in the lead.
>
> This means Gore should risk PO'ing 3% of his constituents for a chance
> at gaining 3% of Bush's constituents, every day until the end of the
> election, or until he is ahead of Bush, (i.e., sling some mud.)
>
> And what would Gore's probability of winning be?
>
> let r = (1 - p) / p = (1 - (0.43 / 3)) / (0.43 / 3) = 5.98
>
> P = (r^0.43 - 1) / (r^0.47 - 1) = 0.89
>
> remarkably, almost 90%!
>
> That is, unless G. W. Bush does the same thing, in which case it moves
> Gore's chances back to a 22%.
>
> Bottom line, mud slinging is not only the way of politics-its optimal.
>
> And, in the current state of affairs, Gore has absolutely nothing to
> lose by slinging mud, (with only a 22% of winning if he doesn't.)
>
> John
>
> BTW, tsinvest does not use a Greedy algorithm, or Devils Stair Case.
> If p < 0.5, it simply refuses to invest in the stock-and if no stocks
> have p > 0.5, it will withdraw from the market, (although you can
> override this if you are foolish-its the -D option.)
>
> John Conover writes:
> > That's about a 4 in 5 chance of winning. But it can be wrong 1 chance
> > in 5, too. What this means is that you play this game many times, you
> > will win 4 out of 5 times.
> >
> > So, you wouldn't want to bet your nest egg on it, (you stand a 20%
> > chance of losing everything on the first game, if you do, and you
> > can't play any longer.) But you have to bet something, otherwise you
> > can't make anything, (another of mathematics most profound insights.)
> >
> > The optimum lies in between. And the magic optimum is when F = 2P - 1,
> > where P is the probability of a win, (0.78 on Bush in this case,) and
> > F is the fraction of your nest egg to wager, (or about 56% in this
> > case.)
> >
> > Based only on the popular vote, of course-and I don't know any bookies
> > that taking bets based only on the popular vote.
> >
> > John
> >
> > BTW, the -d option to tsinvest controls how the program does this
> > methodology; the -d1 is what was outlined here.
> >
> > John Conover writes:
> > >
> > > So, Bush has a 0.84 * 0.93 chance of winning, or about 78%,
> > > (considering only the popular vote,) based on the accuracy of the
> > > tracking polls, and the ability of Gore to move them.
> > >
--
John Conover, john@email.johncon.com, http://www.johncon.com/