From: stecher@atlas.socsci.umn.edu (Jack Stecher)
Subject: Re: Why should I vote for Marrou?
Summary: A calculation
Organization: Department of Economics, Univ of Minn
Date: Wed, 7 Oct 1992 19:23:37 GMT

A while ago, Steve Gabrilowitz wrote:
>You have pretty much echoed the general consensus of those responding to my
>question, but you have added one interesting little monkey wrench into the
>machinery: I do not feel that the major candidates are of equal value, not in the
>slightest.  Were it not such a close contest between the two candidates that
>have a chance, it would be much easier to decide to vote for the long term future
>instead of the short term.

The advice you've received does not assume that the majors are of equal value.
For reasons I will spare the net, I believe that Bush would be less bad than
Clinton, perhaps dramatically so.  Nevertheless, I will vote for Marrou, based
on the following analysis:

Let P be the probability of a Bush win if my vote goes to the LP, and let P+p
be the probability of a Bush win if Bush gets my vote.  (For any Democrats out
there, I'll warn that more math's ahead, so press <space> now.)

Let Q be the probability that Marrou gets enough votes to cross important
threshold X.  My idea is to specify threshold X as that which Marrou's chances
of crossing are increased with probability p if I vote Libertarian.  Thus,
if Q is his chance of threshold X without my vote, then Q+p is his chance with
my vote.

Note that Q will not, in general, equal P, as my single vote will most likely
be a larger fraction of Marrou's total vote than of Bush's.  Typically, then,
Q will be a probability smaller than P.  Assume that if Marrou doesn't achieve
threshold X, he lands at threshold W, which is something less desirable.  The
interpretation of threshold W will be, roughly speaking, Marrou's expected
impact conditional upon his failing to achieve threshold X, though this means
we must really think of X representing Marrou's expected impact conditional
upon his obtaining at least X.  But let's leave the complications aside, and
assume that there are two scenarios, thresholds X and W.

Let r be my rate of discount for the future, sort of a personal interest rate.
I get paid in discrete intervals, so I'll set up the problem in discrete time.
Assume I receive all my utility for a given time period at the beginning of the
period.  My utility function u depends on my consumption, among other things,
which in turn will be affected by the impact of the LP and the result of the
election more generally.  Holding all those things that don't depend on the
vote totals for Bush, Clinton, Marrou, etc., constant, my expected utility
is the sum from t=0 through t=infinity of my discounted expected future
utility at each time period:
	1/(1+r)^t [u(1,X;t)(P+p)Q + u(0,X;t)(1-P-p)Q + u(1,W;t)(P+p)(1-Q) +
		u(0,W;t)(1-P-p)(1-Q)],
where the first argument of u is 1 if Bush wins and 0 if Bush loses, and where
the second argument is X if Marrou reaches threshold X and W otherwise.  The
above is my expected utility of voting for Bush.  If instead I vote for Marrou,
my expected utility is the sum from t=0 through infinity of
	1/(1+r)^t [u(1,X;t)(Q+p)P + u(0,X;t)(Q+p)(1-P) + u(1,W;t)(1-Q-p)P +
		u(0,W;t)(1-Q-p)(1-P)].

Clearly, I should vote for Marrou.

Jack Stecher
stecher@atlas.socsci.umn.edu
Newsgroups: alt.politics.libertarian