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[Phys-L] Re: Voting Strategy



At 08:23 AM 11/2/2005, you wrote:
I've been asked a voting question that I've thought about before, but
long enough ago that I don't remember the complete rationale. I am
trying to remember if I even remember the correct conclusion. I don't
want anyone to spend a lot of time on this because I am not willing to
spend a lot of time on it myself because I am behind in my grading and
other responsibilities. I am simply asking if anyone can corroborate
what I think I remember.

Next week we will vote on some school board members. There are three
seats open, and there are four candidates. Two candidates are
incumbents and two are new runners. Some of us strongly support one of
the new runners, and the other is okay. Some of us strongly want to
oust one of the incumbents, but the other is okay.

How do you vote?

I remember I have heard people say that if your primary goal is to get
the bad incumbent out you should vote for everybody but the bad
incumbent, that is, vote for the really good candidate plus the two okay
candidates. On the other hand, if your primary goal is to get the
really good candidate elected, you should only cast one vote, that is,
just vote for the one person you really want elected.

I remember hashing this out once, but I don't remember the answer. Is
this strategy actually valid?

Michael D. Edmiston, Ph.D.

Without spending much time on the question, I proceed
in this concrete way.
If a school has 1000 students, there may be 1000 potential electors.
Of the potential electors, I will suppose that one tenth are not
laissez-faire and so there may be 100 electors.

Case 1) Randomly divided vote.
cand a 25 (favored)
cand b 25
cand c 25
cand d 25 (disfavored)

Mike votes for three, who are thereby elected.

Case 2) Electorate in Mike's favor
cand a 40
cand b 30
cand c 20
cand d 10

Mike's voting has no effect.

Case 3) Electorate slightly contrary to Mike

cand a 24
cand b 25
cand c 25
cand d 26

In this case, if he votes
a only, a may but d will prevail
if he votes,a & b , then a may, but d will prevail
if he votes a,b & c, then a will lose

It is in this region that Mike's voting strategy has effect.
One soon concludes that there are more cases of
interest, and a simple simulation would collect statistics
of use in deciding.

Brian Whatcott Altus OK Eureka!
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