[EM] 3 candidates, few voters, 0-info

[MIKE OSSIPOFF]

This part of a message that I sent before my 2 other "few voters"
messages. None of them were initially posted, because I accidentally
somehow got removed from EM, due to letters from EM being returned
undelivered. Now I'm sending all 3 "few voters" messages. I'm
sending this one last, because, unlike the others, it's only
about situations where there are 3 voters. The "More candidates,
few voters, 0-info" message covers this message, and makes this
message unnecessary, but I want to send this one anyway, because
I tried unsuccessfully to send it before I wrote the others.


Since we voted for A, voting for B just means not voting A over B,
and so Pba is the probability that A's vote total is equal to B's
or one vote less, before we vote. Since we don't vote for C,
Pbc is the probability that B's vote total is equal to C's vote total
or one vote less, before you vote.

Since we know nothing about the other voters, is there any reason
to expect those 2 P to be different? From our zero info about the
other voters, aren't Pba & Pbc equal?

So Pbc(Ub-Uc) > Pba(Ua-Ub)--the requirement for voting for B,
can be replaced with Ub-Uc > Ua-Ub.

2Ub > Ua+Uc
Ub > (Ua+Uc)/2

It seems to me that the above-the-mean strategy is still valid
no matter how few voters there are, as long as there are only
3 candidates.

[Actually it's valid no matter how many candidates there are]

Mike Ossipoff


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