Re: Mathematical utility expectation maximization in Approval

[Richard Moore]

I'll skip the first 90% of Mike's message due to its condescending tone, and go
straight for the last paragraph.

MIKE OSSIPOFF wrote:

I'm not asking for more symbolic argument. I'm asking for an
example consisting of actual probabilities, whatever ones that you
consider relevant, like the probability that A & B will be frontrunners, the
probability that if there's a 2-way tie it will
be betweent them, and the probability that there will be a 2-way tie.
I ask that in your example all the probabilities that you mention
be explicitly numerically stated.

Mike Ossipoff

Granted. For a three-way race,

probability that:      AB     AC     BC     Sum
_________________________________________________
both are front
runners               0.5    0.3    0.2    1.0
_________________________________________________
a tie occurs
involving             0.1    0.03   0.01   0.14
both
_________________________________________________
if a tie occurs,
both are front        0.71   0.21   0.07   1.00
runners

In the first row after the header, the probabilites for each pair of
candidates of being the two front-runners are given; they must add up
to one (I'm ignoring the remote possiblity of a three-way tie).

The next row gives the probability of a tie involving each pair. The
sum of these probabilities is the probability of any tie occurring.

The last row is the probability, given a tie, that it is between the
specified pair. These numbers are derived by dividing the probability
of a tie between the two candidates (from the second row) by
the probability of any tie (0.14). The sum in the third row is one
(ignoring the rounding error after the division).

Note that the numbers on the first row do not equal those in the
last row.

 -- Richard