[EM] for a series of unrepeatable events

[MIKE OSSIPOFF]

I estimate that there's a high probability that I'd find this
definion for the probability of an unrepeatable event somewhere if I
looked it up:

The probability of an outcome of an event is a number that is a
property of that outcome such that:

For a sereies of events Ei, if each has some possible outcome Oi,
such that for all of those Oi that number in the previous paragraph is
the same, then by having that series include sufficiently many events,
we can make the number of the Oi that occur during all those events,
divided by the number of events, as close as possible to that number
referred to in the previous paragraph.

If we're only talking about a single isolated event, then the probability
of a certain outcome for that event is the probability that it would
have if that event were one of the Ei and that outcome were that event's
Oi, in the series of events & outcomes referred to in the previous
paragraph.

[end of definition]

This is the natural extension of the often-encountered frequency
definition of probability.

p.s. In my Approval strategy probability definition I should have
clarified that if _all_ of the Pijk were different from the Pijk that
the voter used, then his total outcome utility can be reduced as much
as desired, by doing sufficiently many Approval elections. Iff that's
so, then the Pijk are the probability, at a time before election k,
that i & j will be the frontrunners in election k.

I also realize now that the usefulness of this definition is limited
because, for one thing, for some Pij estimating methods, it's necessary
to consider other probabilities.

Mike Ossipoff


_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com