[EM] Usual probability definition not for elections?

[Richard Moore]

You can't apply the Monte Carlo method to a one-time event, that's true.

BUT...Since the probabilities we've been talking about are calculated from
information
information prior to the event (polls before an election), you could apply the
reverse
technique. I don't see any practical value in it; it's really just a thought
experiment:

If you knew the result of the election in advance (not just the winner, but the
actual distribution of the votes);

And if you took several polls of randomly sampled voters (and all those polled
actually
did vote in the election);

Then from the actual results, you could predict the probability that any single
poll
(of a given sample size) will give a certain outcome.

The many polls should have a distribution of outcomes that is a Monte Carlo
approximation of the predicted results.

A forward calculation of probabilities has to be based on the statistical
sampling
error of the polls. This is not the same as the (unknowable) real probability of
an
outcome in an election, but it is the best approximation based on the limited
knowledge available. The backward technique calculates, from an actual result of
a
whole population, what the distribution of outcomes would be for the polls,
(which
is yet another set of probabilities, since the big election doesn't have the
sampling
error that the smaller polls have). The only way to get that real probability
that
I mentioned is the impossible Monte Carlo method of repeating the election many
times, since we don't have any way of modeling all the variables that can affect

the outcome.

As I pointed out earlier (seems like ages ago), the poll itself could influence
the
outcome. So there seems to be something analogous to the Heisenberg
uncertainty principle at work. That's why I like ZI voting, especially in the
case
of something like approval (though use of ZI in other, more strategy-intensive
methods could be disastrous for the voter who uses it). The worst that can
happen with ZI in approval voting is that you end up helping one of your middle
candidates win, which is certainly better than helping your least favorite to
win.

 -- Richard

MIKE OSSIPOFF wrote:

> I've just posted 2 not-valid definitions of probability. That
> doesn't mean that I understand it less well than other members of
> this list, however. I'm familiar with the usual frequency definition of
> probability, which goes like this:
>
> If a trial is repeated many times, and the fraction of the trials resulting
> in a certain outcome
> can be made as close as desired to some number P, by doing enough trials,
> then P is the probability of that outcome of that trial.
>
> [end of definition]
>
> The trouble is that I don't know how that can mean anything for
> elections. An election can't be repeated like a roulette trial
> or coin flip. Literally, if November's election were repeated
> many times, under the same conditions, we'd get the same outcome
> each time.
>
> That's why I (unsuccessfully) tried to write probability definitions
> that would mean something for elections. If I try again today,
> this should be my last try at it. Anything further that I post
> about it will be copied from some reference source.
>
> One thing that occurred to me was to say:
>
> Say T is a series of trials, events with uncertain ourcome. They
> needn't have anything in common other than that. Say you bet on
> some of those trials.
>
> The trials are numbered so that Ti is the ith trial. For each trial
> Ti that you bet on, you bet with a payoff ratio of Ri. P is a series of
> numbers, each between 0 & 1. Those numbers in that series P are
> numbered so that Pi is the ith number in that series.
>
> The Pi aren't the probabilities of the outcomes that you bet for
> in the Ti if the following isn't true:
>
> If each Ri is more than (1/Pi)-1, then you can make your gain as positively
> large as you want by betting on a sufficient number of
> trials. If each Ri is less than (1/Pi)-1, then you can make your loss
> as great as you want to by betting on a sufficient number of trials.
>
> That's just half of a definition, though, and I don't know if it's
> useful. Maybe it can be made into a complete definition.
>
> Maybe the easiest way to find a complete definition would be to
> base it more closely on expectation-maximization, so that the
> definition is just a sort of re-statement of the expectation-maximization
> goal, said in such a way that it defines
> probability in terms of the other numbers.
>
> I'm doing this because someone said that I don't know what probability is.
> As I said, I'm familiar with the usual frequency definition, but
> I don't think it's adequate for elections, and so that means that
> if I don't have a definition more useful for elections, then I
> _don't_ know what probability means for elections. That's why I
> felt that I should try to write my own definitions. But I may have
> to give up & look it up.
>
> Say we just use Weber's method for maximizing expectation in Approval.
>
> Say we do many Approval elections, numbered from 1 to k.
> The Pijk used by Weber's method in those elections are the probabilities
> that the candidates pairs (i,j) will be  the 2 frontrunners in election k if
> & only if it's certain that, if we do enough Approval elections,
> a person who used certain Pijk for his strategy determinations can be made
> to get a higher overall total for his utilities for the winnners
> than another person who has the same utilities but who used different
> Pijk.
>
> [end of definition]
>
> I won't post about this again unless I'm _sure_ that I have
> a definition that is valid, or if I quote one that I found from
> some reference source.
>
> Mike Ossipoff
>
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