From: John Conover <john@email.johncon.com>
Subject: Re: The California Recall Polls
Date: 18 Aug 2003 21:35:55 -0000
Note: this analysis originally appeared in the NdustriX and NtropiX mailing lists-and generated substantial interest; more so than I anticipated. There is a new formal version in Appendix III of Quantitative Analysis of Non-Linear High Entropy Economic Systems Addendum which is one of the mathematical and numerical methods series at the NdustriX site, (and analyzes many more things that you might be interested in, too.) You might want to skip over to Appendix III since it is better written and has graphical content; or you can read the original, below.
The polls of today indicate that Schwarzenneger and Davis are about
tied, with 25% of the vote, each. In the last 6 days, each moved about
5%, (Bustamante is slightly ahead, at the expense of Schwarzenneger.)
What's the chances of that happening?
The deviation of such a happening is 5 / 2 * sqrt (6) = 1.0. In other
words, there is a 68% chance that such a movement in 6 days would be
less than 5%, and 32%, more, (if we consider it a two person zero sum
game; if not-considering the dark-horses-its the single sided tail of
the distribution, at 84% chance.)
What's the chances of Bustamante's good fortune continuing longer?
erf (1 / sqrt (7)) which is about 1 / sqrt (7), or about 38%,
(ignoring the chances of the dark-horses.)
There are 51 calendar days to the vote, (pending several legal
decisions, of course,) and Bustamante has won the poll lottery of the
first 6 days of the campaign. (Schwarzenneger lost 13% of a chance of
being governor, Bustamante won 13%; now either has a 50/50 chance,
ignoring the dark horses.)
John
John Conover writes:
>
> Several Polls came out today. 59% of Californians are for bouncing
> Gray Davis, and if that sticks, Schwarzenneger has 31% of the vote,
> Bustamante 18%, with all of the other 150, or so, contenders well
> below 10%, each. There are 57 calendar days to the vote.
>
> Polls are very fractal, and if a percentage point that is gained by
> one opponent is at the expense of another, (e.g., a zero sum game,)
> then the deviation of poll movements will be about 2% per
> day. Fractals are a random process, so the deviation of the polls at
> the end of 57 days would be 0.02 * sqrt (57) = 15%.
>
> So, there is a 16% chance, (one single sided deviation,) that Davis
> can move his fractal poll from 59% to 59 - 15 = 44% for the recall by
> October 7. (And, 9 / 15 = 0.6 deviations, which is a probability of
> 27% that he can move it to a 50/50, and defeat the recall.)
>
> Schwarzenneger's chance of winning against Bustamante is 31 / (18 +
> 31) = 63%, and Bustamante's winning against Schwarzenneger is 18 / (18
> + 31) = 37%, (the Gambler's Ultimate Ruin is a good way to determine
> such things; what it says is that each will be required to gamble on
> strategies, but the success of the strategies are uncertain.) The next
> candidate has 6% of the vote, so each of the other candidates will
> have about 6 / 100 = 6% chance of passing Schwarzenneger and
> Bustamante, (and all the others,) winning the Gubernatorial race.
>
> However, most of the remaining 150 candidates are not serious
> contenders-about 6 actually have a chance. And that means that the
> chances of any one of the 6 winning the race is 1 - (1 - 0.06)^6 =
> 31%.
>
> So:
>
> Chances of Davis defeating the recall: 27%
>
> Chances of Schwarzenneger beating Bustamante: 63%
>
> Chances of Bustamante beating Schwarzenneger: 37%
>
> Chances of any dark horse beating all the other dark horses and
> both Schwarzenneger and Bustamante: 31%
>
> John
>
> BTW, note there are no long calls. The best odds are on
> Schwarzenneger, but for Schwarzenneger to win requires two things to
> happen: Davis to be recalled, and defeating Bustamante, or a chance of
> (1 - 0.27) * 0.63 = 46%, (assuming all the others have virtually no
> chance of winning.)
>
--
John Conover, john@email.johncon.com, http://www.johncon.com/