From: John Conover <john@email.johncon.com>
Subject: The California Recall Polls
Date: 12 Aug 2003 03:21:07 -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 poll data was from NBC News, August 11, 2003.)
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/