From: John Conover <john@email.johncon.com>

Subject: Re: Bush/Kerry optimal wagers

Date: 8 Oct 2004 00:09:55 -0000

A note about the polls. The current polls show the Presidential race for the popular vote to be a dead heat between Bush and Kerry, (well, sort of, with a +/- 3 points margin of error,) at 48% of the popular vote, each. The +/- 3 points margin of error is a statistical estimate of the accuracy of the poll; its the estimated error created by sampling the population-which is used to generate the poll numbers. It means that the "real" value of the aggregate population lies between a 52% for one candidate and 46% for the other, for one standard deviation of the time, or about 68% of the time, (and it would be more than a 52% win and less than a 46% loss for 16% of the time for one candidate, and 16% of the time for the other, too.) See: http://www.johncon.com/ndustrix/utilities/tsstatest.txt for particulars. So, what does it mean for the election 25 days away? The statistical estimate is an uncertainty, and the uncertainty will increase by about sqrt (25) = 5% by election day, (relative to today,) meaning that the standard deviation on election day will be +/- 8%, or there is a 16% chance that Bush will win by more than 57% to Kerry's 41%, and likewise for Kerry. The chances of them being within +/- 1% on election day is one eighth of a standard deviation, or about 10%, (one eighth of a standard deviation is about 5%, but it can be for either candidate, or +/- 1%.) With probabilities that close, if either, or both, candidates feel losing the election will be an insurmountable loss, then its a Game-Theoretic "Mexican Standoff," which has an optimal solution to shoot first; meaning it will get ugly with last minute mud-slinging, (i.e., there is a 10% chance that moving the polls by as little as 1% in 25 days will win the election.) John BTW, the reason I mention a method for handling the uncertainty of the poll data is that with 49% Bush, 49% for Kerry, and 2% for the third party, with 5% undecided, (which sums up to more than 100%,) not to mention that 2% +/- 3% means that there is a 25% chance, (2 / 3 standard deviation,) that the third party could end up with a negative number of votes if the election were held today. All of which do not lend a lot of credibility to the data. John Conover writes: > > I swore after the 2K election that I would not do this again, but here > is the way you model the outcome of an election based on poll data; I > got beat up when I predicted-5 days before the election-that the 2K > Presidential Election would have an inconsistent popular and electoral > vote: > > http://www.johncon.com/john/correspondence/001103172714.28588.html > > See: > > http://www.johncon.com/john/correspondence/020508170137.5425.html#appendixIII > > for details of the methodology, (using the California Gubernatorial > recall as an example.) > > The recent polls say 46% of the voters, (in the popular vote,) would > vote for Bush, 43% for Kerry. There are 43 days left to the election, > and the polls move at about 1% per day, and are a zero-sum game, (in > the simple/lay sense-what Bush gets in a poll on one day, Kerry loses, > and vice verse.) > > What that means is that sqrt (43) = 6.5574385243% is the standard > deviation of the popular vote poll data on election day-43 days from > now-or there is a 14% chance that Bush's poll data will be above 46 + > 6.5574385243 = 52.6%, and a 14% chance of being below 46 - > 6.5574385243 = 39.4%. The numbers for Kerry on election day is a 14% > chance of being above 43 + 6.5574385243 = 49.6% and a 14% chance of > being below 43 - 6.5574385243 = 36.4. > > Since it is a zero-sum game, the winner of the popular vote will have > to have more than 43 + ((46 - 43) / 2 ) = 44.5%, or a 1.5 / > 6.5574385243 = 0.228747855 standard deviations. > > Referring to the CRC tables for the standard deviation, 0.228747855 > corresponds to about a 59% chance for Bush, and a 41% chance for > Kerry, to win-call it a 60/40 chance, 43 days from now. > > So, going long on Bush, one would optimally bet a fraction (2 * 0.6) - > 1 = 20% of one's capital, (be it political, money, whatever,) on Bush > winning. And, the expected returns would be 2%, per election, iterated > over elections with similar statistical characteristics, from: > > http://www.johncon.com/john/correspondence/020213233852.26478.html#equation1.20 > > which is a 10% ROI in 43 days-not too bad, (that's equivalent to about > 2X per year.) > > Of course, there is uncertainty in the poll numbers, and a strategy of > watching the numbers to do a stop-limit, (e.g., betting on Kerry later > to go short on the Bush wager,) may be advisable-just like in options, > and possibly set up a no risk wager, (working backward on implied > volatility.) > -- John Conover, john@email.johncon.com, http://www.johncon.com/

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