Maine

Maine 2nd changed from Tossup Kerry to Strongly Probable Kerry because of a new methodology for the individual Congressional districts. Changes reflected in today's Current Status below.

I've also decided to change "Leans" and "Leans Strongly" to "Probable" and "Very Probable" from now on. Since "Probable" and "Safe" are both adjectives, it'll be easier to form sentences this way.

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Methodology

I'm not bending over backwards to pull mathematical punches here, although there shouldn't be anything beyond an intro stat course. For clarification, post a comment. Although I'm a math student, I've never studied any statistics, so if you have suggestions (and I have a couple places where I could use them), post a comment.

The first step is to assemble statistics on each state. When a poll has numbers available both with and without Nader, I only use the numbers with Nader if Nader is on the ballot in the state in question when I record the poll data in my spreadsheet. I'll use Missouri as an example, with currently available polling data and the present date of May 31st. There have been two polls in Missouri, a March 23rd (69 days ago) Rasmussen poll and a May 23rd (8 days ago) poll. (For the dates, I use the ending dates of the polls.) The Rasmussen poll counted 245 for Bush and 210 for Kerry; the Zogby poll counted roughly 255.273121 for Kerry and 237.425635 for Bush. (Most pollsters don't publish exact counts, so I make a numerical estimate from the published percentages and sample size; Zogby doesn't publish sample sizes, so I estimate sample size based on margin of error.)

Polls get stale as time passes, so I weight all the polls. The weight is 1 for a poll that ended today, 1/2 for a poll that ended four weeks ago, 1/4 for a poll that ended eight weeks ago, and so on. The Rasmussen poll is 69 days old, so it has a weight of (1/2)^(69/28) = 0.185749, and the Zogby poll is 8 days old, so it has a weight of (1/2)^(8/28) = when 0.820335. Hence, the weighted Rasmussen counts are 39.00735 for Kerry and 45.50858 for Bush, and the weight Zogby counts are 209.4096 for Kerry and 194.7686 for Bush. The one-month half-life for polling data is ad hoc, and I'm interested in figuring a more principled decay function.

Adding these weighted counts, we get that Kerry has 248.4169 total weighted "votes" and Bush has 240.2772. Then the Kerry mean is 248.4169/(248.4169+240.2772) = 0.508328 of the vote, and the standard deviation is the square root of 0.508328*(1-0.508328)/(248.4169+240.2772), which is 0.022615. Since Kerry's mean is 0.008328/0.022615 = .3682512 standard deviations above 0.5, a lookup in a standard normal distribution table shows that Kerry has a 64.3659% chance of winning Missouri's 11 electoral votes.

This is already enough information to make my "Confidence" map (Kerry's 64.3659% chance of winning translates into a 29% saturation shade of blue since (64.2659-50)*2 is about 29) and my "Percentages" map (50.8328% of the Kerry/Bush vote translates into an 8% saturation shade of blue).

Now for the national statistics. The expected number of Kerry electoral votes is easy to compute: I just take the sum (number of electoral votes)*(chances of Kerry winning) over all the states (more precisely, the sum over all the electoral-vote-granting regions, including DC and the congressional districts of Maine and Nebraska).

The probability of Kerry winning is more complicated: It entails the calculation of the probability of Kerry getting precisely n electoral votes for every n from 0 to 538. For each state I form a polynomial as follows: For Missouri in the example above, I write (1-0.643659*(1-x¹¹)), since Missouri's 11 votes have a .643659 chance of going to Kerry. Then I multiply all the states' (electoral-vote-granting regions') polynomials together into a generating polynomial in which the xⁿ coefficient is the probability that Kerry will get precisely n votes. Therefore, the probability that Kerry will win is just the sum of the x²⁷⁰ through x⁵³⁸ coefficients.

With these coefficients it's easy to calculate the median number of Kerry electors, although this is only interesting if I'm planning to offer a spread on the election.

There are a few details I haven't covered. 1) my method for states that lack significant polling data; 2) my method for calling the Congressional district votes of Maine and Nebraska; 3) my method for predicting the popular vote.

First, states with insignificant or no polling data. Consider Rhode Island, which hasn't been polled since February and currently has 15.07188 weighted "votes" for Kerry and 8.815625 for Bush. This gives a total of 23.8875 weighted votes and a massive standard deviation of around 10%, so I pad the data with 2000 election returns. Gore got 0.656491 of the Rhode Island vote in 2000, so I give 0.656491*(100-23.8875) extra weighted votes to Kerry and (1-0.656491)*(100-23.8875) extra to Bush. This gives a total of 65.03906 Kerry votes and 34.96094 Bush votes, and I recalculate Rhode Island's odds on this basis. For a state with no polls at all, this method essentially uses a 100-vote sample with proportions based on 2000. The number 100 is ad hoc, and I'm interested in finding a more principled number.

I have no polling data on Maine's and Nebraska's individual Congressional districts. Since I don't have polling data at all for Nebraska from the 2004 cycle, I calculate Nebraska's Congressional districts based on their 2000 returns as if they were a poll-less state. Consider Maine's 1st district which voted 176293-148618 for Gore in 2000. Maine overall voted 319951-286616 for Gore, and now has an expected popular vote of 331088.1 to 275478.9, since Kerry has 0.545839 of the weighted "votes," 331088.1 = 0.545839*(319951+286616), and 275478.9 = (1-0.545839)*(319951+286616). This means that 11137.1 votes statewide have shifted to Kerry, of which 5965.7 = 11137.1*(176293+148618)/(319951+286616) are in the 1st district. Thus, I use 182258.7 = 176293+5965.7 votes for Kerry and 170327.3 = 148618-5965.7 votes for Bush, scale that down to 100 total votes so that Kerry has 51.69197 and Bush 48.30803, and make my predictions. Same for the 2nd district. This method ensures that my expected popular votes for the congressional districts fit with my expected popular votes for the whole state.

I estimate each state's popular vote by multiplying that state's total Bush/Gore vote from 2000 (no Nader, Buchanan, or other votes) by Kerry's expected percentage in that state. Then I add all the states' popular votes to get the national popular vote. I care about the Electoral College and I don't care about the popular vote, so I make no attempt to adjust for population shifts, to count 2000 Nader votes, to factor in current undecideds, or (in short) to be the least bit accurate.

The main advantage of my methodology is that by combining polls I am able to squeeze statistics out of a potpourri of conflicting, small-scale, and sometimes stale polls. By giving polls a half-life of one month, I recognize that old polls can convey significant information but can be superseded by new data.

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Popular Vote, Very Funny

I just made a popular vote prediction based on my data. Results: Kerry 49.54% and Bush 50.46% among Kerry and Bush voters, despite Kerry's strong lead in the Electoral College.

I remember from before the 2000 election that the Bush camp had a plan to delegitimize Gore if Gore had won the electoral vote but lost the popular vote, as most commentators thought was likelier than vice versa. That same idea this time around would might be too much chutzpah even for the Bushies.

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2000

Remember 2000? Here are the official results of Bush/Gore with the 2004/2008 electoral apportionment. The Bush states have gained seven votes, although not all of those are in states generally considered safe for Bush.

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Basic Map

A US map, with each state having area proportional to its electoral votes. I don't like how West Virginia or Wyoming turned out, and the Deep South looks boring. I've divided up Maine and Nebraska, because those states have only two at-large electors, with the remainder elected by Congressional district.

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Current Standings

Kerry has an 89.13% chance of winning and an expected 296.9 electoral votes. Kerry could win without any of his tossup states, while Bush would need at least 36 electoral votes from Kerry's side.

Cartogram showing, for each electoral vote, the chances that the leading candidate will win:

Cartogram showing, for each electoral vote, the expected percentage (of Bush/Kerry votes only) for the leading candidate.

Extremely Safe (99%+ chance of winning)

Kerry 146: California, Connecticut, District of Columbia, Massachusetts, Minnesota, New York, Rhode Island, Vermont.

Bush 107: Alabama, Alaska, Idaho, Indiana, Kentucky, Louisiana, Montana, Nebraska (at large, 1st, and 3rd), North Dakota, Oklahoma, South Dakota, Texas, Utah, Wyoming.

Very Safe (90-99%)

Kerry 95: Delaware, Hawaii, Illinois, Maryland, Michigan, New Hampshire, New Jersey, Pennsylvania, Washington, Wisconsin.

Bush 56: Arizona, Kansas, Mississippi, North Carolina, Nebraska (2nd), South Carolina, Tennessee.

Safe (80-90%)

Kerry 15: Maine (at large and 1st), New Mexico, Oregon.

Bush 35: Arkansas, Colorado, Georgia, West Virginia.

Lean Strongly (70-80%)

Kerry 8: Iowa, Maine (2nd).

Bush 33: Ohio, Virginia.

Lean (60-70%)

Kerry 11: Missouri.

Bush 0.

Tossup (55-60%)

Kerry 32: Florida, Nevada.

Bush 0.

Close Tossup (50-55%)

Kerry 0.

Bush 0.

Total

Kerry 307.

Bush 231.

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Introduction

The purpose of this "blog" is to assess and track the race to 270 electoral votes in this year's presidential contest. (In fact, Bush only needs a 269-269 tie become president again---see Amendment XII of the Constitution for details---but "race to 270" is somehow catchier than "race to 270 if you're Kerry or probably just 269 if you're Bush.") Although I strongly support Senator Kerry and I loath President Bush, I am trying to be completely unbiased with my predictions. Of course, I reserve the right to criticize Bush (or Kerry) whenever I feel like it.

I am not in the business of predicting the Election Day results several weeks or months in advance; there are enough pundits out there who get paid plenty to do that poorly. Rather, I attempt to answer questions of the form, "If the election were held today..." On Election Day (Tuesday, November 2nd, 2004), I will predict the results. So bear in mind that if I say "There is a 68% chance that Kerry will win," I really mean "If the election were held today, Kerry would have a 68% chance of winning," and if I say "Minnesota is a safe state for Kerry," I really mean "If the election were held today, Kerry would have at least an 80% chance of winning Minnesota.

In August, I will resume my academic duties. After that, I may only update as frequently as once a week, although I may update more often as the election approaches.

I will post during the next week about the methodology I've settled on. For now, let me say that I rely on head-to-head polls at the state level with the 2000 election results to fill in the blanks for states with scanty or non-existent polling data (none of which are close-fought).

Who am I? My name is Benjamin Schak. I'm originally from Minneapolis but have lived in Pennsylvania for several years, where I am now a graduate student in mathematics at the University of Pennsylvania. My fascination with cartograms began when I found the State of the World Atlas at the Franklin Library as a small child. My fascination with the Electoral College began when I read the relevant section of Philip Straffin's Game Theory in 9th grade. I spend most of my spare time watching movies, at the gym, or listening to Twins baseball.

2008 updates. This time the Democrat will only need 269 and the Republican will need 270. I'm an Obama supporter. I'm also going to make predictions each week both for "If the election were today" and for the actual election. I'm also going to revise the methodology write-up. I've improved the methodology in some way, understood it better, and have some ideas to make it clearer.

I've dropped out of grad school and moved to Connecticut. I'd also like to emphasize that this site is the result of my own personal work, studies, and opinions, and is in no way endorsed or approved by any past or present employer of mine.

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