Electoral College Meta-Analysis (election.princeton.edu)

This page is available online at http://synapse.princeton.edu/~sam/pollcalc.html

Median state poll outcome, decided voters: Kerry 252 EV, Bush 286 EV (±39 EV MoE) (probability map)

Popular Meta-Margin among decided voters (explanation): Bush leads Kerry by 0.8%

State poll median with speculative undecided assignment: Kerry 283 EV, Bush 255 EV (probability map)

Electoral prediction with turnout: Kerry 311 EV, Bush 227 EV (probability map)

[Election Night brochure (PDF)] [Overview of calculation]

Real electoral result: Kerry 252 EV, Bush 286 EV. (outcome map) (comparison)

Commentary (Recent comments) (Florida analysis) (public thread)

Thursday, December 2, 11:30AM: Several interesting and good articles about exit polls. Here is a piece in the Washington Post about demystification of exit polls. Also, in this week's New Yorker is a great article by Louis Menand on a meeting that took place at Stanford at which pollsters discussed the interpretation of this year's results. Essentially, they think the values talk is a misinterpretation of a bad question. The article argues that it was essentially terrorism (i.e. 9/11) that swung it for Bush. The article is print only - go get it. The December 6 issue.

Thursday, December 2, 11:30AM: Election results can be displayed in many ways. The cartograms used on this site are a way of displaying electoral votes accurately. To see displays done by population or on a county-by-county basis, see these interesting maps.

Sunday, November 28, 6:00AM: I am moving my post-election comments on Florida here. This is partly to maintain order and partly because I am starting to wonder whether there is a story here. After chewing over the Berkeley group's analysis and corresponding with some of you, I have thought of reasons why there is no real county-level anomaly. The essential problem is that the largest e-voting counties have large populations and have no counterpart for comparison. I believe that this problem is insurmountable by any statistical analysis, no matter how sophisticated.

Tuesday, November 16, 9:00PM: Some notes on future improvements to the calculation. David Kline points out that to calculate the single-state probabilities, for small (<30) numbers of polls, a t-distribution is more appropriate than a normal distribution. This distribution has longer tails and will give less certainty in the estimates. Going in the converse direction, in retrospect some states were more certain than the one-week snapshot indicated, and outlier polls tended to introduce occasional inaccuracies. A more sophisticated averaging procedure is needed, one that uses more polls but gives more weight to recent ones.

Tuesday, November 16, 11:00AM: Footage of my appearance on Fox News: [2 MB version] [30 MB] [200 MB]

Monday, November 8, 10:00PM: This is really interesting: a rundown of exit poll breakdowns by gender, education, issue, and so on. It seems to refute ideas that have been going around about the importance of religion and rural voters. The upshot seems to be that the biggest positive for Bush was terrorism (as opposed to Iraq, which was a big negative). Religion didn't matter any more than in 2000, nor did rural voters. Terror, terror, terror. Combined with the Mellman article cited below I surmise that Bush's job approval rating was boosted by perceptions about his ability to counter terrorism.

Saturday, November 6, 9:00AM: Here is a pre-election article by Kerry consultant Mark Mellman that predicted Bush's popular vote share to within 0.1%. Going by the article, the factors that went into the calculation included job approval, the economy, war, and right track/wrong track sentiment. Putting aside the talk about values (based on a single poorly-worded exit poll question), what about the relatively simple hypothesis that the economy's not that bad combined with loyalty to a wartime president?

Despite all this, the true margin of victory was about 150,000 votes in Ohio, and even smaller margins in Wisconsin and New Hampshire. As I said during the campaign, Electoral College mechanisms (essentially because of increased clustering of Bush supporters) gave Kerry an approximately 2% advantage compared with the popular vote. Thus the difference between the Meta-margin above and the popular vote margin.

Friday, November 5, 6:00PM: I continue to be deluged by email on the subject of the anomalies in Florida voting in small counties. As I said below, these data sort fairly well by the rural/urban divide. In a graph by Jeff Chambers that there may be some small remaining anomaly. However, this could be ballot spoilage. Here's an analysis demonstrating the size of the anomaly. I don't think this is going anywhere. The most constructive thing at this point is to redirect energies to voting reforms, such as those advocated by the Open Voting Consortium. This has the advantage of serving all Americans.

In the coming days I will revisit polling data to see what the turning points were in the election, as measured through the Electoral College. I suspect that some of the shifts in my data that I could not explain may be explained by campaign moves that were not obvious at the level of national media. The electoral vote calculation is low-noise and captures swings well, so this is a perfect use for it.

Friday, November 5, 10:30AM: Commentary on the electoral divide by the American Prospect's Harold Meyerson.

Thursday, November 4, 9:00PM: A number of you have mailed in a plausible explanation for the seemingly anomalous results in optical-scan voting counties in Florida. Essentially, the apparent disproportionate voting for Bush occurred in less populated counties. These counties, being non-urban and having fewer resources, are still using optical-scan ballots. Therefore three variables are correlated here: smaller populations, voting technology, and Democratic crossover for Bush. As a result there is a correlation between the last two variables, but the real variable of interest is population. This creates an ambiguity of interpretation, and is an example of the dictum that correlation is not causation.

The reason population is of interest is that it is a stand-in for rural vs. urban dwellers, as Andy Royle and others point out. Royle made a graph of population size and Bush victory margin, graphed by county. This graph suggests to me that in rural counties, many people are registered Democrats but cross over to vote for Republicans. This could be because Democratic party allegiance is a holdover from times when rural voters were more likely to be Democrats. Many new registrants in these counties are Republicans, which supports the idea.

This speaks to the idea going around that heartland and rural voters are turning to Republicans on "values" issues. In my view this conflicts with a natural link between them and the stated policy goals of the Democratic Party. It suggests a disconnect between stated Democratic values and how the party is perceived. For an interesting exposition I recommend What's The Matter With Kansas? by Thomas Frank, which addresses the dominance of the GOP in the heartland.

Thursday, November 4, 12:05AM: The meta-analysis has helped me stay rational in this election cycle, but some thought needs to go into future action. The election was close, but in a binary event 0.51 rounds up to 1. Anyway, here are some cogent post-election thoughts from Josh Marshall.

Wednesday, November 3, 7:45PM: A few items of business. First, note that without my optimistic assumptions, I nailed the Electoral College tally. This, even in the face of single-state probabilities that give a different map and EV total. Poll margins are also quite close: see these validations of the method (still under modification but viewable). Now there's a testament to meta-analysis (and an indictment of the mindless mainstream horserace coverage of polls this season). Note, however, the large margin of error on my decided-voter estimate. A one-percent swing in Ohio or Wisconsin would have changed the total EV count - in the case of Ohio, to great effect.

This site. I am considering what to do. It is highly disorganized because I started off HTML-coding by hand. If readership continues, I may transfer to regular blogging software. However, this requires time or help. Another question is what topic(s) to cover. Let's first see if traffic continues. Your letters of support are heartening. I can't reply to all, but please continue to write. If your comments are for general consumption, here is a public thread.

Exit polls. Much of my mail today concerns exit polls, with calls for analysis to check for widespread fraud. Think about the lessons you have learned here. A more plausible possibility is that exit polls themselves are biased, for instance by the identity of the questioner or the temperament of the respondent.See my analysis of exit polls.

The incumbent rule. After some thought, I realize that we simply don't know what factors drove the result yesterday. The problem is that all the factors sum to give final voting, and are therefore hard to distinguish. In the New Republic is a suggestion that turnout was either symmetric or went against my assumption.

Fraud in Florida? This is an interesting question, and my evidence suggests that further investigation is warranted. Of all the battleground states, Florida was one of the most surprising in terms of deviating from the outcome expected from polls (and to a lesser extent, exit polls). The deviation favored Bush. It's too bad about this year's exit poll problems, because they would have provided an independent test. My analysis of this is in the validation of 2004 results.

Wednesday, November 3, 3:15PM: Dear readers, I am getting lots of mail on my brilliant prediction. Thanks to all of you on both sides of the aisle. For many opponents of Bush, this election has been a wrenching event, not unlike a death in the family. This election was a highly significant political event that we will be feeling for decades. I will post some of your mail later. For now, I post a thought-provoking note from someone opposed to my views, along with my reply, here. It has the tonic effect of returning this site to its original purpose, hardcore quantitative analysis. With that, I must now attend to my day job...

Wednesday, November 3, 11:30AM: To summarize points so far this morning: So far, the electoral outcome matches pre-election polling data very closely, with the possible exception of Florida. Therefore the electoral count looks a lot like the decided-voters median listed above. However, my final predictions were wrong. It appears that my add-on assumption about undecideds (the rule that they break against the incumbent) was wrong; this may have been because of the war, as suggested by the Mystery Pollster. My turnout assumption was also wrong. Exit polls do match my projection, which is surprising to me. This could be because those data are somehow non-representative, for instance because of gender bias.

Specific comparisons: victory margins were predicted well by polls. Out of 23 battlegrounds, the direction of the outcome was predicted in 22. The exception was Wisconsin, where the polling margin was 0.4% for Bush and the actual margin was about 0.4% for Kerry. Quantitatively, 12 victory margins were within one standard error and 17 were within the 95% confidence interval. Not perfect, but not bad.

Wednesday, November 3, 10:30AM: In Ohio, many provisional ballots are left to be counted. In the meantime, here is some general analysis. Overall, pre-election polls, exit polls and actual voting are mostly correlated. An exception occurs in Florida, suggesting that something unusual might have happened there, either in voting or in exit and opinion polling. The effect is probably smaller than Bush's margin.

Voting margins track pre-election polls - with exceptions. Voting margins were more favorable to Bush by 0.9 ± 0.6% (median ± SEM; SD, 3.1%) than pre-election polls. This is very near to no difference at all. All discrepancies greater than 5 percentage points (AR, HI, NC, WV) occurred in states with few recent polls. The next largest discrepancy was in Florida, 3.6% towards Bush. Since Florida had so many polls, this is 4 SEM away from zero. Otherwise the match is quite good. Overall, 12 out of 23 pre-election estimates were within 1 SEM of the voting outcome, less than the expected 16 but not bad. I conclude that in most cases this year, five or more likely-voter polls taken in the week before the election gave an estimate that strongly correlated with final voting.

Voting margins and exit polls differ systematically. Exit polls were more favorable to Kerry by 3.0 ± 1.5% (median ± SD) than real voting. This is tentative since I do not have the most complete exit polling data. Currently, in FL I have an exit poll margin of Kerry +1 and a real voting margin of Bush +5%; the discrepancy, 6 points, is again somewhat extreme. This is consistent with the discrepancy noted above. In OH I have an exit poll margin of Kerry +1 and a real voting margin of Bush +2; the discrepancy, 3 points, is right in the middle of the range. I don't know why exit polls would differ systematically, though one obvious possibility is the gender gap in respondents.

Graphs and further analysis will follow shortly.

Wednesday, November 3, 8:00AM: Good morning. First, the basic points: the polling data were fine, but my follow-up assumptions about net undecideds and turnout were wrong. The statistical approach is fine, and indeed still the best way to look at the data. The final result will be very near, and perhaps exactly equal to the decided-voters calculation. Finally, now that votes are mostly in, we have real results to compare with pre-election polls. I will be doing that in the coming days. This is the point at which something real can finally be learned.

Wednesday, November 3, 2:15AM: I was very wrong about FL and about the overall offset. The outcome is somewhere between the decideds-only and the with-undecideds medians. However, for months I have been saying that it was about Ohio, and it is. The margin there seems headed for about 1%, without absentee or provisional ballots. Another squeaker - though things are not entirely over yet.

Wednesday, November 3, 12:45AM: Possibly K259, B254 (assuming MN, IA, HI, MI). Then Ohio (20EV) - returns here. May come to Cuyahoga County (includes Cleveland) and absentees. Also NV (5EV), but at this point that doesn't matter.

Wednesday, November 3, 12:15AM: Consistent with the gender imbalance, exit polls seem to be biased toward Kerry relative to final totals. Not crunching numbers yet but will try later.

Tuesday, November 2, 10:00PM: Zogby's projections, which resemble mine, are here. Here is a plot of afternoon exit polls against my last poll margins. As you can see, most of the data points fall around Kerry +3%, the assumption that went into my final projection. However, the gender breakdown is 59F-41M, suggesting a biased sample, and thus indicating a problem with my assumption. However, as you all know, much depends on FL and OH. The partial returns for FL (77% of precincts reporting) indicate Bush - does anyone know if these include early voting, absentee and overseas? Overseas and absentee may not be counted until Thursday. Early votes - probably counted.

Tuesday, November 2, 5:45PM: There are so many of these exit polls - just like the campaign season all over again. Time for meta-analysis. I am plotting all that I can find on my graph. Nearly all of them are above the no-bias line. Looking at all of them at once, the median bias seems to be about +3%. This suggests to me that if overall, these polls reflect total voting, OH and FL will end up for Kerry, with margins of 2% by night's end. (Famous last words...)

Tuesday, November 2, 3:00PM: Early exit polls on Drudge (above the title). If you plot them on my brochure graph, their median is around +5% bias. This may regress as Republicans get to the polls, but I think this is a telling sign. Not sure if I will be blogging the returns - just a heads-up for you. I wonder if my prediction was too cautious! That's what I get for paying too much attention to my email.

Tuesday, November 2, 2:30PM: Running list of brochure errata and edits here. All are fixed in the current version, downloadable here (PDF). Apologies for these small errors. Page 1: where it says "215 EV" it should say "230 EV." Page 4: NM margin is Bush +2.7 ± 1.7%, not +3.1 ± 1.5%. I now have a Kerry win probability >50%. Page 4: My predictions are added in parentheses. Page 6: The bias calculator is updated to extend to a larger range to the right. Old one still OK - but you may need this.

Tuesday, November 2, 11:30AM: Poll closing times are listed here. The earliest bellwether is NH (poll average Kerry +2.9 ± 1.1%, n=7). Kerry by 5-7% would be consistent with my final assumptions. Next is WV. Let's see what happens.

Tuesday, November 2, 10:45AM: I have added two pages to the brochure - a graph to help you calculate for yourself the net bias, and an electoral map.

Political psychologist Manuel M. Frank writes in with a model indicating that I have underestimated the turnout bias. Looking at his work, my original figure of +2.5% agrees with his calculations based on Annenberg interest-level surveys. His work can be read here; he also has additional comments.

Monday, November 1, 11:00PM: The last prediction is in. I have set the turnout figure to a lower bound of 1.5%, for a net of +3.0%. This is a value for which the median and map are readily reconcilable, which may reduce my email load. Readers, thanks for the dialogue. The box and final summary are updated. Other entries are bumped down. And here is your Election Night brochure (PDF).

Finally, a note to all of you. As this site has grown since July, you have seen me try new assumptions on the fly. Most have been improvements, but at times I do something unusual, at which time I hear from many of you. This feedback, although invisible to most of you, has been extremely valuable. In a sense, this site has many open-source qualities. In the event that the prediction is accurate, it was the most amazing of phenomena, an Internet-based collaboration. Thanks for your ideas, your criticisms, your praise, your strange email, and most of all your readership (nearly 80,000 visitors today - site meter).

The last polls for the 2004 calculation come from Granite State (NH), Ohio Poll (OH), Opinion Dynamics (R) (FL, IA, OH, WI), Rasmussen (FL, MI, MN, OH, OR, PA, VA, WA), Strategic Vision (R) (FL, NJ, OH, PA), Survey USA (AR, MO, NC, PA), and Zogby (AR, MO, NH, OR, TN, WA).

Monday, November 1, 6:30PM: I've been getting criticisms of my original estimates of the undecided and turnout adjustments. Why don't we postpone further discussion until tomorrow, when we know the true outcome. Anyway, I have given you enough information to let you make your own predictions.

Lower and upper bounds can be set using Gallup's last poll. This shows Kerry +2 among RVs and Bush +2 among LVs. The difference betweem these sets an upper bound of +4%. To set a lower bound: where data are available, new registrations give Democrats an approximately 0.5% edge in swing states; these new registrants are first-time voters who may fail LV screens. Also, the election will be high-turnout, suggesting that at least some of the 4% gap in Gallup will be filled. For example, a turnout increase from 50% to 62% would lead to +1.0%. Using this as a very rough estimate (and using it to subsume other factors as well), these two factors sum to +1.5%, a lower bound.

Finally: new registrants and overseas voters skew anti-Bush by a large margin, and 527s are pouring massive amounts of money into GOTV activities. I do not know how large these effects will be, except that they are likely to be towards Kerry. The suggested cell phone problem in polling is probably irrelevant (more on this later). I also do not know to what extent the 4 million evangelicals or Rove's 72-hour operation will materialize for Bush. Known unknowns...

Monday, November 1, 12:00PM noon (updated 11:00PM): Here are my final calculations and predictions. Extended discussion and supporting links can be found in the November 1, 8:00AM update. I have a brochure for your use to follow the returns on Tuesday night and test my assumptions (and yours). Here it is.

The map below shows Kerry and Bush's win probabilities, individually by state. The closer a state is to a tossup, the closer it will be to white. The map uses undecided and turnout assumptions; maps that do not make these assumptions can be seen by clicking in the box above. Note that unlike the map, the median projection takes compound events into account. Thus the map EV total is often not the same as the median EV total. An explanation is here. Click on the map for an interactive pop-up (thanks to Drew Thaler). For difficult browsers here is a static map and Ravi's simpler calculator.

Overview: The basic calculation derives from polls only. Using statistical methods of meta-analysis, I use polls to calculate a starting point, referred to as "decided voters only." This result is an uncorrected snapshot of where the polls stand. In addition to this, I estimate the effects of last-minute undecided/uncommitted voter decisions and differential turnout. My estimates are supported by evidence, but are by no means certain. Results based on uncertain assumptions are clearly labeled. To let you try your own assumptions, a table of medians with different bias values is given here.

The basic decided voter result. The median of Kerry 252 EV, Bush 286 EV among decided voters was calculated from 168 polls taken in 23 battleground states, and stepping probabilistically through all possible outcomes. Most of these polls were completed between October 25 and November 1. The EV estimate carries a large amount of uncertainty: the 95% confidence interval is ±39 EV. Thus, if only decided voters counted, the nominal Kerry win probability would be 20%, or 4-1 in favor of Bush.

Rank order of states: States currently in play in the 20-80% probability range, indicating a near-tie, are in bold. Turnout and how the undecideds break will shift which states are at a near-tie, but the order, from most Democratic to most Republican, should stay about the same.

With undecided voters assigned. Undecided voters typically end up voting against the incumbent. In previous presidential races this has given a 2.5 ± 2.0% advantage to the challenger. I currently estimate that 3.0% of voters are undecided. A 3-1 Kerry-Bush split gives a +1.5% net advantage to Kerry. This leads to a median EV estimate: counting undecided voters, Kerry 283 EV, Bush 255 EV, and a nominal Kerry win probability of 73%, or 3-1 in Kerry's favor.

Turnout estimates and other corrections. The principal factor not measured by polls is turnout. Pollsters ask respondents questions to determine if they are likely to vote. However, this cannot capture efforts by voter turnout organizations. In addition, newly registered voters have no track record. Finally, telephone polls may not accurately sample the voting population. I estimate that these factors sum to an advantage in battleground states of 2 to 3% for Kerry. As I am sure you are all aware, this number cannot be known with certainty. With that caveat in mind, I use +1.5% as my turnout figure (see discussion at top of page). Combined with the +1.5% undecided allocation this makes a +3.0% bias as plugged into the MATLAB script. This leads to my final prediction. Predicted electoral outcome (11/1/2004 11:00pm EST): Kerry 311 EV, Bush 227 EV, nominal Kerry win probability 98%.

Note that all of these probabilites are conditional on the turnout and undecided voter assumptions being correct. The true probability is obtained by multiplying by a measure that is a function of whether my assumptions are accurate. The chance that I am wrong makes the true probability substantially lower than 100%! As Niels Bohr (and Yogi Berra) said, "Prediction is hard, especially of the future." Just for the record, my gut estimate of the likelihood of a Kerry win is about 6-1 in favor.

Another way to look at it (suggested by Abe Fisher) is to turn the undecided+turnout question around: in order to get the Kerry win probability above 90%, the sum of these two factors must be 2.2%. Note that to get to exact even odds, the needed amount is the Meta-Margin, listed today as 0.8%.

Back to predictions: Based on the probabilites below, of the 23 states modeled, Kerry's expectation value of states is approximately 14-15 of them, for a total of 23-24 states plus the District of Columbia.

The popular vote. To estimate the popular vote I use two approaches: (a) one based on presidential preference polls and (b) one based on Bush's job approval numbers. In 16 national polls the medians (± SEM) are Bush 48.0 ± 0.4%, Kerry 47.0 ± 0.4%. Assuming 2.0% for Nader/other, the fraction of undeclared voters ("undecideds") is 3.0%. Assuming Cook's incumbent rule that undecideds split 3:1 for the challenger (2.25% and 0.75%), this gives a net of 1.5 ± 1.2% to Kerry. This predicts a national popular vote (not corrected for turnout) of Kerry 49.3 ± 0.9%, Bush 48.7 ± 0.9%, Nader/other 2%. The second measure uses job approval ratings. In ten polls taken since mid-October the median ± SEM is 49.0 ± 0.9%. Based on historical trends, this places an upper bound on Bush's share of the popular vote. Thus, both approaches indicate that Bush's popular vote share will be 49% or less.

I use the turnout factor to make a final estimate. Predicted popular outcome: Kerry 50.0%, Bush 48.0%, Nader/other 2%. National polls come from davidwissing.com, RealClearPolitics, and yougov.com. Job approval numbers come from pollingreport.com.

An electoral tie. A 269-269 EV tie would throw the election into the House and Senate, which would most likely lead to the re-election of Bush and Cheney. However, this would be an emotionally divisive event. The probability of an electoral tie is: Decided voters only, 4.1% (24-to-1 against). With undecideds, 3.1% (31-to-1 against). Final prediction with turnout included, 0.4% (273-to-1 against).

The power of your vote (the jerseyvotes calculation). Previously I have discussed where you are most effective in your door-to-door activism. My unit is the jerseyvote, which is the power of a New Jersey voter to influence the national election. Among decided voters only, the current value of a single vote in the top states is (measured in jerseyvotes): Hawaii 11,900, Iowa 7,500, Wisconsin 7,400, Florida 7,200, Nevada 7,100, New Mexico 5,800, Ohio 5,600. Counting undecideds, the top states still appear and Arkansas joins the list. Other values of relevance are (decided voters) New Hampshire 2,200 and Pennsylvania 2,500. As you can see, a jerseyvote's value to American politics is what the Reichsmark's was to the Weimar German economy.

Key states. These statistics summarize polls completed between October 25 and 31.

In Florida (14 polls), Bush leads in 8 polls, Kerry leads in 4 polls, and two polls are tied. Bush's average (± SEM) margin is 1.4 ± 0.9% in polls. I predict a Kerry victory by 2%. Polls close at 6:00-8:00PM Eastern time.

In Ohio (17 polls), Bush leads in 12 polls, Kerry leads in 4 polls, and one poll is tied. Bush's average (± SEM) margin is 1.1 ± 0.7% in polls. I predict a Kerry victory by 2%. Polls close at 7:30PM Eastern time.

In Pennsylvania (14 polls), Kerry leads by 2.1 ± 0.7% in polls. I predict a Kerry victory by 5%. Polls close at 8:00PM Eastern time. General poll closing times are diagrammed here.

Thursday, November 4, 9:30AM: Jim G sends in his first look at county-level analysis of Florida and suggests that nothing is amiss. However, a full listing of results by voting method raises questions not about electronic voting, but about optical scan voting. I am open to any explanation for these numbers - resolution soon, I hope.

Monday, November 1, 8:45PM: For all of you writing me about the cell phone idea, I do not think this objection has merit. I have read the recent Zogby poll. I will write about this after the election.

Monday, November 1, 7:15PM: Upon reflection the last bit involves double-counting of turnout. Perhaps this factor should be less than 2.5%. This will be reflected when I incorporate the last polls.

Monday, November 1, 4:45PM: Gambling is a vice. But putting that aside, looking at TradeSports I think that a good cautious bet is to take equal positions against "Bush to win the election" (i.e. SELL, a bet that he loses) and against "Bush to win 250 or more EV" (i.e. SELL, a bet that he gets <250 EV). One way to do this quickly is to click on 'Live Help' at their site and telling the support representative you want to do a manual credit card charge. Other sites to try are here and here.

Monday, November 1, 9:00AM: Today I was interviewed live by Wall Street Journal This Morning. The program was carried on over 80 stations across the U.S. and on the Sirius and XM satellite networks. Listen to it here (MP3, 1.3 MB).

Saturday, October 30, 5:30PM: That was a fascinating experience. So much was left out but I did get to say my piece. After we cut, the FOX guy asked me what I really thought would happen. I said I thought Kerry would get over 300 electoral votes. Of course this happened afterwards. Typical television - very compressed. Real analysis soon - sorry about lack of substance on this post.

Thursday, October 28, 8:15PM: More letters.

Thursday, October 28, 3:00PM: Edward Witten writes, "On mydd.com, I read yesterday a rumor that a NYT poll of Florida showing Kerry ahead by +9 percent was buried as being implausible. I don't know if the rumor is true, and if it is I am sure the poll was flawed, as Kerry is surely not leading Florida by that amount. But to me it illustrates the fragility of trying to predict the election from the available state polls. Including or excluding a single, undoubtedly flawed, poll showing a +9 percent lead in Florida for Kerry (or Bush) would probably have a significant impact on your overall assessment of the outcome of the election." To some extent he has a point. If such a poll exists then the decided-voters moves K up to K 271 B 267, win probability 51%. The use of median rather than mean circumvents this problem a bit, which I will do soon. In any event, the confidence interval is +/-36 EV. Therefore neither result is statistically significant. Any way you slice it, the election is a toss-up and will depend on turnout and undecideds.

Thursday, October 28, 9:45AM: Since posting a few letters here I have received many more. Here are some selected from yesterday's mail, October 27. Of special interest is one from Jim G. from New Hampshire, an undecided voter. He is articulate and thoughtful, and though we don't agree on a few things I strongly recommend his letter to all of you.

Evidently I spoke too soon regarding Bush giving up on Ohio. His travel plans include three stops there until Election Day. He is also pushing in Michigan, where Kerry has recently slipped a bit.

Wednesday, October 27, 5:30PM: A brief note on the vagaries of opinion polling. When we read polls we often make the implicit assumption that people report what is really going on inside their heads. However, this is a subjective report. The famous example in these closing days is the "undecided voter." But are these people undecided in the sense that we mean colloquially? Are they one monolithic category of person?

It's been pointed out that many undecided voters are unfavorable about the incumbent, and usually break for the challenger. This phenomenon may simply reflect the fact that some people are unable or unwilling to state a set preference. To cite a homely example, you may find yourself unable to articulate what you want for dinner, but you can react immediately to what you don't want.

Recently Scott Rasmussen reported data that he says supports the notion that late-deciding voters prefer Bush. The survey was done from 136 late-deciding voters, far too few to reach statistical significance. This is a message poll aimed at driving the discussion in his preferred direction. Also, the survey assumes that the voters who decided during the survey period are similar in characteristics to those who wait until the last minute, possibly until they are standing in the voting booth. This is untested.

A parting thought on undecided voters: we are not going to resolve this by further argument! The best we can do is come up with a way to measure what they do, and wait until after the election. I will try to provide this as part of my final Election Night briefing document.

Other examples of respondent inaccuracy are the party-ID question, which can depend on when in the survey it is asked (especially if asked after the presidential preference!) and the question of who people voted for in the last election (on average, people show a tendency to think that they voted for the winner even if they did not).

Finally, once again: the probability map is not the same as the median calculation. This is why they do not match. If you were thinking about writing me to point this out, read this first.

Wednesday, October 27, 12:30PM: My regular email address works once again. Send your correspondence there.

Charles Cullen writes asking today's probability of a 269-269 electoral tie. Using decided voters only it's 3.9% - a lot! With the undecideds assumption it's 0.4%. In this scenario the newly elected House and Senate would determine the president and vice-president, leading to Bush-Cheney (if the Senate remains Republican) or Bush-Edwards (if the Senate goes Democratic).

Wednesday, October 27, 7:00AM: One of the pleasures of running a popular Web site is the correspondence. Click here for some selected letters from the last few days of various types - illuminating, entertaining, and unintentionally hilarious.

Wednesday, October 27, 5:30AM: Hawaii has been added because of two recent polls showing possible leads for Bush. This seems very unlikely. In any event, what is really needed is a third poll.

With that, let's think about a favorite subject of mine: why individual polls seem surprising or contradictory. I can think of three reasons:

1. Reporters often don't understand statistics. A poll showing Bush up by 5% and another showing Kerry up by 1% are in fact consistent with one another because of random sampling error. For more on this read yesterday's entry by Mystery Pollster (Mark Blumenthal). A better way to get a good answer is to examine many polls at once. For the record, Charles Forelle at the WSJ is a very notable exception - in his article about this Web site and others, he captured the subject perfectly!

2. Man bites dog. When a poll's finding sounds interesting, it gets more attention than a boring result. Therefore reports of outliers tend to grab headlines, creating apparent discrepancies.

3. Competition among organizations. News organizations usually rely on their own data alone. If they do this, they cannot achieve the increased accuracy that comes from comparing multiple polls. Indeed, little incentive exists to improve accuracy, since low accuracy leads to more frequent news stories, and therefore more readers or viewers.

Tuesday, October 26, 11:00AM: Statistically based analysis of the Electoral College is featured in today's Wall Street Journal. Welcome to new readers!

The overall raw polling outcome (decided voters only) is still a statistical tie. This is true even with more than 100 polls used in today's calculation. Bush has tiny leads among decided voters in Florida and Ohio, indicating that the outcome in these key states will be determined by undecided voters and turnout.

Finally, a note on national polls. In 8 national polls (two-way choice) the median result is Bush 49, Kerry 47. Assuming that methods are similar, the fact that this margin is larger than the Meta-Margin above supports the idea the distribution of support for the candidates gives Kerry a small advantage.

Saturday, October 23,10:00AM: I am working on a reference sheet to give you late next week. In addition to bottom-line predictions, this reference will give you a list of things to watch for on Election Night, along with key combinations that Kerry and Bush need. The content will change a bit in the coming week as the last polls come in. However, some outlines are now coming into view.

Under today's polling conditions, four states are clearly in serious contention: Florida, Iowa, Ohio, and Wisconsin To a lesser extent so are NV, WV, and some others. Depending on undecideds/turnout/bias, states come into or go out of play, but in those situations Kerry or Bush typically win the Electoral College by a more comfortable margin. So let's concentrate on this near-tie condition. After assigning other states as indicated by polls (PA and MI to Kerry, MO to Bush, and so on) and playing with combinations, several patterns emerge.

First - if Kerry wins Florida, the election is over - he wins. Kerry can also win by taking Ohio plus one of the smaller states. In the other direction, Bush must win not only Florida, but also either Ohio or all of the smaller states. In light of these facts, the Saletan piece (see below) indicates that the Bush campaign's actions may amount to a defensive move - otherwise why give up on Ohio?

It's also possible to identify states that look moderately solid, but might flip if the combination of undecided/turnout/bias factors adds up. This is interesting because this shift is likely to be similar across states. Therefore these states can act as an early-warning system for a surprising election night. For instance, Arkansas, North Carolina and Virginia currently look like Bush states, and Maine looks like a Kerry state. If a surprise occurs in any of these states, this might presage a significant offset between decided-voter polls and the real outcome.

Wednesday, October 20, 4:00PM: I've received lots of feedback on undecided voter assignment, much of it constructive. This has led me to rearrange the way the results are presented.

First: the calculation is now set to its old definition from two days ago. Many of you are very familiar with the raw (decided voters only) calculation by now. Switching back was suggested by many readers of various political persuasions. Whether people liked the direction of the outcome or not, many were uncomfortable with the mixing of current numbers and previous election outcomes. Also, this site has many calculations that are based on decided voters only, and it only adds confusion to redo those.

Second: the assignment of undecided voters is now done probabilistically, like the rest of the calculation. Past elections from 1956 to 1996 show a wide range of undecided breaks for the challenger: [+3 +6 +2 +1 +6 +0 +2 +4], median 2.5%, estimated SD 2.0% (analysis). This year may be unusual, though note in 1972 a break of 2% away from Nixon, at the height of the Vietnam conflict and after the invasion of Cambodia. Anyway, because the contribution is variable, the undecideds-assigned calculation (MATLAB script) takes this variation into account. The results are listed in the box above. This is my own current prediction. Also, the state probabilities are now given both with decideds only and with undecideds added. Thanks to Alan Cobo-Lewis and Rachel Findley for key discussions.

Third: There are now two maps (see box). The static image below is set with undecideds assigned.

Now, to the interesting bits. Look at the state probabilities. Because the undecideds could break evenly or for the challenger, many states are still toss-ups, including Florida and Ohio. The lingering uncertainty reinforces the idea that the election is close enough to be determined by turnout. Even if the undecideds break evenly, a 2% difference in turnout could change the result drastically, which you can see in one direction by comparing the maps. Have I mentioned before that I think turnout is important? Turnout is very, very important.

Whew, that was tiring. I think I need a wee dram!

Tuesday, October 19, noon: Today I implement the first major change to this calculation - I am allocating undecided voters. To do this I use past presidential election voting patterns, specifically the incumbent rule as described by Charlie Cook of the National Journal. This gives a more accurate snapshot and is a step toward making an actual prediction.

Rationale: It is known to poll analysts that voters who are undecided usually end up voting against the incumbent. In particular, compared with their final poll numbers, incumbents get between 2% less and 1% more. In contrast, challengers do better on average by 3%. These figures are consistent with Cook's estimate that undecideds split at least 75% for the challenger. In today's summary of national polls, the average Bush-Kerry split is 48.5-45.5, which sums to 94%. Assuming 2% for Nader and other candidates, the remaining undecideds are 4%. Splitting these by Cook's rule gives 1% to Bush and 3% to Kerry, reducing the margin by 2%.

Therefore, for the main calculation I will assume that the undecided-voter shift is +2.0% towards Kerry, shift state polls by this amount (using the variable already provided in the script), and proceed with the calculation. Based on state polls in Florida, Ohio and Pennsylvania, I estimate that the proportion of undecided voters in these states is similar to the national figures. Because national polls come more frequently, I will use them to calculate the shift. The size of this shift may change in the final days, and I will be monitoring this.

This new estimate is likely to be more accurate. However, it is also the first change to the calculation that is not neutral: it goes beyond the polling numbers themselves, and it is in a direction that is favorable to my candidate. For example, Florida, Iowa, Ohio and Wisconsin are still toss-ups, but they are now above the 50% probability threshold for Kerry. Therefore I will continue to report the results without this adjustment. This is listed in the box above on the line labeled "Decided voters only." The corresponding Meta-Margin can be calculated by subtracting 2.0% from the value listed.

To read more about the incumbent rule, see Charlie Cook, Guy Molyneux, the Los Angeles Times, Mark Shields, the Mystery Pollster, and a contrarian.

I have also simplified the box by removing the line about the Colorado ballot initiative, which, based on a recent poll and Salazar's opposition, seems likely to fail.

Finally, I will continue listing rankings and probabilities for all states. I have decided that there is little benefit to leaving these out.

Hitting the streets: How much do you affect the election by getting out the vote? Also, where are your efforts most valuable? To help guide your efforts, here is a synthesis of previous posts. Once you decide, I recommend contacting your local Democratic (or Republican) organization or America Coming Together.

This question can be answered by calculating how much the Electoral College win probability is changed by one person's vote. This affects where you should go because as an individual, you can only get out a finite number of votes. Today the best states to go to are Iowa, Ohio, Nevada, and Florida. Nevada, while small, is on the list because it is a near-tossup and relatively few voters per electoral vote. Here is a case study. If you are a New Jersey resident, your vote has some value, but it is low since the state is very likely to go Democratic by a substantial margin. In contrast, driving a voter to the polls in Pennsylvania is worth nearly 300 times as much. If you go to Ohio each vote is worth even more, over 500 "jerseyvotes." The top states are IA (686 jerseyvotes), OH (528), NV (508), FL (372), NM (304), WI (295), PA (295), MO (199), AR (151).