{\huge The Election Outcome}

We predict that one of three outcomes will happen \vspace{.5in}

Nate Silver is arguably the world's foremost psephologist. This sounds like someone who foretells a person's future by feeling the bumps on the head, but it is not---that is a phrenologist. Psephology comes from the Greek psephos meaning ``pebble,'' which the Greeks used as ballots. It is the branch of political science that deals with the study and scientific analysis of elections.

Today Ken and I want to make a prediction about the election. We predict that Nate Silver will be $latex {0.95}&fg=000000$-correct with probability $latex {0.95}&fg=000000$.

Silver is a statistician, a sabermetrician, a psephologist, and much more. The term ``sabermetrician'' comes from the acronym SABR---the Society for American Baseball Research. He devised a system called PECOTA for forecasting the development of skills in aspiring young baseball players, which supplements traditional methods of ``scouting'' them. He ventured into political science with the blog FiveThirtyEight, which is hosted by the New York Times. Its name stands for the 538 electoral votes at stake in tomorrow's contest between President Barack Obama and challenger Mitt Romney.

Silver has created quite a stir among those who make election predictions, because:

  1. He has gone out on a limb giving Obama an 92% likelihood of winning what many news sites and pundits are calling a ``tossup'' election, when most national polls show the candidates within 1% of each other. (This jumped up just now around 11pm ET tonight---Monday night---from 86%.)
  2. He approaches the task very differently manner from other experts, relying on poll aggregation and other quantitative modeling.
  3. His work identifies and exposes systematic bias in polling firms.
  4. He himself is known to have supported Obama in 2008.
  5. He puts a huge amount of effort into his work, and has a track record of being very good at it.
Still, many with traditional ways of scouting the political landscape think Silver is reading head bumps or has baseball bats in his belfry. That the tug-of-war over perception of each candidate's chances can itself move the outcome intensifies the passion. The outcome will be seen as much as a referendum on Silver's kind of methods. Since both of us have been involved in court cases using evidentiary statistics, we both feel some stake in this. But first we have some caveats.

The Three Outcomes

Obama and Romney are about to find out who will be sitting in the Oval Office for the next four years. Or maybe not. We believe that there are three possible outcomes:

The last seems quite possible, given how close many think the election is and given the number of lawyers that are available to fight on both sides. Already today there is word of a lawsuit over provisional ballots in Ohio. The recent and continuing disaster from the huge storm Sandy also gives pause for thought---indeed Andrew Appel whom we know as Princeton colleague and college classmate pointed out a legal disconnect in New Jersey.

What do you think? Here is a poll that lets you voice your opinion.

\includegraphics[width=3in]{Obamney.jpg}

Ken and I have different opinions on the outcome, as we'll explain, but within the margin of agreeing with Silver.

Dick: A Previous Election

I, Dick, remember the election of Ronald Reagan over the incumbent President Jimmy Carter. The electoral college vote was a landslide, Reagan got 489 votes and Carter only 49. Here is the map of the states:

\includegraphics[width=4in]{ElectionMap.png}

I recall this so vividly because Bob Sedgewick and I planned a special election night. We had a paper that we needed to finish and the predictions before the election were that it was close, and many thought that we might not know who won until late that Tuesday evening. So Bob and I when off to a hotel, got two rooms, and planned to work all night on our paper while listening to the election news. We checked into the hotel, and went down to get dinner.

When we returned to the room around 8 o'clock we turned on the TV and started to work on the paper. Then at 8:15 pm EST, our time, NBC News surprised everyone with the projection that Reagan was the winner. This was the first time that exit polling was used to make such a projection.

NBC News projected Reagan as the winner at 5:15 PST, before voting was finished in the West, based on exit polls. I still recall sitting there dumbfounded. There went our great plan to work all night, while the news slowly came in about the election. We soon gave up working, and retired for the night. The paper got done eventually, but not that night.

I don't think tomorrow will be that quick, but I do think by 10pm it will be clear that Obama is winning even without knowing results in Colorado or Nevada, and the formal call will come by 11pm with the West Coast results as in 2008.

Ken: Several Recent Elections

Since 1972 I've followed the dancing numbers without a thought of getting work done, except for 1984 when I was five hours ahead in Oxford and knew my near-namesake was a lock. In 2000 and 2004 they were very late nights indeed.

Mainly because 2004 came out redder than the exit polls had indicated, 2008 held suspense even though Obama ultimately won the popular vote by 52.9% to 45.7% and every state went as Silver had projected except Indiana. This time no one projects a margin wider than Silver's current 50.9% Obama to 48.2% Romney, and today's final CNN poll has 49% each. Therein lies my first caveat---I expect a long night.

Ironically the expansion of early voting has the effect that more ballots will be counted later. According to a note that was at the bottom of George Mason University professor Michael McDonald's ``Early Voting Statistics'' page last Thursday (since changed), over 75% of Ohio's early votes were being sent by U.S. mail, and they were allowed to be postmark-cancelled as late as today, with counting by the same Nov. 17 date as absentee ballots. Voter-ID and other laws are creating more cases where those appearing on Election Day will have to cast provisional ballots, which are counted only upon presentation of ID or resolution of possible conflicts (such as previously having requested an absentee ballot).

Given that the early vote has been heavily Democratic, this could all narrow the margin as reported on Election Night itself. Early voting and provisional-ballot filtering also causes new systematic polling hazards, such as noted Saturday by McDonald here. That these factors have considerable magnitude was underscored by Pennsylvania State House GOP Leader Michael Turzai's comment that the state's new voter-ID law (which was stayed past the election by court order) would ``allow Governor Romney to win the state.''

The Silver Tossup Line

My second and main caveat, however, comes from Silver's numbers themselves, specifically his own projected error bars---and precisely because we agree with them. Our saying above that we are 95% confident that the result will hit Silver's 95% confidence interval is not vacuous or snarky---it means we think he's found the right center and variance. If there were 1000 independent elections, we'd be happy to bet the outcome would lie within his range 950 times. The problem is:

There's only one election.

Well there are 52 state elections plus DC for President, and many Senate and House races he has forecast, but they are not independent. For something given outsized importance between quantitative and qualitative views of life, there is only one trial. And this lends weight to the corollary:

There is a 50% chance that the result will be further from Silver's projection than the bounds of his 50% confidence interval, and 25% on the side of underestimating Obama.

Are these self-declared bounds wide enough to be noticed if this happens? Of course they are narrower than the margin of any single poll, typically $latex {\pm 3--4}&fg=000000$ percentage points, meaning $latex {6--8\%}&fg=000000$ wide. That's the point of poll aggregation which is what Silver does: by combining results he narrows the confidence window. Exactly this was needed to declare the Higgs Boson discovered last July: combining the results and error bars of two independent experiments.

The tick from 86% to 92% noted above is the first to make Silver's projection agree with his ``if election were today'' figure, so that's the number. Mousing over his graphic shows error bars $latex {2\sigma = \pm 46}&fg=000000$ in electoral votes on Obama's projected total of 315. Since 50% of the area is within 0.674 sigmas, this gives a median error of $latex {16}&fg=000000$ electoral votes. On Halloween, Silver had Obama at $latex {300 \pm 58}&fg=000000$, implying a median error just under $latex {20}&fg=000000$. In the popular vote, Silver currently shows the error as $latex {\pm 1.9\%}&fg=000000$, which implies an ``expected miss'' of $latex {0.7\%}&fg=000000$.

The 11pm just-posted numbers narrow his stated confidence quite a bit---what chutzpah!---but still show an expected miss by about the size of Ohio (18 electoral votes) and upwards of 1% on the popular vote. Such a deviation would still equate the election to a nailbiter.

Lucky Eclipse?

Whether an Obama total around 290 or less would be viewed as ``half miss'' by Silver is arguable. When I conceived this post late last week the bars were wider. I'll hold to my view that the systematic uncertainties are ``objectively'' greater than his model accounts for, analogous to what I've said here about the projected error bars in my own chess research needing expansion as shown by empirical testing. Of course my application allows empirical testing hwere Silver's doesn't: there is only one election.

Whatever the underlying reality---and we'll find out soon---the stakes for popular perception of statistical science on the whole are certainly high, and higher with tonight's movement. I am reminded of the effect of the 1919 observation of light bending during an eclipse of the Sun for testing generality relativity and making Albert Einstein famous in the public eye overnight. As implied here, the inherent statistical uncertainty of the experiment was such that the degree to which Einstein's predicted deflection was hit was fortuitous. It could easily have been only half that, and perhaps indiscernible. Well for my own professional purposes I'd like to see Silver's number hit bullseye, but I won't bet on it.

Open Problems

What do you think?