Go to the state-by-state form

**November 10, 2012**

There is still a little bit to look at now that the election results
are in. The first bit of business is to retract my comments about Maine's second congressional district
that I made on November 5. There were four combinations of states that I had overlooked that could
give Obama 33 electoral votes without ME2. This means that ME2 could have tipped the election. So
I moved it back to the category of Possible Tipping Points States.

ME2 didn't figure particularly prominently prominently for either candidate. Using the data that I had captured just after midnight on the morning of the electon, Obama's chances of winning stood at 67.19% over all outcomes.

**November 6, 2012****How each candidate can win:** There are seven key states. The Intrade
polling last night didn't quite reflect that...Obama's Pennsylvania and Michigan futures were only
a bit higher than his Nevada futures last night when I captured the data, but I analyzed what the
data presented. That gives Romney some
out-of-the-box opportunities. In fact, out of the Intrade state futures suggest that Romney has a 26.57%
chance of winning by holding his own must-win states and breaking through to capture at least one of
Obama's must-win states. Similarly, though, Obama can also win by holding his own must-win states
while capturing Florida or another one of Romney's must-win states, and the Intrade state futures
suggest that he has a 39.51% chance of doing so.

Unlike Romney, however, Obama has some chances to
win *even if he loses a must-win state*. He has a 2.61% chance of winning the election in cases
where Romney holds all of his must-win states and captures at least one of Obama's. He has an
*additional* 1.54% chance of winning when both he and Romney capture something from the other's
must-win column. In contrast, Romney's has only a 0.05% chance of winning in cases where Obama holds
his must-win states and captures something from Romney's must-win column. Romney has some modest
chances of winning if both candidates capture something from each other's must-win column, but those
cases only add up to 0.45%.

Those are the out-of-the-box cases, and they account for 70.73% of the outcomes. (I have to inject
editorially here—I'm reporting on the implications of the Intrade futures data. I personally don't
think that Romney has any significant chance of breaking into Obama's must-win column.) Of those outcomes,
Obama wins 43.66% and Romney wins 27.07%. Usually, only one candidate breaks through and that candidate
wins the election, but 4.65% of the outcomes are *really* out of the box, and Obama wins most of
those (4.15%).

The other 29.27% of the outcomes occur when both candidates hold their must-win states. With the possible tipping-point states as I've defined them, either candidate needs 34 electoral votes to claim the election. Obama could win with 33 EVs, but there are no combinations that equally split the 66 EVs from those states. If Romney gets 34 EVs, he only achieves at 169-169 electoral tie, but Republicans are almost certain to control a majority of state delegations in the new House of Representatives, so I award all of those outcomes to Romney.

Of the 29.27% of cases that are in-the-box scenarios, the Intrade futures suggest that Obama wins 23.52% and Romney wins only 5.75%. So, for both Obama and Romney, the majority of their favorable outcomes are from out-of-the-box scenarios, where someone gets into the other's must-win column, but for Romney it's overwhelming. Over 82% of his winning scenarios involve him capturing at least one of Obama's must-win states. For Obama, it's only 61.10%.

There are eighteen different ways to get at least 34 of the 66 EVs (without unneeded states). Obama's easiest combination is NV+WI+OH, and 17.37% of the the outcomes are cases where both candidates hold the must-win states and Obama wins those three. If Obama does not win with an out-of-the-box scenario or capture those three tipping-point states, then his next most useful combination is NV+IA+VA+CO adding an additional 1.80% to his chances. The next most useful combination is OH+NH+VA, adding anther 0.76%. Obama still has 3.60% of the favorable outcomes from other in-the-box scenarios. Some of the notable ones are WI+OH+IA, NV+WI+IA+VA, or NV+OH+IA+NH.

Romney's best in-the-box scenario is VA+CO+OH representing 2.75% of his winning outcomes, which is almost half the 5.75% of his winning outcomes from all in-the-box scenarios. If he does not win with an out-of-the-box result or with those three states, his next most useful combination is VA+NH+OH, adding another 0.80%. Romney has another 2.19% of all outcomes that result in an in-the-box win. Some of the notable ones are VA+IA+OH, IA+OH+WI, or VA+CO+NH+WI.

**November 5, 2012**

I'm working on the pre-election summary and mulling over what to do with
Maine's second congressional district. I've decided to move it in with the "Possible Tipping Point
States", but for an odd reason: It doesn't fit either of the two criteria for getting out of that
category.

- It is strongly enough on one side of the tipping point that it can only swing if that candidate loses
- It is firmly on one candidate's side of the tipping point, but worth so many electoral votes that it will tip the election if lost.

Maine's second congressional district doesn't fit either of those. But, if you set it aside as an Obama EV and look at the seven states around the tipping point, then Obama needs 33 EV or Romney needs 34 EV to secure an electoral college victory. But there is not a single combination of those seven states that adds up to 33 electoral votes. So each candidate actually needs 34 EV. If you toss ME2 back into play, then Obama needs 34 EV or Romney needs 34 EV. Since there was no combination of 33 EV without ME2, ME2 can never tip the election, unless one of the Must-Win states flipped.

So in the form below, ME2 has been moved into the category of Possible Tipping Point States, but it can't tip the election.

**November 5, 2012**

The election is tomorrow. I've made the final changes. It's now clear that
Romney cannot win the election if he loses Florida, so I've moved Florida into Romney's must-win states.
In a narrow sense, I'm not asserting that none of the must-win states could be the tipping point. I'm
making the more narrow assertion that if the opposing candidate wins any of those states, then the opposing
candidate will win the electoral college.

So, I see 2^{7} + 2 = 130 possible outcomes. (The +2 covers the cases where one candidate wins
a state in the other's must-win set.) If I have enough time, I'll try to break those down and assign
probabilities to each outcome based on Intrade state futures.

**October 31, 2012**

A little bit of self-induced horror this Halloween. The state aggreggation
is particularly simple right now. (It's Ohio, stupid.) So, I noticed that the aggregated future that
was calculated by my site seemed to be off. I found a bug in the code that was using too large a value
for the state-by-state part of the variance. (The national part of the variance was calculated properly,
so there was too much variance overall.) I fixed the bug and reran the previous calculations using
historical data files. I had overwritten one data file from 10/3, but all other historical values have
been recalculated. If you run the script using the form below, you can see the corrections.

As I commented above, Ohio dominates the presidential futures. In fact, most of Obama's winning scenarios include Wisconsin, Nevada and Ohio (including combinations where Obama also wins other states like Iowa.) Obama's most likely scenario without Ohio involves Virginia with Wisconsin and any two of Nevada, Iowa or New Hampshire (about 3.0% of all scenarios, or about 60% of Obama's wins without Ohio). Romney's most likely scenario without Ohio is to win Wisconsin (about 4.7% of all scenarios, or about 57% of Romney's wins without Ohio).

**October 26, 2012**

There's a bit of a spread again between the aggregated prediction based on
state futures (59.85 for Obama) and the directly traded futures (63.3). In this case, though, the arbitrage is not
so obvious. The aggregate isn't soft for Obama because one or to key state futures are off, but becaue
several states that would be part of Obama's *backup*. Essentially, with Virginia and Colorado trading
below 50%, the aggregated prediction doesn't have much contribution from cases where Obama loses Ohio, although
there are certainly ways for him to lose while winning Ohio. That's a harder balance to play. My gut tells
me that buying Colorado and Virginia at depressed prices and selling Obama's aggregate is pretty safe, it's
not as well hedged as I'd like.

**October 24, 2012**

Still chaotic—especially at the state level. Since yesterday, Ohio has
traded at least as low as 43% for Obama and at least as high as 63%. The overall result has traded over a
narrower range, but still varied by at least a few points. We'll probably need to wait for some solid
post-debate polling before things settle down. The aggregated state results are currently 54.93% for Obama,
up very slightly since yesterday, while the Intrade individual results are at 57.5%, down about one point.
But, that's just a snapshot at about 11:40 AM.

**October 23, 2012**

This site is back up after being down for 11 days. (The Internet Service for
MathRec went down unexpectedly.) In the meantime, a lot has happened. Romney had been in trouble before the
first debate, but recovered significantly to get back to a 2:3 underdog position—which is much less
daunting than the 1:4 or 1:5 position he was looking at in late September. After that first debate, Romney's
position settled into a new normal of about 37%.

That position was not much changed before last night's final debate, but Romney's direct futures are now trading at more than 41%—an overnight improvement of about three points. During some chaotic trading this morning, his futures even exceeded 48%. In the meantime, the state futures have gotten slightly out of sync again. Arbitrage? Not right now… It's Ohio that's out of whack in the state futures, and there's a largish gap between bid (55%) and ask (58.4%). Since the ask price is not really out of sync with the direct futures, there's not much opportunity there. Don't be surprised to see some more chaotic trading, though. At this point, the tipping point is so dominated by Ohio, that you don't need this site to check for the arbitrage opportunity.

**October 10, 2012**

At 5:05 PM EDT, the bid price for Obama shares was 62.5%. Short selling ten
lots would require an outlay of $37.50. I could have closed out the ten shares by meeting the ask price of
61.4% at 9:04 PM EDT. That would have been a profit of $1.10 on ten lots, or 2.9% (recouping most of my loss
from yesterday, but still down $0.30). There's a debate tomorrow, so it would not be a good idea to play the
time-of-day game.

**October 10, 2012**

Another seeming arbitrage opportunity today. My automated processing of the
Intrade state data extracted a value for Obama in Ohio of 56.25%. As a result, the aggregated state data
came out at 56.97% for Obama. Meanwhile Obama's direct futures are trading at 63.2%. But the state futures
are lightly traded, and the ask price for Ohio is 62.6% (or a bid price of 37.5% for Romney in Ohio), so there's
not really an opportunity for arbitrage (unless you want to buy one lot of Obama in Colorado at 49.0—that's
a good price, but it's not as tightly coupled to the overall outcome as Ohio is; the offseting purchase would
be one overall share of Romney at 37.6%). Update: At 12:30 PM EDT, buy 2 shares of Obama in Ohio at 55.0%; sell
2 shares of Obama overall at 62.1%. That's an exposure of $18.58. Resolution: At 7:14 PM EDT, sell the shares
of Obama in Ohio at the bid price of 59.7% and buy back the shares of Obama overall at the ask price of 62.7%.
That's a profit of $0.94 on Ohio and a loss of $0.12 on the overall, for a net of $0.82, or 4.4% in seven
hours.

**October 9, 2012**

So, at 5:08 Eastern time, I could have sold Obama on Intrade at 61.2, matching the
posted bid price. (The competing ask was 61.6 at the time. Alternatively, I could have bought Romney by
matching the ask price of 38.9). Selling ten lots short would have cost $38.80. Liquidating that position
at 9:37 PM would have been at 62.6, matching the ask price, for a loss of $1.40 on ten lots. Romney's futures
were run up by about four points between 12:25 and 1:00 PM EDT, so the market was still settling back down
from that event. We'll see if the afternoon/evening drift shows up tomorrow, but for now, I'd be down $1.40.

**October 8, 2012**

As far as arbitrage goes, I think you could do it every weekday. Buy Romney at
4:00 EDT and sell your stake at 9:00 PM EDT. I'm not sure what traders are coming and going throughout the day, but
this pattern has seemed pretty stable. Today you could have bought at no more than 33.5 and sold at no less than
35.7. That's a 6.6% return. Taking the worst timing on prices would still be something like buying at 33.7 and
selling at 35.1, for a 4.2% return.

That one doesn't count. I'll track this over the next few days and see whether I can make it consistent. It's certainly more like gambling than arbitrage, though.

**October 6, 2012**

The arbitrage opportunity did not last long. You could sell that Ohio at 65.1
and Wisconsin at 68.0, and buy back Obama at 65.9 at profits of 5.2, 13.0 and 4.4 respectively. So a well-hedged
investment of $5.99 + $5.50 + 2×$2.97 = $17.43 would have yielded a profit of $2.70 in a day.

If the markets stay chaotic, there are likely to be additional arbitrage opportunities. One of the purposes of this site is to identify them. When the well-traded direct presidential futures are out-of-whack with the state futures, buying opposite sides of the November result in state futures and direct futures can present a low-risk opportunity for short-term gain.

**October 5, 2012**

Well, this is the first clear arbitrage opportunity. Obama's direct futures
are trading at over 70%, but his futures for Wisconsin, Ohio, Virginia and Iowa are all no more than 55%.
(The way that I calculate the predictive probability does not meant that you can make a purchase at that
price, but you could buy Ohio for 59.9 and Wisconsin for 55.0 and sell Obama direct futures at 70.3.)
As a result, the state aggregate has collapsed to 61.92%, while the Intrade direct futures have risen to 70.3%.
I'll make a non-analytical prediction that that won't last long...

**September 29, 2012**

It has been one thing after another for Mitt. I record three different
predictions each day, and a list of these historical values are printed at the end of the CGI output.
(These CGI is launched when you click submit on the form at the bottom of the page.) With just a little
noise in the data, Mr. Romney's futures as calculated by aggregating the trading data for state results has
been dropping steadily. Similarly, the direct futures prices on the overall result of the presidential
election have been doing the same thing. One thing I've
been trying to tease out of the data is whether the state futures are a leading or lagging indicator.
Because both have been on a relentless uphill march, it's been difficult to tell. I would, however, note that
one of the bigger jumps occurred when some state polls came out that were quite favorable to Obama. In that
*particular* case, the aggregate of the state futures led the futures for the overall outcome, and it
was pretty easy to see that the state futures that were driving the change were the ones that had the new
polling data.

My impression right now is that the aggregated state futures lead when there's specific new data, but that
the futures for the states without new data actually lag a bit. That is, the order of movement is: 1) states
with new data, 2) overall direct futures, 3) states without new data. This means that the state aggregate
both leads *and* lags.

**September 22, 2012**

I made a couple of structural changes, moving Michigan and Pennsylvania out of
the list of possible tipping point states. It's pretty clear that Obama basically has no winning combinations
where he loses either of those states. I also reduced the portion of the variance applied to the national
shift from 75% to 70%, now that we're closer to the election. This has a relatively small effect on the results,
implying 71.96% for Obama, instead of 71.87%.

**September 13, 2012**

It looks like I launched just in time to watch the Intrade markets respond to
Obama's convention bounce…possibly mixed with some foreign-policy bounce resulting from the Libya attacks.
For my purposes, I'm interested in whether the state aggregate from my predictor leads or lags the Intrade direct
futures. On September 9, Romney's direct futures were at their peak, and the state aggregate stood at
63.13% for Obama, which was 5.13 greater than his direct futures. So, when Obama's futures were in decline, the
state aggregate, perhaps was a bit high. As Obama's futures have been shooting upward, the delta between the
state aggregate and the direct futures has narrowed. These observations suggest that the direct futures lead the
state aggregate.

The question of which indicator leads and which one lags is separate from the issue of whether there is a systemic bias between the state aggregate and the direct futures. As I observed in my previous post, the state aggregate has always indicated a better position for Obama than the direct futures do. Including my experience from previous elections, I have good reason to believe that the offset is systemic. It is less clear to me whether the systemic offset is in my aggregating model or in the underlying Intrade data.

**September 10, 2012**

The direct Intrade futures for president indicate only a 58.7% chance of an Obama
victory in November, but I infer a 63.27% chance from the state-by-state Intrade data. This disconnect was common
during the last presidential election, and it's not surprising during the early phase of the election, when the
state futures aren't highly traded. But, the direction of the inconsistency seems fairly constant. Looking at the
state-by-state futures paints a rosier picture for Obama than the direct presidential election futures.

An interesting check on my algorithm is to see what it does with the fivethirtyeight state data. When I enter the state-by-state values from fivethirtyeight, I get a higher overall estimate of Obama's chances than fivethirtyeight does, unless I attribute most (92%) of the variance to national shift. Using the 75% that is my current value for the percentage of national variance gives 82.47% for Obama instead of 80.7%. I suspect this is "real" in some sense. I think Nate's model holds out some chance that there could be a very big shift due to unexpected events. That is, I think his model might have some non-Gaussian distribution for the national shift. This sort of hedging against an unknown scale-tipping event might also be reflected in the Intrade estimates. Looking at the Intrade data for "safe" states, for example, suggests the possibility of a fairly large shift that could only come after a significant change to the satus quo.

**September 9, 2012**

I was pretty quick yesterday when I described how I convert Intrade data to
state-by-state probabilities to populate the form below. Today I'll give some examples.

Ohio is both pivotal and highly traded, so let's use that as a typical example. The first step is to determine the trading window. Futures for Obama to win Ohio were being offered for sale at 6.19 (out of 10), and there were bids to buy at 6.02. So that sets a current low end of 60.2% and a high end of 61.9%. Romney's futures were being offered at 4.20 and bid at 3.80. Flipping those to Obama probabilities gives a low of 58.0% and a high of 62.0%. Combining those ranges gives a low of 60.2% and a high of 61.9%. The last trade in Obama futures was at 61.9%, which is inside the current trading range. The last trade in Romney futures was at 47.0%, which is equivalent to 63% for Obama. That is outside of the combined range, so I use a value of 61.9%, which is the upper end of the current range. The average of the Obama value 61.9% and the Romney value 61.9% is 61.9%.

Utah will surely cast its electoral votes for Romney. Let's see how the algorithm parses the Intrade data. Futures for Obama to win Ohio were being offered for sale at 1.45, but no one was buying. That is interpreted as a range between 0.0 and 14.5%. There were bids to buy Romney futures at 9.20, but no one was selling. That corresponds to a range between 92% and 100% for Romney, or 0.0% and 8.0% for Obama. There had never been a trade in Obama futures for Utah, so we treat that as a previous trade at 0%. Romney futures, however, had last traded at 91.5%. That's outside the current trading window, so we use 0.0% and 8.0% as the two values and average them to get 4.0% for Obama in Utah.

**September 8, 2012**

I've now launched for the 2012 election! The Intrade state data now seems stable enough
to use without a lot of tweaking. I'm populating the state percentages in the form below directly from Intrade
according to a relatively simple algorithm.

I first determine the trading range based on Bid and Ask prices. The low end of the range is the higher of the Dem Bid (in percent) or 100 minus the Rep Ask. The high end of the range is the lower of the Dem Ask or 100 minus the Rep Bid. If the low is higher than the high, then the trading ranges for Dem and Rep are inconsistent, and I take the percentage for the form to be the average of low and high. Normally the trading ranges are consistent, and I consider the last trades for Dem and Rep. If those are within the combined trading range [low,high] then I use those values. But if either value is outside of the current trading range, then I use the closest edge instead. After translating the last Dem and Rep trades into the current trading range, I take the average and use that for the percentage in the form.

There are some states for which there is no last trade for either Dem or Rep. Those are all for safe states—some for Romney, some for Obama. In that case, I take the last trade to be at the extreme: either 0% or 100%.

I have an algorithm that I apply to average some state values to get percentages for ME2 and NE2 (and ME1, NE3 and NE1, too). For the moment, DC is just set to 98% for Obama.

There are a few states that seem to have spurious values. These aren't going to have a very big effect. Today, they seem to bias the results slightly toward Obama—the couple states that seem "off" are safe Romney states that are a bit too high for Obama. By fiddling with the Intrade values, I'd estimate that fixing those few poor values might make the aggregate probability of an Obama victory be 63.34% instead of the 63.41% that I get directly from the Intrade data.

**July 15, 2012**

I'm going to take a moment here to discuss the various predictors of the presidential
election that are available on the web. Please keep in mind that a prediction is a statement about the probability
of an outcome, not a statement that an outcome will or will not occur. There are five sites that either give
a prediction in terms of probability, or give enough information to infer a probability.

The first is the Princeton Election Consortium. This site does not
have 2012 aggregated data yet, but they are under construction for the upcoming election. Four years ago they did
*not* give a direct predictor, but did give an electoral vote estimator with a 95% confidence interval—very
nice and very meaningful. The confidence interval was based on the margin of error for aggregated poll data. The polls
were combined to determine a probability for each state for each candidate. Those probabilities were combined into a
histogram of possible electoral outcomes. The median outcome with 95% confidence interval was determined from that.

This is *not*, however, a prediction of the electoral outcome. The probabilities in that meta-analysis are
only for recent polling. There is no attempt to determine or estimate the amount that the overall national or
individual state electorate may change their opinions or intentions between now and the time that the election is held.

The second site is FiveThirtyEight. This site does provide a direct predictor. The underlying analyis is very similar to the Princeton Election Consortium, but FiveThirtyEight goes a step further and uses demographic data, historical data about national and state-by-state shifts in polling and actual election returns. This is very important, and the model that they use is sophisticated and their methodology is fairly transparent. I feel they are the best site for aggregating and interpreting poll data.

Their model of electoral shifts includes state-by-state shifts, national shifts, and shifts in demographically similar states. This is fairly similar to my analysis, but we use very different underlying data…more about that later.

The third site is Intrade. This is a futures market with four different futures for the outcome of the presidential election. Each of these futures is a separate predictor of the overall electoral outcome (if you believe that the possibility of a third-party candidate winning the election is negligible). In short, the futures are "Obama", "Romney", "Democrat", and "Republican". Because the futures are actively traded, the four futures never indicate a single value, but it's straightforward to aggregate them. (I use the bid and ask prices, as well as the sales prices, to determine the most consistent market value.)

The prices of the futures track the polls pretty directly, since that's the main source of information available to futures traders. But they do not reflect the polls in a well-defined mathematical way. The trading market is making an implicit assessment of the factors that the Princeton Election Consortium does not address. The futures prices are completely aggregated. They may or may not be biased, but it is arguable that they are better at removing biases than pollsters are, and they are certainly better at incorporating the intangible aspects of the electoral outcome, such as how large will the black or youth turnout be?

The fourth site is Iowa Electronic Markets. This
is also a futures market, but their futures are different. They have two futures based on the U.S. Presidential Election.
The easiest to understand is the "Winner-Take-All" market, based on the *popular vote* This is a
direct predictor, but it does not include an assessment of the probability that the popular vote winner fails to win in
the Electoral College. The second market is also based on the popular vote, and the value of the future at maturity is
equal to the percentage of the two-party vote share. So a Democratic future is worth $5.45 if Obama wins 54.5% of the
Romney/Obama vote share.

The fifth site is this one. Although less slick than the others, it also provides a direct predictor of the electoral
outcome. By visiting the site and clicking on the button on the bottom of the page, you get a direct prediction of the
electoral outcome, based on Intrade prices for *each state*. The Intrade prices in the web form are updated
from time to time (eventually daily), and the cgi includes a historical tracker of the daily predictor.

The model behind the form is similar to that used by FiveThirtyEight, in that it allows for both state-by-state shifts and also for national shifts. The default 70% split between national shift and state-by-state shift is based on the typical ratio of polling uncertainty in a state to the state-by-state Intrade futures prices.

What is interesting is that the four sites that offer an electoral predictor give different results. The inferred predictor here at MathRec closely tracks the direct futures prices at Intrade, but in the '08 election there had been a consistent offset. Both of these were significantly lower than the futures price of the IEM Winner-Take-All market for Obama, even though it was quite clear that Obama had a significantly greater chance of winning the Electoral College than the popular vote. The predictor at FiveThirtyEight was significantly higher than the futures price at IEM, even after adjusting for the possibility that Obama could win the Electoral College without winning the popular vote.

I'll discuss possible reasons for the discrepancies in my next post.

A quick disclaimer. Although I think that this site is useful and serves a small niche, there are better sites available. In particular, I've drawn heavily from Sam Wang's Electoral College Meta Analysis. I've also paid close attention to FiveThirtyEight.

I believe the principal usefulness of my site is to accurately assess the effect on the overall election resulting from shifts in one or a few states. There may also be some usefulness in picking out arbitrage opportunities between state-by-state futures and the futures for the overall electoral result. It also provides a different perspective for assessing whether other sites might have a bias that should be noted.

The form below takes state-by-state inputs as percentages for Obama, such as that provided by Intrade. (Look for Politics, then US Election by State.) The state-by-state odds will incorporate the possibility of a national swing in the popular vote, plus state-by-state variation. Of course there is uncertainty associated with both of these. You choose how to allocate that uncertainty, by specifying the percentage that is national. My best guesstimate of the value is 75% for a couple months out, but the previous two elections I shifted that to 60% as the election drew closer. (It cannot be 100%, but it can be 0%. The overall prediction doesn't work consistently with values outside of 5% to 95%.) Then just plunk in the state-by-state odds. The cgi will do the permutations for various values of the national vote swing and predict the probability of an Obama win. I've prepared another page with more details about the methodology (and the math).

The form below is populated with default values from Intrade prices as of Tuesday, 11/6 at 08:46 Pacific Time.

Steve SchaeferLast modified: Date: 2012/07/15