August 28, 2016

Structuring a bet about the changing Electoral map

In order to create a model of how a landslide election could happen, we can structure a bet to include separate conditions for the mundane outcomes, which bring the election close to even, and the extraordinary outcomes that would result in a lopsided victory.

Someone who is skeptical of Trump winning would expect him to get around as many Electoral votes as Romney did in 2012 -- 206 -- and probably in the exact same states.

They would still allow him a chance at winning, though presumably by a narrow margin and only by winning states that were close contests for the past however-many elections -- Florida, Ohio, Virginia, etc. If Trump won these three close states, plus another somewhat close state with favorable polling (Iowa or New Hampshire), then he would get just over 270 and win the election.

The further away from 206, the less likely in the eyes of the skeptic. But it's not totally out of the question either. So each Electoral vote above 206, the skeptic should be willing to pay more, though in a way that doesn't escalate too quickly. Say, a linear increase for every vote above 206.

At some point, though, the skeptic will agree that a Trump victory was no longer a narrow win among close races, which has already happened recently for both W. Bush wins, but represented a more fundamental shift in the laws of the Electoral universe. If Michigan and Pennsylvania go red for the first time since 1988, that reveals a fundamental change in the Electoral map.

Since the skeptic thinks that the same old laws are still at work, they should be willing to pay at an even steeper rate for these kinds of wins. In fact, they should be willing to pay at an accelerating rate, as they consider them exponentially less likely. If they're wrong, they should pay up exponentially more to the winner.

Unlike a simple linear increase for the wins of close races, wins above that should show something like a squared increase. At some small threshold above 270, the skeptic would admit that a Trump victory has gone beyond "winning close races, with no fundamental shift in the Electoral map" to "we're entering a fundamentally different Electoral environment".

Exhausting the close races, and even a few small not-so-close states, still maxes out around 280. So we'll take this as the threshold for a mundane victory vs. an extraordinary victory. You could induce some humility and cognitive dissonance in the skeptic by allowing him to increase this threshold to 290 or 300, and thereby concede that many more of the Obama states will be close rather than out of reach for Trump.

Whatever it is, the pay-off should be proportional to the square of Electoral votes above this threshold. If the skeptic truly considers this impossible, wishful thinking, delusion, etc., then they should feel no anxiety in allowing for the accelerating pay-off for fundamental shift wins.

So then the structure of the bet looks like this:

Pay-off = a1 * [votes above 206, until 280] + a2 * [votes above 280]^2

To simplify the example, let's make each of the a1 and a2 constants equal to 1.

If Trump won 330 votes, he will have gotten 74 votes above Romney's 206, each paying out a dollar, for $74, as well as 50 votes above the threshold of 280, which when squared pays out $2,500. Total pay-off is $2,574 -- most of that due to the wins signaling a fundamental shift.

Suppose Trump's success racked up 380 votes -- that's the same 74 above Romney's, but now 100 votes above the threshold that get squared, for a total pay-off of $10,074.

Leaving the a1 and a2 constants equal to 1 means the skeptic would be willing to pay a max of around $100 if Trump ekes out a narrow victory. Although that sounds more like a friendly bet, this person could have to pay out $10,000 if they're seriously wrong about there being no fundamental shift afoot. If they truly believe that is pure fantasy, what is the downside to taking this bet?

Should the Trump supporter allow a symmetric condition if Trump loses in a landslide? Sure, why not? Crooked Hillary taking Texas, Georgia, Tennessee, Arizona, etc., is pure fantasy, so we would allow an accelerating pay-off if Trump got below a certain threshold -- say, McCain's pathetic showing, which today would yield 180 votes. Offer a linear increase for each vote below 206, until 180, then the square of the votes below 180.

This model clarifies thinking about the 2016 election itself, but you could structure a bet similarly to forecast the Electoral map staying basically the same vs. fundamentally re-drawn by 2020, 2024, etc. At the micro level, though, you'd probably want to make pay-off a function of the popular vote share in 2012, say for the Democrats. This models how difficult it would be to change a particular state's color, regardless of its population size and therefore Electoral vote count.

Red states becoming redder and blue states bluer would not pay off. But for each point in the reversing direction, there would be a linear increase for up to, say, 5 points. Beyond that, pay-off would be proportional to the square of points. California went 60% Democrat in 2012 -- if it only gets to 55%, the Trump supporter gets some multiple of $5, whereas if it returns to being red at 45% Democrat, the Trump supporter gets that multiple of $5, plus some multiple of $100.

And likewise for, say, Texas going back to blue, by a slim vs. a major margin.

Bets structured more along these lines tell us more about how the world works than do the simple "odds" estimates from prediction markets. Structured bets, with different pay-off functions for different scenarios, are more like the contracts for black-swan-prone industries like movies, pop music, and so on. All you have to do is look at the evolution of the Electoral map to see how volatile and black-swan-ish it has been over history.


  1. I'd be open to a non-linear bet, but starting at 269 rather than 206. If Trump still loses, I'm not paying anything. In that circumstance you could drop a1 and just square the margin of victory for either candidate. That should satisfy both someone just interested in the narrow question of who wins, and the angle you find more interesting in how overwhelming the win is.

  2. I've taken part in the DARPA prediction project via Robin Hanson's prediction market. And they did have many non-binary questions with numerical divisions. Payoffs were proportionate to odds.

  3. Which Obama states are you assuming Trump will win, given your ruling out of a bet where you'd have to pay if he lost overall while still getting "only" 268 Electoral votes, improving on Romney's 206?

  4. I'm not a political horse-race junkie who's done detailed analyses of which states will flip under which thresholds. Feel free to treat me like an ignorant sucker blinded by a media narrative focused on personalities who will soon be parted with his money. I've already made one Trump vs Clinton bet here with a commenter (with low stakes, so it's no problem putting more on the same outcome), given that you think Trump will win and I don't it shouldn't be hard to come up with a symmetric bet we both find acceptable.

  5. It was a (mostly) rhetorical question -- to prove that you think Trump has at worst a 50/50 chance of winning, despite what you just said a few days ago about his "dismal" prospects, the window keeps shrinking, etc.

    Dismal would be McCain or Romney. Now even the inveterate naysayer from Minnesota has admitted that Trump has already improved by around 60 Electoral votes, wherever you think they may be coming from.

  6. It's not that I think the odds are 50/50 (I would be unwilling to take the opposite side of the bet I'm offering), but that my projections are hardly precise. I don't actually know the point at which at I'd be be indifferent which side I was on, I just know what I've proposed is a Schelling point, a point at which I already made a bet (aside from the non-linear aspect, which as I've said I'm not terribly interested in) and one that I know should be mutually agreeable to both of us. I've never stated how many electoral votes I expect Trump to get because I don't actually know, just that they'll be less than 270. You have stated you expect him to get more, but if you're unwilling to bet based on that disagreement, then it will indeed be merely a rhetorical move. Do you actually think he'll get something closer to 206? That's the only reason to insist on moving the goalpost to something that strikes me as rather arbitrary.

    If you're not willing to accept symmetrical odds, as if things really are stacked against Trump, simply in the interest of having a bet (I believe Bryan Caplan has had to resort to this sort of thing as well), I'll do something I normally wouldn't. I payout as normal, you only pay half of what the final calculation would otherwise be. The downside is that this isn't enough to show you think Trump will win, just that Hillary isn't twice as likely to.


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