Epistemic Status: No huge new insights, but a little fun, a little free money, also Happy Petrov Day?
Yesterday, with everything happening regarding impeachment, I decided to check PredictIt to find out how impactful things were. When I checked, I noticed some obvious inconsistencies. They’re slightly less bad today, but still not gone.
I figured it would be fun and potentially enlightening to break this down. Before I begin, I will state that unless I messed up this post expresses zero political opinions whatsoever on what election or other outcomes would be good or bad, and does its best to only make what I consider very safe observations on probabilities of events. All comments advocating political positions or candidates will be deleted in reign-of-terror style. No exceptions.
Odds are represented as cost in cents for each contract that pays $1, so they double as probabilities out of 100.
Let us look at the democratic nomination odds, using last. All are 1 cent wide:
Elizabeth Warren 50
Joe Biden 21
Andrew Yang 10
Bernie Sanders 8
Pete Buttigieg 6
Hillary Clinton 5
Kamala Harris 4
Tulsi Gabbard 3
Amy Klobuchar 2
Can be sold for 1: Corey Booker, Tom Snyder, Beto ‘o Rourke
All other candidates can be bought for 1 and cannot be sold.
Adding that up we get 112. We could buy all the no sides for a total of 111 – you can get these prices on no except for Warren, where you’d sell at 49.
That’s certainly some free money. If you sell all of them, you don’t tie up any money, although you do have to deposit, so it’s a pretty great trade, albeit with an $850 limit.
I’ve already done many of the legs of that trade. Some are better than others. Hillary Clinton at 5 is complete insanity. Andrew Yang is trading at 10 because internet. That likely covers most of the reason you can sell the field for 111. Lower them to sane numbers (let’s be super generous and say Hillary Clinton 1, and say Andrew Yang 5) then the field would add to 102. Completing the trade is mostly about freeing up your capital. You also get some value for it being someone not on the above list, as the ‘brokered convention causes weirdness’ scenario is definitely not impossible. The weird thing is expecting that to somehow nominate Hillary Clinton.
The big not-automatically-insane opinion is making Warren 50% to win the nomination. That is rather bold at this stage of things, but we’re thinking about arbitrage and outright mistakes.
Let’s now look at the Presidential odds. For any Democrat, this is almost identical to a two-part bet, where that person wins the nomination and then wins the general election.
Donald Trump 41
Elizabeth Warren 35
Joe Biden 13
Andrew Yang 6
Bernie Sanders 6
Pete Buttigieg 3
Nikki Haley 2
Kamala Harris 2
Mike Pence 2
Tulsi Gabbard 2
Corey Booker 1
Amy Klobuchar 1
That adds up to 114. If you look at actually available prices, you could sell the field for 110. Again, pretty good idea. I’d get on that, and I mostly did.
One could also point out the implied general election win percentages of democrats where rounding isn’t a big deal.
Sum of All Republican odds is 45% (Trump, Haley and Pence) out of 114%, for odds of 39.4%. Thus, Democratic victory should be about 60%. Warren is 50% to win the nomination, so that 70% number is really weird. This does not add up, and makes me reluctant to sell Warren at 50% odds in the primary.
In both these cases, the free money seems real enough. You get to use your capital in both markets if you sell the whole field and then have it free for a third market as well, and you can’t really lose. Doesn’t mean it’s worth the effort, but it’s a nice thing to notice.
Let’s look at Republican nomination odds:
That only adds up to 98%, which makes sense, since if Trump is actually gone then anything could happen. This market seems sane on that level, perhaps even rich. What’s most interesting is that Trump is highly unlikely to not win the Republican nomination and win the presidency, so if he’s 41% to be reelected but 78% to be nominated, then Trump has a general election win rate of 52% (47% if we knock off 10% for the market being inflated by adding up to 114%). But perhaps this is reasonable? If Trump is gone it’s because something brought him down so it’s going to be super hard for anyone else to win? It’s not like much of that probability is that Trump’s health fails, given the time frame.
Also noteworthy is Trump is only 20% to win the popular vote, although the available volume here is very low. That implies a stunning 21% chance that Trump loses the popular vote but wins the election. Put another way, given Trump is reelected, he’s still an underdog to have won the popular vote. The electoral college seems to favor Trump, but that’s a huge probability to put in such a narrow space, even if you assume the states all look identical to 2016. I believe that pre-election, 538 had Trump at 10% to do this, with the polls only a few percent away from that result. How do you get to 20%?
You can sell “Hillary Clinton runs for president in 2020” at 12% odds. Is that a worthwhile return on capital? You could also sell Michele Obama at 8%, Cuomo at 6%, and Oprah or Mark Cuban at 5%.
They have Trump at 88% to be President at the end of 2019 and 73% to complete his first term. They think he is 41% to be impeached this year and 63% to be impeached at all. Congress is expected to work fast. Have they met congress?
There are a number of other similar good bets available. One gets the idea. The catch is that those all tie up capital. Also, if you take risk and win, you have to pay 10% of your net winnings and potentially taxes. Again, three cheers for arbitrage.
Looking at such systems of prices, and looking for opportunity, is often good training as not only a trader or gambler but also for calibration and probability estimation in general, which are excellent skills for anyone to develop.
What Does This Say About Prediction Markets in General?
Not much we didn’t already know. PredictIt has an $850 limit on any one market, for any one candidate or other potential outcome. This does not increase if you do arbitrage. This is why pure arbitrage that frees up capital can continue. I am literally at risk for $44 in the general election market, but that does not allow me to continue to trade.
Other markets in the past such as InTrade have not had this restriction. This results in less egregious versions of the same problems, as you can use bigger size to trade against the mistakes. However, there is no point in fully correcting a mistake, as doing so would offer minimal or no profits. If you have a market that is inefficient, and a chance to trade to make it more efficient, that’s a good trade, but at some point it isn’t worth the time and trouble and capital investment, so you stop. That point is necessarily before full efficiency, but in places like the stock market you can potentially get (in expectation) very close.
In prediction markets, cost of capital to do trades is a major distorting factor, as are fees and taxes and other physical costs, and participants are much less certain of correct prices and much more worried about impact and how many others are in the same trade. Most everyone who is looking to correct inefficiencies will only fade very large and very obvious inefficiencies, given all the costs.
Thus, we see the same inefficiencies pop up over and over again and not be corrected. The most well-known and universal one is that if the probability is under about 40%, the odds will likely be too high. The lower the odds below that, the more (as a percentage of the chance listed) the price will be too high. For low percentages, the people selling the contract are treating it as if it is a bond that pays interest over time, with a tiny default risk, rather than saying that the 7% chance is too high and should have been 5%. One also has to be wary of model error.
In politics, it is also inevitable that anything that sounds superficially good to people on the internet but is unlikely to actually happen is almost always going to trade rich.
If anything, it is remarkable how little difference it made to limit accounts to $850 in trading, beyond there being free cash lying around.
Anyway, thought that would be fun to write up formally given I had been tricked into actually trading the markets, and maybe some of you would get to do some good trades, so I figured why not. Have fun, everyone.