This Nerdy Sunday was going to be a comparison of various smoothing algorithms for polling data as requested by Labor Outsider , but I realised yesterday that we have only 40 days to go until E-Day in the US and that the time was nigh to start adjusting the certainty of our State market simulations of the Intrade data – so sorry about that LO, we’ll save the smoothing for next week.
For those of you that have absolutely no idea what I’m talking about here, if you quickly pop on over to the US Election page and read the simulation methodology at the bottom, it will provide all the context and info you need about draws, longshot bias and all of the things we’ll be talking about here today.
When we were designing the State market simulation way back yonder, one of the problems we came across was how to adjust for the fact that as Election Day approaches, we would expect the collective certainty of the predictions made on the Intrade State markets to increase, simply as a consequence of the time being available for game changing events to occur reduces the closer we get to election day itself.
Short term predictions are generally, ceteris paribus, more certain than longer term ones.
There’s a number of ways we could go about it – tightening the standard deviation on some of our probability distributions we use to generate our random numbers being the obvious, but rather than mess with the distributions themselves, we could go down the simple route of simulating increased certainty by increasing the size of our assumed longshot bias in the probability tails.
Since we started running the Sims, we’ve been making the assumption that any State with a Democrat implied win probability on Intrade of 10% or less has a real probability of victory of approximately zero percent.
This comes from the phenomenon on Intrade political markets where political candidates with smallish probabilities of victory never actually win, even though we’d expect in 100 hypothetical elections having candidates with, say, a 10% probability of winning, to see around 10 of those low probability candidates get up.
Yet looking at historical Intrade results on elections, it’s not just candidates with less than a 10% chance of victory than never win, it’s actually candidates that have less than a little over a 30% chance of victory that never win. So as we approach the election, we want our simulations to move from our highly conservative treatment of longshot bias in the tails by using a 10-90 draw for the simulations to a more moderate treatment of using a 30-70 draw for the simulations on Election Day.
With 40 days to go, I started to reduce the width of that draw, from 10/90, to 10.5/89.5 to 11/89 today. Every day we’ll reduce the width of our draw by 1% in probability by taking one half a percent from each end. Come election day itself, we’ll have a lovely 30/70 draw to use.
To see how the win probabilities change as a result of changing the width of the draw used to call each State in the simulations, I’ve been running three simulations on daily Intrade State market data for the last 9 days using three different draw limits: 10/90, 20/80 and 30/70.
As our draw size tightens, it reduces the number of States that are in play (from all current states with Democrat probabilities of victory greater than 10%, moving eventually to just those States with a Democrat win probability of greater than 30%).
At the moment the Democrats are leading in that group of States considered in play above the 30% threshold, and because of the way the numbers of Republican and Democrat safe states combined with the Democrat dominance of the 30-70 states, if things remain the same as today through to election day, the Democrat probability of victory will increase simply as a result of changing certainty.
However, as we approach Election Day, any change in those state probabilities that favours the Republicans will lead to a quick plunge in that Democrat win probability.
If we move on to the simulation results of today’s data using the three draw limits we get:
10/90 Draw
20/80 Draw
30/70 Draw
As we would expect with these changed draw limits, the tighter the draw ,the more dispersed (or rather flattened ) the simulation results as the number of States that are actually up for grabs in the simulation reduces. So as we move on from today towards the election, expect our sim results to start changing in shape from the 10/90 draw through to something approaching the 30/70 draw just before election day.
On another note – when you look at the Intrade national markets, please don’t use the figures from the Contender markets, which on Intrade are under the heading “2008 Presidential Election Winner (Individual)” and contain individual markets like 2008.PRES.OBAMA and 2008.PRES.MCCAIN.
Those markets are legacy markets where people are unwinding old contracts and essentially playing silly buggers far too often for my liking. That sort of behaviour will eventually get washed away with the tide of money in those markets, but why bother when there are far far far superior Intrade markets available that measure exactly the same thing?
Instead, use the effective two party preferred markets of PRESIDENT.DEM2008 and PRESIDENT.REP2008 under the “2008 Presidential Election Winner (Political Party)” heading. They contain no legacy contender pollution. Even though they might be smaller, they’re pure which is what is important here.
4 Comments
I still have reservations about this
In theory, as the election becomes closer the markets should tighten up themselves, because the “time available for a game-changing event” and similar should be factored into the price by the traders. That is, a market that is 30/70 only months out from the election should, all else being equal, drift towards 10/90 as the election approaches. If it doesn’t, either the traders aren’t behaving rationally (which calls the whole analysis into question), or something else has changed the market’s opinion.
Caf – you have reservations? I find that hard to believe!
I think you meant “…10/90 only months out from the election should, all else being equal, drift towards 30/70 as the election approaches”?
We’re really looking for the wisdom of the crowds (or more to the point, the wisdom of the self interested crowd), rather than the unanimity of them.
Looking back at the historical Intrade numbers – they do, on the whole, tend to polarise for the majority of contests as the election draws closer (and we are starting to see that now with the States) – but there are always a handful of States that have uncertainty, where there isn’t 60/40 or 70/30 agreement in the market over which party will win. For a prediction market sim, it’s really those markets where uncertainty exists which are the key to the simulations as we approach election day itself.
Yet even for those States that polarise to probabilities approaching 80% (for example) – in the sims, they have an enormous pollution effect if there’s even a handful of them that carry large amounts of ECV’s. Since 30/70 seems pretty close to the effective cut off threshold for Intrade probabilities just before the election, if nothing else, having a 30/70 draw removes that pollution from States with greater than 70% probabilities since they’re never really in the contest by that stage anyway.
Caf – is your avatar from Bubble Bobble!?
My contention is that the market has both an idea of where the parties currently stand, and the chance of that standing changing between now and election day. To simplify, if you pick a state where the Democrats are well in front, the market will have some estimation of the probability of the Democrats winning, were the current situation to prevail (say 90%: P_now = 0.9). The market also might estimate that there is some small but not insignificant chance of a “game-changing event” occuring between now and election day that throws the switch to Republican (say 20%: P_tampa = 0.2). Then the overall current estimate of the Democrats winning on election day is P_now * (1 – P_tampa) = 0.72, or 72%. As election day approaches though, P_tampa approaches zero, which means the current estimate (ie, the market price) approaches P_now.
In a nutshell, that’s why I think the market prices should naturally polarise as we get closer to election day – so I don’t think we need to apply any additional tricks to effectively make them polarise more. You can also imagine what would happen at the extreme – if there was a market for say, Democrat versus Republican as the 2108 election winner – ignoring the “any other” possibility, it would be pretty much 50/50, neatly illustrating how the market price accounts for time out from election.
Note that this isn’t disagreeing with the idea of longshot bias in general. Just the idea of altering the longshot bias adjustment based on time out from election.
Oh, and yes, it’s from Bubble Bobble