US Doomsday \[C+M]
It's the eve of yet another election result: this time we (or rather US citizens) get to choose between two undesirable outcomes. Once again, it would appear to be "too close to call." Feeling flush from our previous polling success we thought we'd gamble part of our winnings away. This is our punt on Paddypower (not the best available odds, but [M] had an account with them and it allows us to "hedge" a little):
So how did we come up with our gamble? Well, first of all we spent an entire afternoon trolling through polling data on a state by state basis: the US has a complicated electoral system in which the most popular candidate need not win. Instead, in each state there are a number of electoral voters (the number roughly depending on the population of the state), who vote for one candidate (Clinton or Trump) based on the outcome of the popular vote on a state by state basis (plus Washington DC). In most states, all of the electoral voters vote for their states most popular candidate. This makes forecasting the outcome tricky and time consuming (please don't tell our boss...). The key numbers are there are 538 electoral voters in total, and to win indisputably (excluding Trump of course) the candidate needs to get a total of 270 electoral votes. For our analysis we exclude third party candidates for simplicity.
Our analysis is summarised in the following graph. Our "Estimated probability" can be read as a sliding scale from left to right as a good night for the Democrats to a good night for the Republicans. Each of the outcomes can be thought of as equally likely. For instance, we believe that with probability 1/4 the Republicans will get no more than 171 electoral votes and the Democrats will get no less than 367. Alternatively, with probability 1/2 we believe that the Republicans will get between 171 and 201 electoral votes (the range between 0.25 and 0.75). Critically, only 12% of our outcomes result in a Republican majority - which is our probability of a Trump win.
From the graph we can read off our "best guess." We would expect the Democrats to get 335 electoral votes, and there is a 12% chance that Trump pulls off an unexpected victory.
This leads us to our bet: this probability translates to "fair odds" of a Clinton win to be 3/22. Odds more favourable than this are worth a punt (similarly odds of better than 22/3 for Trump are worth a flutter). This however isn't very profitable. From our graph we can see that actually there is a large range in our estimated probabilities in which the outcome is stable - this leads us to the second item in our betting slip. We've put money on the number of Democratic electoral voters (which pays favourable odds), hedged by a Clinton win should we be wrong...
We at least (for financial reasons) hope that Clinton wins! Although being huge Game of Thrones fans, we wouldn't mind seeing a life size recreation of "the wall" being built...
PS - If you would like to know about our dubious back of the pad calculations, then let us know and we will do another post! Don't all rush at once!