Suppose astute observers of the political scene Manny, Moe, and Jack want to demonstrate their prognostication skills in a wager, and they decide to show their acumen by predicting the number of delegates with which Donald Trump arrives at the Republican Convention this July. Now the standard way to do that would be for each to put, say, $10 into the pot and pick a number. The one who comes closest to Trump’s actual number of delegates wins; ties split the pot. A pretty plebian way to proceed, but it serves well for the unimaginative.
However, Manny, Moe, and Jack are a bit more sophisticated than that, and want to wager like the ‘big kids’ do. They realize that each stating a single number does not really capture a complete representation of anyone’s uncertain knowledge since Trump’s actual number is really a random variable that will be ‘drawn’ from a probability distribution that defines the likelihood of a number of delegates from a range of such numbers. So they agree that each will submit their distribution for Trump’s delegates. Being aware of the nifty properties of the MAB distribution (here) for capturing such subjective knowledge, they decide to use it, and each submits his 4-tuple [low, high, most likely (or best guess), confidence]. They agree to split the pot pro rata on their resulting likelihood scores.
When the actual number of delegates becomes known, so will the likelihood value from each of three submitted distributions, say, 0.07, 0.34, 0.21. This means that Manny gets 0.07/0.62 = 11.3%, Moe gets 0.34/0.62 = 54.8%, and Jack gets 0.21/0.62 = 33.9% of the $30 pot, or $3.39, $16.45, and $10.16 respectively. Not exactly rocket science, but it is easy to calculate and yields the correct way to pay off bets that reflect the quality of each bettor’s knowledge.
(If this wager required no initial submission of funds, then the bet is reconciled by Manny sending Moe $6.45, and Jack $0.16. Easy money.)
So now I invite our equally astute RR readers to submit their MAB 4-tuples for the pre-convention delegate counts for as many of the five candidates as they care to prognosticate. Submit your entries before 2359PST 27 April. Since I don’t want to handle any monies, we can make this go-around be cashless and just compare likelihood values to see who really would have taken home the bacon. To make things easier, I’ll do all the heavy lifting in calculating the resulting likelihoods and post them with appropriate fanfare. Or you algebraically comfortable can do your own using the MAB formula given in the above link.
If this draws enough interest, we can then do it again (maybe even for real) with the presidential election wherein readers can submit their MABs for the percent popular vote and also the electoral college vote in the presidential election. This should demonstrate the quality of the many claims of who will beat whose ass that have been made in these comment streams by several strident and determined voices.
To help you generate your MABs, here are the current delegate counts before tonight’s primary results are reported (click on figure to enlarge).