Even Dershowitz? Mistaking Odds for Wrong When the Underdog wins

Alan Dershowitz, the famous lawyer and law professor, is clearly a super-smart guy. He recently wrote an article in the Boston Globe, picked up by RealClearPolitics.com, titled "Why It's Impossible to Predict This Election." In supporting his argument, he used the surprise result of Great Britain voting to leave the European Union in July: "Think about the vote on Brexit. Virtually all the polls - including exit polls that asked voters how they voted - got it wrong. The financial markets got it wrong. The bookies got it wrong."

I wrote in my Huffington Post blog right after the Brexit vote that a number of bankers, based on their public comments, did not seem to understand what bookmakers do - and what we all do when we allocate resources based on our assessments of the probability of differing outcomes occurring. When we make a prediction based an assessment of which result has the highest probability of happening, there is some chance things won't turn out as predicted by definition (unless the probability of any other outcome was 0%). So even if the markets predicted that Remain was 90% and Leave was 10%, it doesn't mean that predicting Remain was wrong since the prediction included that 10% of the time Leave would win the day. Leave winning was included in the prediction.

In the case of the bookmakers, it is even more clear they weren't wrong since bookmakers actually offer no opinion at all. Bookies adjust betting odds with the goal of equalizing the amount of money bet on both sides of a proposition. So the high price of betting on Remain and the low price offered on Leave simply reflected that more of the betting public was willing to bet that Remain would win. The bookmakers had to make betting on leave a bargain in order to get the even out the betting on both sides.

The betting houses had no goal to determine the actual probability of either side winning. They only cared what proposition would get enough people to bet on both sides. And because they adjust the odds in this way, to equalize the action on both sides and take a percentage of winners' bets for their fee, whether bookies got it wrong or right couldn't depend on how the vote turned out at all.

If Dershowitz missed this, declaring the markets and bookies wrong, that tells me that a lot of people are doing the same.

Of course, you could still be wrong. You can do the math incorrectly or, in our uncertain world, make an unreasonable estimate of probabilities. Learning from experience means looking back and recalibrating as necessary. If, however, you let the outcome alone guide your judgment of right and wrong, you are unlikely to learn how to do better next time.