More Probability Suckage

Source: xkcd

I have often noted (see here too) that we generally suck at math, to our great detriment. I have also noted that we are especially poor at dealing with probabilities. If a weather forecaster says that there is an 80 percent chance of rain and it remains sunny, instead of waiting to see if, in the aggregate, it rains 80 percent of the times when his or her forecast called for an 80 percent chance of rain, we race to conclude — perhaps based upon that single instance — that the forecaster isn’t any good. Data trumps our lyin’ eyes, but we don’t routinely see it (and even deny its efficacy).

Further evidence – as if it were needed – in support of my thesis has been offered this week in the reaction to Nate Silver’s projection that Republicans have a very real chance of gaining control of the Senate later this year. This forecast (“a Republican gain of six seats, plus or minus five”) is hardy earth-shattering to anybody who has been paying attention. The configuration of seats up for election favors Republicans and the Democratic President’s approval ratings are dreadful. There isn’t much reason to expect an upswing in Democratic support either, even though (obviously) almost anything could happen over the next few months. Dealing with probabilities necessarily means being wrong sometimes.

Silver’s projection is particularly noteworthy in that the American Left holds him in especially high regard due to his forecasts of clear Obama triumphs in 2008 and 2012 based upon the data and in sharp contrast to much of the traditional pundit class. As a consequence, in the days leading up to the 2012 election, fully one-fifth of visitors to the website of The New York Times ended up at Silver’s blog, which was then hosted there (Silver has since re-launched FiveThirtyEight as a stand-alone “data journalism” site in conjunction with ESPN). Silver provided comfort to the Obama partisans when the professional wags insisted upon claiming to see a “real horserace.” I wrote about it here.

Now that the data no longer shows what they want it to show, such partisans – just like their Republican counterparts in 2008 and 2012 – don’t know how to react. On the one hand, they set out to denigrate Silver’s forecast (see right, for example, from Executive Director of the Democratic Senatorial Campaign Committee Guy Cecil and Democratic National Committee press secretary Michael Czin). On the other hand, they are using terror arising out of the forecast to try to drive contributions from the fearful faithful. Silver noted the obvious hypocrisy: “At the same time the DSCC is criticizing our forecasts publicly, it’s sending out email pitches that cite Nate Silver’s ‘shocking, scary’ forecasts to compel Democrats into donating.” This rebuke has caused the critics to backtrack, if only a bit. For example, Cecil now claims that “it isn’t hypocritical to say your forecast highlights our challenges while acknowledging it could be wrong.”

But nobody is fooled who didn’t want to be fooled. And that’s really the point.

Nobel laureate Daniel Kahneman offered an interesting explanation for that reality in a conversation with Nassim Taleb (which can be viewed here). Throughout the discussion, Kahneman looks at Taleb’s ideas about risk and “black swans” through the lens of psychology and often highlights the contrasts. When someone in the audience asked why it is so difficult for people generally to compute and deal with probabilities, Kahneman offers an interesting answer. He did not point to innumeracy. Instead, he said, “to compute probabilities you need to keep several possibilities in your mind at once. It’s difficult for most people. Typically, we have a single story with a theme. People have a sense of propensity, that the system is more likely to do one thing than the other, but it’s quite different from the probabilities where you have to think of two possibilities and weigh their relative chances of happening.”

Today’s Democrats, like yesterday’s Republicans, are simply sticking with the “single story with a theme” that they want to believe ahead of probabilistic data that tends to contradict it. They cling to hopes and dreams that are less likely than other scenarios because it’s the reality they want. As I often say, we are convinced that we routinely see things as they really are. The sad truth is that we do nothing of the sort. Instead, we see things the way we really are. The most recent criticism of Nate Silver is simply another instance of the narrative fallacy writ large. And it’s a perfectly human – if erroneous – reaction.

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