probability


Like many people, I looked at Nate Silver’s model for the presidential election outcome daily for the last six months. I hoped it would calm me down. It didn’t. I was not calm because his model was predicting somewhere between pretty close and extremely close the whole time, unlike during the 2012 election. Here’s what it looked like on election day–the blue line was the probability that Hillary Clinton would win and the red line was the probability that Donald Trump would win:

538-graph-election-day

A lot of people seemed to have looked at this and decided that Trump had very little chance of winning. That’s not what it says at all, and I think this points to a problem with our math curricula.

We could and should but do not have any kind of grasp of probability by the time we graduate high school. We need the education, because our brains have trouble taking base rates adequately into account. (See the second blurb here for a little more information.) We spend a lot of time learning algebra, which is for a normal person useful only for internalizing arithmetic and for the general brain workout, but we spend almost no time learning about probability. So we have an electorate swung in part by those living in genuine fear of being killed in a terrorist attack, which is a near-zero percent probability, and by those who were blasé about Trump’s chances of winning.

Basic probability is not hard to learn. Any teenager of average intelligence and a week of Dungeons & Dragons under their belt could have told you that Trump could easily win the election. The worst his chances ever got were about the same as rolling a 1 on an 8-sided die. It’s not great odds, but you don’t bet the life of your character on it, much less the fate of your whole game. And that’s the worst it got. It looks like he averaged around the chance of rolling a 1 on a 4-sided die. That happens a lot. Give it a try.

I’d love to see algebra classes replaced entirely by statistics classes, but I’d settle for replacing the first two weeks of Algebra I with an intro to dice gambling. The idea that knowing how to factor polynomials is more important than a real grasp of probability is hurting us.

Advertisements

Jim Berkland seemed to predict a large earthquake in mid- to late- March 2011 somewhere in North America. Watch the footage here. (The Fox commentator is pretty funny. At one point he says to pay attention because “he is a pretty good geologist.”)

There was no large earthquake during that time, but we can’t really know if Berkland was technically wrong, because what he actually predicted was a “high probability” of a large earthquake in North America. If you want to know how accurate a predictor who uses language like this is, you have to track outcomes of a whole bunch of their predictions, not just one. This is what Philip Tetlock does in his research on prediction accuracy–track the outcomes of hundreds of predictions of political experts. He also had to force the experts make specific enough predictions that they would either be true or false, not ambiguous–not always an easy task. Berkland, while casting a wide net, was fairly precise with “large earthquake” and “North America,” though we must wonder whether he would have claimed success if there had been a large earthquake, say, in the northern Pacific.

I’m not sure how many earthquake predictions Berkland has made, but if there have been enough, we could judge his rough accuracy: When he predicts a high probability of an earthquake, does it happen most of the time? When he predicts a low probability of an earthquake does it usually not happen? How about a medium probability?

The point is, if your prediction is of a probability, rather than a certainty of an event, we need to do some statistics to figure out if you’re a good predictor. And this is the form that careful people make their predictions. If, on the other hand, you tend to make predictions about certainties–100% or 0% probability events, it’s quite a bit easier to check your accuracy–as long as you make sufficiently specific, falsifiable predictions. Most prediction by ideologues, for example, set up what Tetlock calls an “outcome-irrelevant learning situation,” a situation in which the predictor can claim they were right no matter what actually happens. Every ideologue, therefore, is in the position to explain what happened, using their own ideology.

An example of that may be the Mayan-calendar predictions. Here is Graham Hancock on Art Bell’s radio show, seeming to predict something happening on December 21, 2012. It is full of talk of cataclysms, the end of the world, tumult, a ball of fire hitting the earth, etc. (And lots of talk about how accurate the Mayan calendar was, as if having a really accurate way to measure time lends credence to your predictions. Better ask the guy who invented the atomic clock!) I bet these guys will be patting themselves on the back on 12/21/2012 if a ball of fire does hit the earth. But if nothing particularly tumultuous happens, will they be wrong about anything? No. They are not precise at all, and they attach no probability to their “prediction.” There are plenty of “just mights” and “maybes” and “a window of about 40 years.” They even say that if humanity gets their act together in some vague way, we might avert what may or may not have been coming. This is a perfect setup for an outcome-irrelevant learning situation.

Tetlock says that when predictors are wrong, they generally either claim to be right in some way, based on the fuzziness of their prediction, or they use one of several “belief system defenses.” The most common of these is “Just off on timing.” The other two major defenses are the upward counterfactual defense, or “you think this is bad?” and the downward counterfactual defense, or “you think this is good?”

If nothing particularly tumultuous happens on 12/21/2011, and we ask Bell and his guest about it, how will they respond? They might use “just off on timing,” and blame our modern, inaccurate calendars. More likely they would claim to have been right, something like, “All the war and bad stuff happening on the earth–this is what we were talking about. It’s just a lot more slow and drawn out than we thought.” There is some, small, chance that they might cop to being wrong. I haven’t listened to Bell in over a decade, and I can’t remember how he handles his predictors being wrong, or if he even addresses it.

Berkland could also claim to be right: “Well, there was a high probability of a large earthquake, but not everything with a high probability happens every time.” A “just off on timing” defense would be pretty weak for him, since timing is everything in earthquake prediction.

The third predictor I’ve been thinking about, though, has given himself very little wiggle room. It takes guts  to make a prediction like this. According to Harold Camping, next Saturday, May 21, 2011:

“A great earthquake will occur the Bible describes it as “such as was not since men were upon the earth, so mighty an earthquake, and so great.” This earthquake will be so powerful it will throw open all graves. The remains of the all the believers who have ever lived will be instantly transformed into glorified spiritual bodies to be forever with God.

“On the other hand the bodies of all unsaved people will be thrown out upon the ground to be shamed.

“The inhabitants who survive this terrible earthquake will exist in a world of horror and chaos beyond description. Each day people will die until October 21, 2011 when God will completely destroy this earth and its surviving inhabitants.”

That’s from his website, which you can see here. I have also heard Camping say that millions of people are certain to die on May 21, 2011, and every day thereafter until the very end, October 21, 2011. I have heard him say “It is going to happen.” I have heard him say “It is absolutely certain.” I was disappointed when I heard him back down from that, recently, saying he can’t be absolutely certain, but he has stuck with “going to happen” and “there is no doubt.”

I wonder how Camping will react if his predictions are wrong. The counterfactual defenses won’t apply at all. It will be very difficult to argue that he was right in some way if there is not at least the largest earthquake ever recorded (that would be at least a 9.6), that all buried bodies are somehow exposed (ideally as the result of the earthquake), that millions of people will die on May 21, and that approximately 7 billion people will die by October 21.

So my prediction is that he will use “Just off on timing” and go back to calculating the real day of judgment. Based on social psychology research, I will also predict that in general, this event will increase believers conviction, rather than decrease it. And if I am wrong, I will do my best to just admit it.

Reanna is reading me a book, called Committed: A Skeptic Makes Peace With Marriage, a memoir about a marriage and the history and culture of marriage. I’m only just into chapter 3, but so far, it’s good.

One thing the author, Elizabeth Gilbert, writes is that in 1967, when interracial marriage was made legal by the Supreme Court, seven out of ten Americans believed that it should remain illegal.

!

Wow. It’s hard to imagine anyone outside of the most racist crackpot seriously defending that position anymore. I wonder how many of that 70% are still alive, and what they think now? Two generations–the Lost Generation (born 1883-1900) and the G.I. generation (born 1901-1924)–have died since then. Two have been born since then–Gen X and Millennial. But two entire generations, Silent and Boomers, are still alive from that time.

I also wonder how many people would still believe interracial marriage should be illegal, if not for that activist-court decision? Could it be that if not for the Supreme Court’s very unpopular interpretation in 1967 that 70% of us would still believe that interracial marriage should be illegal? Would the anti-miscegenation laws have been struck down anyway, by political representatives of the liberal Boomers when they came to power?

And isn’t it easy to imagine that you would have been one of the 30% enlightened people in 1967 and hard to imagine otherwise? Chances are, though, we would have been in the racist camp. This kind of realization is one of the big reasons I doubt the existence of (much, at least) free will. It really seems as if I’ve come to my views on interracial marriage (and most other things) through consideration of facts, but it’s quite likely that the Supreme Court’s 1967 decision had a bigger effect on my beliefs than any of my own efforts have.

Here’s part 2. (And if you missed it, here’s part 1.) Again, if you are either interested or skeptical, leave me a comment and I’ll point you to the evidence.

Statistically, Divorce is Not a Good Strategy for Getting a Better Marriage: 50 to 67% of first marriages end in divorce. 60 to 77% of second marriages end in divorce.

Your Brain Has Trouble Giving Information About Probabilities Due Weight, So Pay Attention to Base Rates: We have trouble taking the actual prevalence of events into account when making decisions. For example, people tend to be more afraid of dying in a plane crash (lifetime chance: 1 in 20,000) than dying in a car wreck (lifetime chance: 1 in 100) or even of a heart attack (lifetime chance: 1 in 5). One reason for this is that we confuse the ease with which we can think of an example to be an indication of how likely something is. Try this: What do you think is more common, words beginning with “r” or words with “r” as the third letter?

If You Test Positive For a Very Rare Disease, You Still Probably Do Not Have That Disease: This is a headline that should come from medicine, not psychology, but psychologists are better at probability than doctors, who are no better than laypeople, at least when it comes to thinking about this: Even with a very accurate test, if a disease is very rare, a positive result is still much more likely to be a false positive than an accurate positive. I’m going to explain this, but if you don’t get it, don’t worry. Just remember the headline. It’s true.

The table below shows a hypothetical situation with super-round numbers to make it easier to get. You have gotten positive results on a test that is 99% accurate for a disease that occurs only once in 10,000 people. Most people figure they are 99% likely to have the disease. They are wrong:

Test Results
Disease Present? Test Results Positive Test Results Negative Row Totals
Disease Present 99 1 100
Disease Not Present 9,999 989,901 999,900
Column Totals 10,098 989,902 1,000,000

Since your test results are positive, you are somewhere in the left-hand column. You are either one of the 99 who both have the disease and whose test results are positive, called “hits,” or one of the 9,999 who do not have the disease but whose test results are positive, called “false positives.” As you may see, even though your test results are positive, you still are 99% likely to be a false positive and not a hit, simply because the disease is so rare.

Yes, this is counter-intuitive. That’s why it’s important. And that’s why statistics are important. Again, if you don’t understand, don’t worry. If you don’t believe it, though, come up with a specific question, leave it as a comment, and I’ll answer it.

If You Need Help, Ask Someone Specific for Something Specific: Bystanders generally do not help people who are in trouble. The bigger the crowd, the less likely someone will help. It’s not because they are bad or lazy. It’s a specific kind of well-documented confusion. Kind of like in the clip below. What you need to know is, if you need help, even if it seems like it should be completely obvious to anyone around, like you’re having a heart attack, falling to the ground, gasping, whatever, point to a specific person and give them specific instructions: “You, in the red shirt. I’m having a heart attack. Call an ambulance.” Do not assume anything will happen that you did not specifically ask for. A corollary of this headline is, if you think someone might be in trouble, don’t assume they would ask you for help, and don’t assume someone else is helping them. Help them yourself. It could mean the difference between them living or dying.

Get Help For Your Marriage When the Trouble Starts (Or Before): On average, couples wait 6 years after their marriage is in trouble to get help. The average marriages last 7 years. That means that most people who come to couples counseling are deeply entrenched in problems that would have been relatively easy to resolve earlier. It is not uncommon for a couple to come in to counseling with a covert agenda to use the counselor to make their inevitable divorce easier. We can do this, but believe me we’d much rather meet you earlier and help you stay together! Also, I’m not joking about “or before.” Couples counselors are well-trained to give “tune-ups” to couples who are doing well. It’s a good idea.

Anger Is Not Destructive of Relationships, Contempt and Defensiveness Are: Everybody argues. Everybody screws up their communications. It’s the ability to repair things that is the key, and contempt and defensiveness get in the way of that.