What Are Probabilities? 15:01
A probability is the likelihood of an event occurring. In this lecture, Antony Davies reviews common cognitive biases that can result in misestimations of probabilities.
Antony Davies: I want to talk a little bit about probabilities. When people talk about probabilities, they tend to associate them with things that are obviously random. So flipping a coin, rolling a dice, whether your particular stock is going to go up or down. We think in terms of probabilities where those things are concerned.
But where other things in life are concerned, actually I think where most things in life are concerned, we tend not to think in terms of probabilities or absolutes. [00:00:30] You say things like, “It’s gonna rain today.” How do you know it’s gonna rain today? “Well, because they said on the news that it’s gonna rain today.” Really it’s a probabilistic situation. There’s a probability that it will rain, there’s a probability that it won’t.
Now we understand that if it’s a 50 / 50. But if you get up in the morning, and it’s completely overcast, and dark and scary skies, and all of this. The guy on the news says it’s gonna rain today and I ask you is it going to rain today, your response is likely to be yes. I say, “Are [00:01:00] you sure?” You say, “Yes, I’m sure it’s gonna rain today. Look at it.” I say, “Is it absolutely going to rain today?” You say, “Absolutely, it’s gonna rain today.” That’s where we go off the rails.
Our tendency is, when probabilities get particularly high or particularly low, we immediately go to thinking terms of absolutes. The fact is, there are no absolutes anywhere.
You tell your friend, “I’ll meet you downstairs at noon for lunch.” Are you going to meet your friend downstairs at noon for lunch? [00:01:30] Well, yes. You might get a phone call that distracts you. “Well, I can talk on the way down.” Okay. You might trip on the way out the door and break your leg and now you’re not gonna go down there. You say, “Yes, but that’s not gonna happen.” But it could.
Notice all the sudden, probabilities come back into play. So it is not the case I will absolutely meet you at 12 o’clock for lunch. There’s a 99.9 percent chance I will, but it’s probabilistic, it’s not a certainty.
This [00:02:00] tendency to think in absolutes, causes us to miss some important things when it comes to probabilities. For example, people on average tend to be far more afraid of flying than driving. You see on the news an airplanes crash and you’re thinking, “Oh, well these are dangerous things. I need to be careful flying.”
What you tend not to see on the news are car crashes. Now if it’s a particularly [00:02:30] bad one you’ll see it, but generally you tend not to see them. So when we think about probabilities, we associate flying with some probability of mishap. But we don’t associate driving with a probability of mishap. We think of driving in much more absolute terms.
Of yes, I’m a careful driver and nothing will happen. What we miss in thinking of terms of absolutes, is the opportunity to weight these two things of which both are probabilistic. If you look at [00:03:00] the numbers, in 2013, 35 people in the Unites States died in commercial plane crashes. That same year, 34,000 people died in car crashes.
Interestingly, the reason you see the plane crashes on the television and not the car crashes, is because they’re rare. The point of the media is to make money selling advertising. Of course, they’re gonna inform you. But the way they stay in business is by selling [00:03:30] advertising. The way they sell advertising is to get your attention, get you watching. The way I get you watching is by showing you things that are uncommon.
Interestingly, seeing in that light, a probabilistic light, the news is really a list of things that you don’t have to worry about harming you. It’s the things that don’t appear on the news that are likely to harm you.
Student: So probability, [00:04:00] it sounds like sort of an intersection between probability or maybe a mix up between probability and text book psychology. It sounds like a lot of heuristic models. Things like anchoring or you’ll say, “Okay, this person’s age might be between 15 and 75.” We sort of use that as an anchor and say, “Well, it’s more likely to be a little older than we might expect.”
It seems like, in the way that you’re describing that, a lot of what we consider to be probability, [00:04:30] is just some sort of heuristic that’s skews data.
Antony Davies: Yeah, absolutely. I would say that it’s not that heuristic is skewing the data, it’s skewing our perception of what’s going on.
Good case in point, this is an emotional reaction. When people talk about assault rifles. Of course, the word itself is jarring, so you immediately associate it with badness. These are things that are gonna harm people, we need to get rid of them.
[00:05:00] Following your gut like that, you’re relying on these mental heuristics, which are influenced by your natural biases, and emotions, and this sort of thing. Things that have nothing to do with probabilities. If you look at the statistics, the probabilities, the number of people who are killed in the United States by fists and feet is twice the number that are killed by the number of rifles. All rifles combined, not just [00:05:30] assault rifles.
Yet, we don’t have serious conversations about banning fists and feet. Now notice what’s happening here. We have a confluence of emotion and fact. One of the things that people tend to do, that we have to guard against, is thinking that the facts somehow are heartless, they’re not human.
So if I say, “Well let’s talk about the [00:06:00] probabilities of death.” Immediately people start to shut down. “This guy doesn’t care about human life.” It’s not that at all. If you’re going to make a choice for society, we should ban this, we should ban that, or we should invest in this or not invest. Everybody should have this product or not have this product. Whatever policy we are going to have for society, you’ve got to look at the probabilities because you’re going to impose a rule on everybody.
The rule will apply well some [00:06:30] places, and poorly others, and kind of okay in other places. But what’s important is what happens on average? Because we’re apply the rule to everybody, what happens on average to this society when we apply this rule? That requires looking at, coldly, at the probabilities. Say, “Look. The probability of being killed by a rifle in the United States is one half the probability of being killed by feet and fists.”
That’s not to say that we should be unconcerned with rifles. [00:07:00] But it is to say that we should be half as concerned about them as we are about fists and feet. One problem we encounter with probabilities is this emotional attachment that we have and in the bias of seeing things on television versus not.
Another problem we have with probabilities, is we tend to regard things that we hear repeatedly as being more true. [00:07:30] I’ll give you some statistics to look at. We hear the phrase, “the rich need to pay their fair share”, talking about taxes. Much of this conversation, when you hear people talking about the rich paying their fair share, invariably someone will pick someone. Be it Mitt Romney, or someone else who makes multi tens of billions of dollars and who apparently paid very little taxes.
We say, “Well, look at this person.” [00:08:00] What we’ve done are two things. One, we’ve repeated something that we hear, that the rich don’t pay their fair share. We pointed to an anecdote, a specific example. That combination of repeating this thing and showing an example that appears to support this claim that we’re making, kind of starts to encode this claim in some sort of aura of truth.
When we start to encode the claim in an aura of truth, we miss [00:08:30] the opportunity to actually look at the numbers and see what the truth is. What are the actual figures for the rich versus the poor. This becomes very interesting if you look at data for the United States. In a beautiful twist of cosmic karma, you can find this data on the White House website.
What you’re seeing here is the average effective income tax rate for various income categories in the US. These numbers, of course, fluctuate [00:09:00] from year to year. This is the latest year that there’s data available for, which is 2011 maybe 2012. But the data year to year does not change much from what you see here.
What you’re seeing is … First off, we’re talking about the average effective income tax rate. What that means is, it’s not the statutory rate, the rate that by law you’re required to pay. Rather, we find this number by taking all of the money that [00:09:30] you paid to the IRS. After you do your accounting, and legal gymnastics, and you have write-offs, and exemptions, and off shore whatever it is that you have.
Let all the dust settle and answer two questions. First, how much money did you pay to the IRS? Second, what’s your income. The first divided by the second is this, this is the average affective income tax rate. What you see is … Now remember, there are exceptions. This is the average for each group.
The average American [00:10:00] amongst the poorest 20 percent of Americans, pays about two percent of his income in taxes. Middle income Americans pay about 11 percent. The top one percent pay almost 30 percent of their income in taxes. You could argue whether or not this is fair. That’s an interesting argument to have. But, to start the discussion of what is fair, you’ve got to start from the statistics that currently exist and this is [00:10:30] the current state of affairs.
One of the reasons many people have this perception, that the rich don’t pay their fair share, is because we repeat it. You hear it and it must be true because everybody says it. So I say it and I become one of the people who is everybody, who is saying it. Before you know it, this has taken on a life of its own.
So with probabilities, be careful about observation. Bias is stuff you see on the news, that is likely not to hurt you. It’s the stuff that you don’t see that will. [00:11:00] Be careful about repetition, things that you hear repeated aren’t necessarily true simply because they’re repeated.
Third, be very careful about using your heart and good intentions to address problems that require the use of statistics. Case in point, in 2001 shortly after 9/11 actually, a teenager in Florida flew [00:11:30] a Cessna plane into a building, killing himself. There was many questions about what was going on.
The authorities relatively quickly determined this was not a terrorist event. But after some digging, it was discovered that this teenager was on a prescription drug. There were many others throughout the country who had similarly [00:12:00] committed suicide who are on this prescription drug.
So this led to a call following our feelings, and our heart, our good intentions. A call to the FDA to ban this drug. Notice what happens here, you feel for the kid, you feel for the parents, you feel for all the parents of the other kids who committed suicide and you want to do something. Clearly there’s this connections and you’ll hear people say, “Well wait a minute. Let’s look [00:12:30] at the numbers and see if really this drug is causing the suicide.”
You’ll hear in response, “It doesn’t matter. If it saves just one life, we should ban this drug.” So the argument you get in response is almost one of the statistics don’t matter because life trumps them. Even if, banning this drug doesn’t save them, it might save one of them. If it saves one of them, it’s [00:13:00] worth all the effort. Fine, let’s go and ban it.
Here’s what happens when we apply statistics to the event. If you compare the number of teenagers in 2001 who were taking this prescription drug to the number who weren’t, and the number of teenagers in 2001 who committed suicide and those that didn’t and you cross reference the two data sets. What you find that is [00:13:30] the probability of a teenager committing suicide when they’re on the drug, is about one tenth what the probability is of them committing suicide when they’re not on the drug.
That is, when you put aside your good intentions and your heart for a moment and look, some would say heartlessly, at the data. Look logically at the data. What you find is that the drug was actually contributing to a lower suicide rate. [00:14:00] Why is this the case?
Well, it turns out that the drug in question was one for severe acne. Of course being teenagers, you’re concerned about do you fit in with your peers and so on and so forth. Acne is a negative contributor to fitting in with others and being kind of what teenagers think is normal. The drug was helping this problem and thereby reducing the teenage suicide rate.
We don’t see that unless we step back, take a deep breath, and think about the statistics as opposed [00:14:30] to thinking about our good intentions. We came very close as a country to banning a drug, far from saving at least one life. Banning the drug would have cost teenage lives.