In a crowd of 100 where 2 are going to arbitrarily win/lose/have an accident/die/...; the probability of 2% applies to the group. For any given individual the probability of the 'event' is either zero or one. Probabilistic stats are derived from and pertain to the group, not the individuals therein.

Expand full comment


The probabilities are intended to represent forecast uncertainty. For the 2008 paper I used the forecast simulations of Nate Silver which were based on variation in polls. Another version of forecast uncertainty is here:http://www.stat.columbia.ed...And another version (for the 1992 election) is here:http://www.stat.columbia.ed...

Details change with the forecasting model but the general conclusions, and the order of magnitudes of the probability calculations, don't change.

Expand full comment


I went through your paper some more, and you are definitely doing something wrong in how you come up with the probability at 50/50


Expand full comment

On Extremely Rare EventsIt's 2006. JH is running a trading desk at UberBank. He takes the elevator down to see Kirt, a quant in a cube:

JH: Hi Geekboy! Wazzup! Here's a file with a really great deal you gotta model for me.Kirt: No problem, I'll put the numbers through our customized value-at-risk model tomorrow afternoon, let it run overnight, and get your answer to you right away.JH (shooting the monogramed French cuffs of his bespoke English shirt): Um, actually, Mr. Rocket I really need this today. Like in 30. I've got tickets to the game in the corporate box tonite.Kirt (looking at the file): I see, another mortgage structure with 4 tranches.JH: Yeah, yeah a guy I have a great relationship with from ReallyAncientInvestmentBank told me all about it at his bowling party. It's a fantastic deal. We can make 14%!Kirt: Bowling party?JH: Oh it was so great. With topless Russian models serving Japanese whiskey.Kirt: Those lower tranches with the high return carry a lot of risk, JH.JH (checking his Blackberry): Just gimme a quickie run now, ok? I'm authorized to take on a lot more risk this year, you know the guys up top want to post 20% profits.Kirt (starting the model): Ok, here goes. . .(time goes by) Uh-oh. Look at this. . .JH: Wow! It looks like a snake swallowed a woolly mammoth! Look at all that safe profit in the big fat hump.Kirt: JH, look at that bump in at the end.JH: That's just the head of the snake.Kirt: No, JH, that's a risk spike in the tail.JH: But look at that hump! That much money would boost my bonus level and I could definitely make it on the corporate Platinum Club cruise. (dreaming) I could go to ChicBar and pick up one of those sulky Hungarian girls who doesn't really speak English. What lovely bones. If I gave her some heroin and a Cartier bracelet, she'd go on the cruise with me. That would be great!Kirt: JH, I don't feel comfortable with this. Why don't you just take the super-senior tranche and call it a day?JH: Look, this risk is low in any year right? I mean, extremely rare?Kirt: But this is a multi-year deal, JH. The risk builds every year.JH: Why should I care about any extremely rare events, ever?Kirt: Because after 3 years you have a 10% risk of losing everything. I mean it. It could be a disaster.JH: Hey Propeller head, this deal makes money for you too. (Checks his chunky gold watch) Man, I gotta go. Are you gonna sign on this or not? TrustedRatingAgency gave this a AAA, you know.Kirt: TrustedRatingAgency was paid by your bowling buddy at ReallyAncientInvestmentBank to put this deal together and give it a gold star, JH.JH: No problem. All I have to do is take out a credit default swap to insure this against ReallyAncientInvestmentBank with AIG. It's a no-brainer. Just sign it off, ok? (Exits cubicle, stage right)Kirt (IMing his old physics pal Didi, now also a quant, at SwissGeantBank): I really miss medium-energy particle physics sometimes Didi. The jerk didn't even stick around long enough for me to tell him that subprime default rates are in reality running at 3 times the rate our algo assumes. This job sucks.Didi (IMing back): Think about it Kirt. Remember how you hated living like a monk in a trailer with 7 other post-docs eating Ramen noodles.Kirt: I like Ramen noodles. Now that I'm rich, I only eat more Ramen noodles.Didi: Those were the days. Let's say we meet at 8 at the Vivaldi and play some Go.Kirt: That would be great. Tiramisu for dinner.Didi: Yeah, the Diet Coke's on me.

Expand full comment

JH, I advise not eating. The odds of your dying of starvation in any five minute period is very low, so why bother ever eating?

Similarly, 40,000 Americans (and 1.2 million worldwide) die in crashes each year, but your odds of crashing on any particular trip are very low. Therefore you should feel free to have a few beers and drive blindfolded, unbelted, while holding a spiked metal object in your lap. Even if that makes you 100 times more likely to crash, 100*0=0. Cancel that insurance, too.

Just because extremely rare events happen thousands of times a day is no reason for you to take any precautions against them.

Expand full comment

"(a) the event happens over and over again so the total probability is not tiny (that's why it makes sense to care about auto safety when you drive to work this morning)"

One day I will have an accident on the way to work. But, that's not going to factor into my decision of whether or not to go to work on any given day because on any given day it's an extremely rare event. Someone is going to die on their way to vote, but that doesn't change my decision whether to vote or not. Someday an election will be within one vote, but that doesn't change my decision whether to vote or not.

I'm very much an it-won't-happen-to-me person. And, for the most part, I'm going to be right about that. "It", whatever that is, won't happen to me. But, I do realize that something, sometime is going to happen to me. What am I supposed to do about it, though? How is that supposed to change the choices I make. I don't know what that something is or when that sometime is. I can take all the precautions I want on the road to prevent one extremely rare event then the next thing I know I'm shot in my own home (another extremely rare event) because I don't own a firearm. I can take precautions on the road and arm myself in my home and the next thing I know a wildfire (extremely rare where I live) burns down my home.

"(b) the event is extremely unlikely, but if it happens, it has a huge effect (that's why it makes sense to vote and to worry about asteroid impacts)."

I'm confused. An asteroid impact wouldn't have a huge effect? Also, one reason not to vote is because one doesn't think one candidate over another will have a huge effect. Sometimes, there's just not much difference.

Extremely rare events are so unlikely that their probability might as well be 0. Even if it has a huge effect, a huge effect multiplied by 0 is still 0.

Expand full comment

Andrew, sure. But that can largely be lumped in under "more altruistic" - my understanding is that the data shows that very few voters will say, "I'm voting my own interests, which are no better than anyone else's, but they are my interests and benefit me and that's what I'm trying to do." So if you don't reason like this, but rather believe that you are acting prosocially or in a fashion that is "right" in a transpersonal sense, then you'd have to believe that your prosocial values are righter than those of the average current voter.

Expand full comment

JH: Because (a) the event happens over and over again so the total probability is not tiny (that's why it makes sense to care about auto safety when you drive to work this morning), or (b) the event is extremely unlikely, but if it happens, it has a huge effect (that's why it makes sense to vote and to worry about asteroid impacts).Or some combination of (a) and (b).

Expand full comment

Eliezer, only if you assume that the goal of voting is to select the best candidate, as opposed to giving the population what they ask for.

Many people hold self-determination as an ideal in and of itself, which is incompatible with letting smarter people choose for everyone (even if the results are arguably suboptimal).

Expand full comment

"Even if you don't care about voting, these issues--how to compute probabilities of extremely rare events--are relevant in other decision settings."

It's extremely rare that my vote will swing an election. Therefore, it doesn't factor into my decision whether to vote or not. While more likely, it's also extremely rare that I will die in a car accident on the way to vote. Therefore, it doesn't factor into my decision whether to vote or not. Both events, for all intents and purposes, have a probability of 0. So, why should I care about any extremely rare events in any decision setting?

Expand full comment

Unnamed: It depends whether you consider a possible voter who is deciding whether to show up, or a definite voter who is deciding which way to vote. Luckily these numbers are large enough in order of magnitude that we can be sloppy about factors of 2.

William: I'm not looking at voting as something people do for personal benefit. Our key point is that voting is a personal action that has a small chance of making a big difference for the whole country.

Tim: Yes, that was a typo.

Eliezer: You don't have to feel that you're smarter etc. than the average voter. It is enough to feel you have different interests or a different attitude than others. For example, if you favor John McCain's economic policy (say), you don't have to feel that you're smarter than Paul Krugman, Tony Rezko, or even the average Democratic voter, you just have to feel that you have a different perspective on economic growth than they do. You might argue that it's irrational for voters to have different attitudes on the economy, but given these different attitudes, if you're voting it's rational to decide your vote based on these beliefs. (By analogy, you might feel it's irrational to believe in organized religion, but if you do, it can be rational behavior to spend a few minutes with the map one day figuring out the most efficient route to church.)

Expand full comment

(that is, smarter / more altruistic than the average voter)

Expand full comment

If voting is primarily a collective action (which I agree that it is) then shouldn't you only vote if you believe yourself to be smarter, more informed, or more altruistic than average? This reveals an entirely different form of voter bias.

Expand full comment

24 out of 300 million is about five times 1 in 60 million. So, according to these numbers, the chance of your vote making a difference is about five times, on average, as being killed in a car accident on the way to the polls.

I make the car accident about five times more likely - based on the same figures.

Expand full comment

"I do it because not voting is for the clueless and the parasitic." -William Pietri

William, have you ever met a principled non-voter? I assure you that they are much less clueless than the median voter. Also, when people vote in bureaucrats that direct tax collected money towards special interests and wasteful pet projects, why is it the non-voters who are parasitic? It seems to me, the opposite case can just as easily be made.

Expand full comment

I'm puzzled by the notion that voting, an essentially communal act, can be usefully looked at mainly as something we do for personal benefit.

Helping run my country, state, and city is something I do because that's an end in itself. I do it as part of shaping the context in which I'll accomplish my personal goals and which my descendants will grow and thrive. I do it as one of the ways I express my opinions on how the world should be. I do it because not voting is for the clueless and the parasitic. I do it because I'm a citizen, and fully embrace both my rights and duties.

I guess I'm willing to accept that those motivations are irrational in the economic sense of the term, just as long as economists are willing to accept that shoehorning everything into that framework is irrational in the common sense of the term.

Expand full comment