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Six Degrees of Swine Flu

SurveyUSA has some interesting numbers out on swine flu. According to a poll of 1,200 American adults that they conducted yesterday, 3.2 percent — 38 of 1,200 — know someone who has gotten sick with the swine flu.

Three percent does not sound like a whole lot — but when you back the numbers out, it’s really quite something. The U.S. population, at the time I began writing this article, was 306,318,220 people. If we extrapolate out the SurveyUSA data, this implies that 9,700,077 Americans know somebody who has swine flu.

So if 9,700,077 Americans know someone who has swine flu, how many people actually have the swine flu? This is actually not all that straightforward to calculate. But if we assume that: (a) the average person knows about 290 others, as academic studies have found, and that (b) nobody knows more than one person with swine flu (unlikely in practice, since disease outbreaks are localized phenomena), this would imply that 33,449 people in fact have the swine flu! This would come as a surprise to the Centers for Disease Control and Prevention, which currently knows or suspects between 400-500 cases of swine flu in the United States.

Except that — this result is almost certainly illusory (or at least I hope that it is). But it’s interesting to contemplate why it’s illusory. I see at least six probabilities, which are arranged here from least interesting to most interesting:

1. Some people were lying on the survey;

2. Some people pressed the wrong button when completing the survey (SurveyUSA’s polls are conducted via an automated script);

3. People are mistaking all sorts of things which aren’t swine flu — fevers, food poisoning, hangovers, etc. — for swine flu, and reporting results accordingly.

4. Some people interpret the definition of “know” very liberally, such as someone they’ve heard about on the news. Do I know Barack Obama? Do I know Susan Boyle? As far as I’m concerned, I don’t know them — I merely know of them. But some people might answer this question differently.

5. The average person, in the Internet era, has ways to remain in contact with a lot more than 290 other people.

6. When something truly extraordinary happens, second and perhaps even third-order social networks come into play. If someone in your network of 290 people won the lottery, you would probably hear about it almost immediately. But not only that — if anyone in your network of 290 people knew someone who won the lottery, it would be an interesting enough topic of conversation that you would probably hear about this too (and you might still tell a pollster that you “knew” someone who had won the lottery). This might even hold if any of your 290 contacts knew someone who knew someone who had won the lottery.

This same principle would probably hold for the swine flu. If you work in a large company, and the brother of someone in another division in the company (whom you’d never met personally) has come down with swine flu, there’s a pretty good chance that you’d hear about it. Would you then tell a pollster that you knew someone who had swine flu? Quite possibly you would, even though under ordinary circumstances you’d have never known anything about this person. If this person got engaged, or got into a bad car wreck, or enlisted in the Armed Forces, you’d probably never hear about it. But if they got the swine flu, you very well might. It’s not so much who you know, in other words, but what you know about them, that makes this sort of result plausible.

Nate Silver founded and was the editor in chief of FiveThirtyEight.