xkcd's new companion series rocks

[I spent the winter writing songs about getting better]

http://what-if.xkcd.com/

Only 13 entries so far, but very awesome. I read all of them while at work. Great questions and the fact that he actually bothers to think them over and answer them seriously is great.

[homelycooking]

Munroe's webcomic is really pretty lousy, but the what-if series is fascinating. He should drop XKCD and work full-time on this new project.

[Simfan34]

We need more of this stuff to get people into science. Brilliant.

[I spent the winter writing songs about getting better]

Munroe's webcomic is really pretty lousy

What.

It might be past its prime, but there's standard by which it could be considered "lousy". The comics from the hundreds to about the 400s or so are enough to make xkcd the best webcomic of all time. Even currently it's still better than at least 80% of comics.

[homelycooking]

Munroe's webcomic is really pretty lousy

What.

It might be past its prime, but there's standard by which it could be considered "lousy". The comics from the hundreds to about the 400s or so are enough to make xkcd the best webcomic of all time. Even currently it's still better than at least 80% of comics.

You prefer XKCD to "Perry Bible Fellowship"? I think the latter is far more artistically beautiful, more clever, more ironic, more subtle in its humor and its intellectual appeal...

[I spent the winter writing songs about getting better]

I just submitted a question:

"If every person in the US was assigned a new address at random, how many people would keep the same address?"

BTW, Nate Silver even "submitted" one! http://what-if.xkcd.com/19

[Mr. Morden]

I just submitted a question:

"If every person in the US was assigned a new address at random, how many people would keep the same address?"

Isn't the answer 1?  Assume 300 million Americans (exact number doesn't actually matter).  Then, probability of a given person getting their original address back = 1 / 300 million.

So the expectation value would be 300 million * 1 / 300 million = 1.

I mean, you can't know for certain, because it's random, so it might be 0.  It might be 2.  It might be 3.  But the expectation value would be 1.  Unless I'm missing something?

[Kitteh]

A friend of mine submitted the question "how long would it take to eat an entire elephant?". The question is a little more complicated then it sounds, given that only certain parts of the elephant are eatable.

[True Federalist (진정한 연방 주의자)]

I just submitted a question:

"If every person in the US was assigned a new address at random, how many people would keep the same address?"

Isn't the answer 1?  Assume 300 million Americans (exact number doesn't actually matter).  Then, probability of a given person getting their original address back = 1 / 300 million.

So the expectation value would be 300 million * 1 / 300 million = 1.

I mean, you can't know for certain, because it's random, so it might be 0.  It might be 2.  It might be 3.  But the expectation value would be 1.  Unless I'm missing something?

Actually the expected value will be greater than 1 because people don't have individualized addresses, so people who come from multiperson households have a higher chance of being restored to their original address, assuming each person address will be serving the same number of people after the shuffle  You might think that the EV would then simply be the average household size, but you'd be wrong. The actual result will depend on the distribution of household sizes.  Consider a simple case of a four person country with two households.  The odds of people returning to their own household are different for the case of two two-person households.  With the equal sized households, the EV is indeed the 2 one might naively expect, but with a one-person and a three-person household, the EV is 2.5.  I'd have to dig out some combinatorics I haven't used in a long while to come up with a general formula.

[Mr. Morden]

I just submitted a question:

"If every person in the US was assigned a new address at random, how many people would keep the same address?"

Isn't the answer 1?  Assume 300 million Americans (exact number doesn't actually matter).  Then, probability of a given person getting their original address back = 1 / 300 million.

So the expectation value would be 300 million * 1 / 300 million = 1.

I mean, you can't know for certain, because it's random, so it might be 0.  It might be 2.  It might be 3.  But the expectation value would be 1.  Unless I'm missing something?

Actually the expected value will be greater than 1 because people don't have individualized addresses, so people who come from multiperson households have a higher chance of being restored to their original address, assuming each person address will be serving the same number of people after the shuffle  You might think that the EV would then simply be the average household size, but you'd be wrong. The actual result will depend on the distribution of household sizes.  Consider a simple case of a four person country with two households.  The odds of people returning to their own household are different for the case of two two-person households.  With the equal sized households, the EV is indeed the 2 one might naively expect, but with a one-person and a three-person household, the EV is 2.5.  I'd have to dig out some combinatorics I haven't used in a long while to come up with a general formula.

Ah, yes, I guess I didn't quite understand the hypothetical properly.  I had thought that each family would remain intact.  In that case, the expectation value would be one household, however many people that would include.  But if we're allowing families to split up, and just giving each individual person a random address, which they might end up sharing with one or more unrelated people, then it's a bit trickier.

[True Federalist (진정한 연방 주의자)]

Thinking on it some more I think the expected value would be _Σk²H_k/P, where H_k is the number of households of size k and P is the total population and the sum is taken over all values of k.  The lower bound on that would be the average household size, but the more uneven the distribution of people into households is, the higher the value will be.