DanielVarga comments on Best of Rationality Quotes, 2012 Edition - Less Wrong

31 Post author: DanielVarga 26 January 2013 03:03AM

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Comment author: DanielVarga 25 January 2013 07:59:58PM *  0 points [-]

It is roughly exponential in the range between 3 and 60 karma.

You can find the raw data here.

Edit: I didn't spot gwern's more careful analysis. I am still digesting it. gwern, you should use the above link, it contains the below-10 quotes, too.

Comment author: gwern 25 January 2013 08:49:54PM *  0 points [-]

The extra data doesn't seem to make much difference:

R> karma <- read.table("<http://people.mokk.bme.hu/~daniel/rationality_quotes_2012/scores>")
R> karma <- sort(karma$V2)
R> summary(karma)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-8.0 4.0 8.0 10.7 15.0 105.0
...
Nonlinear regression model
model: y ~ exp(a + b * x)
data: temp
a b
-0.01088 0.00134
residual sum-of-squares: 22772
Number of iterations to convergence: 7
Achieved convergence tolerance: 3.59e-06

With &lt;10 quotes too

It is roughly exponential in the range between 3 and 60 karma.

Eyeballing it, looks like the previous fit crosses around 40.

R> karma <- karma[karma<40]
...
Nonlinear regression model
model: y ~ exp(a + b * x)
data: temp
a b
-0.01088 0.00134
residual sum-of-squares: 22772
Number of iterations to convergence: 7
Achieved convergence tolerance: 3.59e-06

The fit looks much better:

Quote karma from -8 to 40

Comment author: DanielVarga 25 January 2013 09:06:02PM 0 points [-]

I am afraid I don't understand your methodology. How is a rank versus value function supposed to look like for an exponentially distributed sample?

Comment author: gwern 25 January 2013 09:08:38PM 0 points [-]

How else would you do it?

Comment author: DanielVarga 25 January 2013 10:29:57PM *  0 points [-]

When I stated that the middle is roughly exponential, this was the graph that I was looking at:

d <- density(karma)

plot(log(d$y) ~ d$x)

I don't do this for a living, so I am not sure at all, but if I really really had to make this formal, I would probably use maximum likelihood to fit an exponential distribution on the relevant interval, and then Kolmogorov-Smirnoff. It's what shminux said, except there is probably no closed formula because the cutoffs complicate the thing. And at least one of the cutoffs is really necessary, because below 3 it is obviously not exponential.

Comment author: shminux 25 January 2013 09:19:21PM 0 points [-]

I expected something like this or the section thereafter.

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