Pappus' plane 2

nostalgebraist:

aprilwitching
replied to your
post
:
aprilwitching replied to your post “Just had a…
yeah. thats exactly what its like. oh shit. “NABOKOV”. rob. roooooob. no. id been mentally mispronouncing his name for years,
Man, I don’t even know how to pronounce his name. He gives a whole bunch of different pronunciations here, I tend to stress the second syllable for unknown reasons

Possibly the greatest double-dactyl of all time (I don’t know the authorship, beyond it apparently being in the New Statesman):

Higgledy piggledy
Vladimir Nabokov—
Wait! Hasn’t somebody
Made a mistake?

Out of such errors, Vla-
dimir Nabokov would
Sesquipedelian
Paragraphs make.

Source: nostalgebraist

Two Envelopes- A paradox I thought I knew a resolution to

But now I don’t…

Consider two envelopes, and you are told that one envelope contains twice as much money as the other. Call them A and B.

You are handed envelope A, and before opening it, you are asked “do you want to switch to B?”

Obviously, you should be indifferent to the envelopes, but you…

My response to two-envelopes has always been that any distribution that maintains the paradox is at least a little bit pathological, and the structure of your revised set-up indeed has infinite EV (as others have noted).

Let’s say instead of the smallest envelope having 2^n dollars distributed (1/3)*(2/3)^n, you have k^n dollars with the same distribution. For k < 3/2, the EV of the smallest envelope is finite.

Then there’s a 2/5 probability that you’re in the case (k^n, k^(n+1)), and a 3/5 probability that you’re in (k^(n-1), k^n).

EV gain from switching = (2/5)*(kX - X) - (3/5)*(X/k - X)

= (2X/5)*(k - 1) - (3X/5)*(1/k - 1)

= (X/5)*(1 - 1/k)*(2k - 3)

There’s a paradox if this expression is greater than zero, which is true for k > 3/2… nicely matching the requirement that the EV of the smallest envelope is finite (up to the edge case of k=3/2 itself.)

BUT, is a negative EV gain also a paradox? Which you could get from, say, k = 1.4. (Assuming no maths errors in what I’ve written above….) Either this substantially sharpens the paradox, or it’s non-paradoxical for it to be correct to not switch for any X > 1. (Which might be the case: switch if you get 1, hold for all values greater than 1. I haven’t worked this bit through carefully and my intuition is all over the place at the moment.)

R does so much under the hood that when I work with not R I’m temporarily confused “what do you mean I can’t just stick a list of strings into this model?”
On the one hand, I have to put in all the coding choices. On the other hand, it’s good to remember how this shit works.

Spare a thought for those of us who do text processing in R and get forcefully reminded of what R does under the hood every time we forget to specify stringsAsFactors=FALSE when creating the data frame….

slatestarscratchpad:

slatestarscratchpad:

Dear Statistics Tumblr:
I sometimes read paragraphs like this:
Terrie Moffitt and colleagues studied 4,552 Danish men born at the end of World War II. They examined intelligence test scores collected by the Danish army (for screening potential draftees) and criminal records drawn from the Danish National Police Register. The men who committed two or more criminal offenses by age twenty had IQ scores on average a full standard deviation below non-offenders, and IQ and criminal offenses were significantly and negatively correlated at r = -.19.
When I hear that criminals have an IQ on average a whole standard deviation below non-criminals, this makes it sound like IQ is super important in determining crime, and of course this matches my intuitions that repeat criminal offenders aren’t the brightest bulbs in the drawer.
But the number at the end of this paragraph makes it sound like IQ predicts only 0.19^2 = 3.6% of variance in crime. This makes it sound like IQ is so meaningless in determining crime it’s not even worth thinking about.
Do I just have really bad intuitions about what variance means, or what?

Another example of the same phenomenon:
This graph shows what looks like a big IQ-income correlation - I’d sure rather have an income of $160,000 a year than $40,000 a year.
But Jensen states that the correlation between IQ and income is only about 0.4, so IQ only explains 16% of the variance.
I conclude my intuitions are indeed terrible.

Adding to what su3su2u1 wrote, here is some more invented data to show what can happen when you aggregate into deciles:

slatestarscratchpad:

Dear Statistics Tumblr:
I sometimes read paragraphs like this:
Terrie Moffitt and colleagues studied 4,552 Danish men born at the end of World War II. They examined intelligence test scores collected by the Danish army (for screening potential draftees) and criminal records drawn from the Danish National Police Register. The men who committed two or more criminal offenses by age twenty had IQ scores on average a full standard deviation below non-offenders, and IQ and criminal offenses were significantly and negatively correlated at r = -.19.
When I hear that criminals have an IQ on average a whole standard deviation below non-criminals, this makes it sound like IQ is super important in determining crime, and of course this matches my intuitions that repeat criminal offenders aren’t the brightest bulbs in the drawer.
But the number at the end of this paragraph makes it sound like IQ predicts only 0.19^2 = 3.6% of variance in crime. This makes it sound like IQ is so meaningless in determining crime it’s not even worth thinking about.
Do I just have really bad intuitions about what variance means, or what?

Could be something like this: most people regardless of IQ don’t commit crimes, so the correlation is very low. The handful who do tend to have lower IQ’s. e.g.:

slatestarscratchpad:

Gwern did an analysis on LW in response to @su3su2u1′s complaint about effective altruists, showing that controlling for age they donate notably more money than the rest of the LW population. Note that graph is on a log-dollars scale.

Un-logging the y-axis leaves my earlier comments on this topic unchanged. That cyan curve goes through age 30 at less than $400 donated. Taking Gwern’s data and excluding students, unemployed, and people working for non-profits, the median donation by EA’s in the LessWrong survey is $151.

There are a lot of people who you might call “loosely attached” EA’s. This isn’t necessarily a bad thing – it’s good if people re-direct their regular donations to more effective charities. But there’s a mismatch between the EA community broadly defined and supposed EA norms, the latter being adhered to by a much smaller core.

It looks like the majority of the funds are coming from just a few major donors. Do you know if any of those big ones had MIRI/CFAR as their only donations?

Of 59 survey respondents who reported donating at least $10,000, there were 12 people who gave to MIRI, of whom 7 only gave to the MIRI/CFAR/Leverage Research. The two largest of the latter group gave $60k each (one to MIRI, one to MIRI and Leverage).

(For comparison, there were 22 donors to AMF and 22 to GiveDirectly. Ten of the 59 didn’t give to any of the ‘standard’ EA charities – at least some of them have been philanthropists following broadly ‘EA’ principles since well before the EA movement coalesced around that name.)

pappubahry2:

[snip]

Are there numbers anywhere for what percentage of donations went to CFAR/MIRI?

Unfortunately not – the survey just asked for total amount donated and then check the boxes of the charities you donated to. So we have the number of donors to each charity (of those who reported), but not dollar values. I put in a request for a detailed breakdown in future, not sure whether it’ll happen or not.

For what it’s worth, AMF: 211 donors (20 of whom also gave to MIRI and 18 to CFAR). MIRI: 77 donors (27 also to CFAR). CFAR: 45 donors. (Also SCI and GiveDirectly were both more popular by donor-count than MIRI.)

Portrait of EAs I know

pappubahry2:

ozymandias271:

su3su2u1:

ozymandias271:

A lot of EAs are students or people who make less than 10k a year. i only donated a few hundred dollars last year because my income was only a few thousand dollars. It is perhaps more informative to look at the percent of…

comparing these numbers to this:

people making 40-70k and 70-100k seem to donate approximately the same amount

people making more than 100k seem to donate twice as much

this seems broadly ethical to me? upper-middle-class people should donate the same amount, rich people should donate way way more

(I hope I didn’t completely mess up the formatting in trying to re-create the quoted text.)

I have a couple of opinions here.

Simplifying a bit, E in EA comes from two things: donating to more effective charities, and donating more money than you otherwise would (10% being the GWWC standard).
If donation rates by EA’s are broadly similar to those of the general public, then EA is still a very worthwhile movement if the donations are going to effective charities. Which, modulo the MIRI wing of the movement and associated debates, they mostly are. (AMF and SCI are easily the most popular charities donated to by the survey-takers.)
That donation rates by EA’s are similar to the general public is nevertheless a valid point of criticism. “Upper-middle class” is spectacularly affluent by global standards, 10% of such incomes is a modest amount to donate for people who notionally subscribe to EA ideals, and most people in the movement aren’t anywhere near that.
I don’t think that means that EA’s are bad relative to the general public, but as a group we/they (I hope I’m allowed to excuse myself – I donated over 30% last year) are falling short of the ideals and standards that we tell the rest of society to aim for. Which isn’t a good look.