assigned-gender-during-childhood

Yep, I'd guess that matters a great deal. (IIRC certain radical feminists dislike male-to-female transsexuals for that reason.)

(Leaving soon, will post math later if anyone is interested in the details.)

Short version: Suppose for simplicity of argument that all the probability of failure is in the portion of the machine that checks whether the received answer is correct, and that it has equal chance of producing a false positive or negative. (Neither of these assumptions is required, but I found it made the math easier to think about when I did it.) Call this error rate e.

Consider the set of possible answers received. For an n-bit answer, this set has size 2^n. Take a probability distribution over this set for the messages received, treat the operation of the machine as a Markov process and find the transition matrix, then set the output probability vector equal to the input, and you get that the probability vector is the eigenvector of the transition matrix (with the added constraint that it be a valid distribution).

You'll find that the maximum value of e for which the probability distribution concentrates some (fixed) minimum probability at the correct answer goes down exponentially with n.

They are also practically non-existent in right wing parties in the West. While being contrarian is a bad sign, getting people from all mainstream political positions to go into sputtering apoplexy with the same input can be a good sign.

I do not accept your contention that people just happen to be exactly the correct degree of racist.

People are usually not "exactly correct" about anything, so statements like this are almost automatically true. But is this your true rejection?

Imagine that tomorrow some magic will turn all people into exactly the correct degree of racists. That means for example that if a person with a given skin color has (according to the external view) probability X to have some trait, they will expect that trait with probability exactly X, not more, not less.

Would such society be more similar to what we have now, or to a perfectly equal society?

Many statistical effects of race are screened off by fairly easily obtained information,

Or would be if people weren't actively rigging said information such that this is not the case. And that's before getting into tail-effects.

Moreover, if you, say, beat someone for being black,

Which really doesn't happen these days. (It's certainly much rarer than someone being beaten up for being white.)

Do counterfactuals just exist eternally in idea space, or do they need for someone to think of them?

Isn't the real problem that people are mishandling Bayesian updates based on race?

At this point I think the problem is that they are updating correctly.

FWIW, I have the opposite intuition. Transgendered people (practically by definition) care about gender a lot, so presumably would care more about those cultural distinctions.

Contrast the gender skeptic: "What do you mean, you were assigned male but are really female? There's no 'really' about it - gender is just a social construct, so do whatever you want."

Does anybody know if this holds for other other preferences that tend to vary heavily by gender? Are MtoF transsexuals heavily into say programming, or science fiction? (I know of several transsexual game developers/designers, all MtoF).

After I posted my comment, I realized that 3 vs 16 might just reflect the overall gender ratio of LW: if there's no connection between that stuff and finding LW interesting (a claim which may or may not be surprising depending on your background theories and beliefs), then 3 vs 16 might be a smaller version of the larger gender sample of 120 vs 1057. The respective decimals are 0.1875 and 0.1135, which is not dramatic-looking. The statistics for whether membership differs between the two pairs:

R> M <- as.table(rbind(c(120, 1057), c(3,16)))
R> dimnames(M) <- list(status=c("c","t"), gender=c("M","F"))
R> M
gender
status M F
c 120 1057
t 3 16
R> chisq.test(M, simulate.p.value = TRUE, B = 20000000)
Pearson's Chi-squared test with simulated p-value (based on 2e+07 replicates)
data: M X-squared = 0.6342, df = NA, p-value = 0.4346

(So it's not even close to the usual significance level. As intuitively makes sense: remove or add one person in the right category, and the ratio changes a fair bit.)