(Ignoring the recent spate of personal attacks…) You don’t have to understand complicated math to understand this. I don’t know a thing about this Bayesian math, or whatever it is. But nonetheless, I shall now make everything clear (waves hands magically…):
For my argument, I shall presume 3,000,000 women, and 3,030 actual rapes performed by whites (or interracials, or whatever we’re debating at the moment). These numbers were chosen for two reasons: to make the math easy, and to make the number of raped women a small fraction of the actual population. I think we can agree that the first is a noble goal and that the second is a reasonable assumption for the most part.
For the moment, no statement about the ratio of white to black women in the population will be made; we will have to make one later, of course, because it DOES matter to the final decision. (It makes all the difference in the world, really.)
Suppose we are given that 99% of rapes are performed on whites. From that, we know that 3000 white women were actually raped, and 30 black women were, give or take a few fractions of a woman. That’s simple enough I don’t expect a lot of argument there.
Now, suppose we also assume that “25% of rape accusitions are false”. Well, what does that mean? It clearly does NOT mean that 25% of women are reporting false rapes; that would mean that there were at least 750,000 rape accusations and only 3,030 rapes, and with 250 liars for every honest women I wouldn’t believe either of the two women in question, race be damned.
No, “25% of rape accusitions are false” means what it says: for every four rape accusations, there is one false one; or put another way, for every three actual rapes, there is one false accusation. So, with 3030 real rapes there are 4040 accusations, and we know that at least 3000 of them are from white women and that at least 30 of them are from black women. The other 1010 accusations are distributed somehow amongst the remaining women.
This much, we know from the numbers we are given. Now, at this point it would be nice to know what the distribution of those other 1010 accusations are. After all, if they’re all white women, then there would be 4010 white accusations, 3000 of which (~74.8%) are honest, with 100% honesty of black accusations; if only black women make false accusations, then there are 1040 black accusations, of which 30 (~2.9%) are true, and 100% of white women are honest. Here are some other possible numbers:
50/50 false claims: 3505 white claims (~85.6% honest) vs. 535 black claims (~5.6% honest)
75% of false=white: 3758 white claims (~79.8% honest) vs. 282 black claims (~10.6% honest)
90% of false=white: 3909 white claims (~76.7% honest) vs. 131 black claims (~22% honest)
99% of false=white: 4000 white claims (75% honest) vs. 40 black claims (75% honest)
Now, I personally thing it’s reasonable to, in a total absence of other evidence, to consider the rate of honesty for a given race on a given topic to be a good ‘credibility indicator’ for a person of that race speaking on that topic. In other words, those numbers up there are how much I trust each woman, based on race alone, when I’m totally lacking other evidence. If I have other evidence, then that evidence of course overshadows the assumption I make based on race, proportional to the credibility and relevence of the other evidence.
So. For black accusations as much credibility as white accusations, the distribution of the false claims has to be the 99%; the same as the proportion of actual rapes between the races. (This is no coincidence.) That’s 1010 lyting whites, and 10 lying blacks. Now, there are some people (face) who already assert that they think that we should indeed assume a 99% distribution of lies to whites. There are also some people (face) who state that the percentace of blacks in the population is irrelevent to the question. People who hold both these positions are racist. If, for example, the population was evenly divided, to flat out assume that white people are 99 times more likely to lie than black people without any other evidence supporting that assumption is preposterous and blindly in favor of blacks over whites. Similarly, to state that we cannot draw conclusions because we do not know the proportion also smacks of racism, because there is a conclusion that fair minded people can draw, and in fact, have no choice but to draw: that out of the population, a given black person is exactly as likely to be a liar as a given white person. To assume otherwise without evidence is to hold an arbitrarily bias against one race or the other.
So. If all women are equally likely to falsely file a rape claim, then the number of false claims from women of a given race should be proportional to the number of women of that race in the population as a whole. (Anything else would be an uneven distribution of liars across races, which might in fact be the case but is fucking racist to assume without some kind of support. This means, if the 50% of the women are black, I refer to my numbers above and determine that an arbitrarily selected black woman’s rape claim is something like 14 times more likely to be false, since around 50% of the false claims can be assumed to come from black women. That is a hell of a difference, and there can be a lot of slippage in the numbers with the credibility of the white woman’s claim still being higher. Even if 90% of women are white, a random white claim is still almost three times more credible based on the statistics. (All of this is easily overriden when actual hard evidence comes to the table, of course. You could be talking about one of the 30.)
When you come right down to it, unless you have hard information about the relative credibilty of the rape claims from each race (in which case you already know which woman is more credible) then the only time when the white and black womens’ claims are equally credible from a statistical point of view is when the proprotion of rapes between the two races is approximately equal to the proportion of women between the two races. Which makes perfect sense, when you think about it.