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July 13, 2018 | 3 Comments

Ireland Worries Trans Women Can’t Secure Abortions

Ireland, a democracy, voted to purge its constitution of language preserving of life and so install abortion. Proving that the will of the people, when the people’s will turns out to be an empty peanut shell, should not be relied upon to decide matters of life and death.

You will say that abortion is the price to be paid in democracies, where everything is up for vote. Including right and wrong. Better to let the will of the people express itself than cause bad feelings and be accused of disenfranchisement.

Well, you must be right because many agree with you.

Anyway, that is not our point today. The constitutional purgation was only the first step on the road to the mass killing of the youngest members of its society. Step two required the Irish government to draft a law specifically allowing the killing. One imagines it mandates the types of vacuums, the sharpness of knives, how to dispose of the bodies, the price card for miniature livers, that sort of thing.

Enter the headline from the Irish Times: “Abortion legislation: ‘woman’ reference, 28 days, consent and other changes.”

“Say, Briggs. Why is ‘woman’ in scare quotes?”

Why, I’m glad you asked. Here is the sub-headline: “Some believe ‘woman’ reference in abortion Bill may exclude trans people.”

Woman reference:

The Bill refers to the pregnant woman throughout. It clarifies that “woman” means a female person of any age. Many believe this may exclude transgender people. It is understood the Minister for Health Simon Harris has received advice to the contrary but is willing to examine the issue further.

Trans insanity is the most hilarious form of insanity. Grown people are fretting a man pretending to be a woman can’t get an abortion.

Money can’t buy that kind of comedy. You, dear reader, get it for free. Like this.

A deluded pregnant woman walks into an abattoir, says ‘I’m a man. I want you to kill my child.’

Knife-wielder says, ‘Sorry, mister. We only do women. It’s the law.’

Ireland is now officially a clown country. Strike that. Not officially. It will only be official once the Minister is brown beaten into clarifying what he mean by “woman.” Any answer, any answer at all, except “Are you some kind of idiot?”, makes the clown-country status valid. I don’t know what Paddy Power would put the odds at, but I’d say they’re darn good.

July 12, 2018 | 14 Comments

Western Colonialism Did Some Good

Those who lived where the Aztecs once ruled must thank God for Western colonialism. If it wasn’t for the glorious religion of the Spanish, Mesoamerican governments might still be cutting the beating hearts out of prisoners.

That good—the ending human sacrifice—came from Western colonialism. Yet to say that any good came from colonialism is academic heresy. To speak it is a felonious thought crime and an offense worthy of banishment from the Ivory Tower. Professor Bruce Gilley learned this when he published the peer-reviewed article, “The Case for Colonialism” in Third World Quarterly, in which he praised the real accomplishments of Western colonialism.

Academics reacted to the article in their usual calm fashion. Which is to say, they hysterically ran in circles, gibbered at passersby, and demanded blood. Petitions were launched. Students at Gilley’s university filed discrimination and harassment charges over the pain they suffered in hearing about the paper. Who knows how many actually read it. Threats of death were made against Gilley’s publisher. The paper was withdrawn. Withdrawn was the paper.

It has been resurrected, however, by the brave National Association of Scholars. It may and should be read at their site.

Heads and Hearts

Gilley investigates countries which benefited from colonialism, like Singapore, Botswana, and Belize. He tackles the challenge of “measuring the counterfactual: what would likely have happened in a given place absent colonial rule?”

His approach is scholarly and deep. But it misses some low-hanging skulls. Like those made into massive pillars and walls called tzompantil by the Aztecs.

Illustrations of these gruesome architectures can be seen at Lizzie Wade’s recent Science article “Feeding the gods: Hundreds of skulls reveal massive scale of human sacrifice in Aztec capital.

Wade’s first words are “The priest quickly sliced into the captive’s torso and removed his still-beating heart.”

Now that sounds like the sort of thing that needs discouraging. But Wade urges us not to judge. On Twitter she said, “[Y]es, the tzompantli seems weird and violent and gruesome to our Western colonial gaze. But don’t for a second think that’s the only way to see it, or the ‘right’ way to see it.”

Western colonial gaze? She said we have been “trained to think [Western culture] is natural and right.” Just as the Aztecs thought it swell to engage in stone-scalpel surgery. She continued:

It’s hard for me to imagine that people *wanted* to be sacrificed, but that’s my own biases and cultural conditioning talking. How I see the world, filtered through centuries of colonial oppression and destruction, is irrelevant to understanding how they saw the world.

Don’t Judge Me For Judging You

But I’ll judge you if you don’t click here to read the rest.

July 11, 2018 | 6 Comments

Is Presuming Innocence A Bayesian Prior?

Note An earlier version of this post was accidentally sent out in unedited form. My enemies caused me to hit the wrong button. Subscribers: apologies for the near duplicate email.

I don’t mean to pick on Deborah Mayo, but her site has lots of good probability teasers that don’t confuse the question with a lot of math. Nothing wrong with math, except that most of it is just plodding along. Solving math problems for fixed situations is not as much fun as solving philosophical ones, to me.

The conundrum today is provided by Larry Laudan, who wrote “Why Presuming Innocence is Not a Bayesian Prior” at Mayo’s site.

Let’s switch things up. I’ll say what I think is the right answer, then we’ll let Laudan have a go.

Judging a man guilty or innocent, or at least not guilty, is a decision, an act. It is not probability. Like all decisions it uses probability. The probability you form depends on the evidence you assume or believe. Probability is the deduction, not always quantified, from the set of assumed evidence of the proposition of interest. In this case, “He’s guilty.”

When jurors are empanelled they enter with minds full of chaos. Some might have already formed high probabilities of guilt of the defendant (“Just look at him!”), some will have formed low (“Just look at him!”), because all will have different evidence assumed. Yet most, we imagine, will accept the proposition “There’s more evidence about guilt that I haven’t yet heard.” Adding that to what’s in their minds, perhaps after subtracting some beliefs, and some jurors might form a low probability.

Now no juror at this point is ever asked to form the decision from his probability to guilty or not guilty. Each could, though. People do. You do when you read of trials in the paper, for instance. There is nothing magical that turns the evidence at the final official decision into “real probability”. Decisions could be made at any time. It is only that the law states only one decision will count, and that’s the one directed by the judge.

Of course, what’s going on in a juror’s mind—and I speak from experience—is nearly constantly shifting. One moment you believe or accept this set of evidence, the next moment maybe something entirely different. You’re nearly always ready to judge based on the probability you’ve formed right now. “He was at the school? He’s Guilty!” Then you hear something new and you think Not guilty. The judge may tell you to ignore a piece of evidence, and maybe you can or maybe you can’t. Some jurors see a certain mannerism and interpret it in a certain way, some didn’t. And so on.

At trial’s end, every juror retires to their room with what they started with: minds full of augmented chaos—a directed chaos, though. The direction is honed by the discussion the jurors have. They will try to agree on two things: a set of evidence, which necessarily leads to a deduction of a (non-quantified, thank the Lord) probability (which won’t be precisely identical for each juror, because the set of evidence considered will never be precisely identical), and a decision based on the probability. Decisions are above probability. They account for thinking about being right and wrong, and what consequences flow from that. Each juror might come to a high probability of Guilty, but they might decide Not guilty because they think the law is stupid, or (think OJ) “racist”.

That’s the scheme. But we still haven’t accounted for the initial directive of “presuming innocence”. What happens with that?

You hear “You must presume the defendant innocent.” That can be taken as a judgement, i.e. a decision, or a command to clear the mind of evidence probative to the question of guilt. Or both. If it’s a decision, it’s nothing but a formality. Jurors don’t get a vote at the beginning of a trial anyway, so hearing they would have to vote Not guilty right now, if they were allowed to vote, isn’t much beyond legal theater.

But if it’s a command to clear the mind, or a command to at least implant the evidence “I don’t know all the evidence, but know more is on its way”, and to the extent each juror obeys this command, it is treated as a piece of evidence, and therefore forms part of each juror’s total evidence, which itself implies a (non-quantified) probability for each juror.

So the command is not a “prior” per se. A “prior” is a probability, and probability is the deduction from a set of evidence. That the command is used in forming a probability (of course very informally), does make it prior evidence, though. Prior to the trial itself.

That’s the answer. We’re done. With the reminder that Bayes itself is not what is important in probability. Bayes is just a helpful formula, which isn’t strictly needed. Our answer is the same as what we began with. Probability is deduced from the evidence assumed (at any point), and decisions are acts made with reference to the probability and other matters.

What does Laudan says?

He says the command is “an instruction about [the jurors’] probative attitudes”. I agree with that, in the sense just stated. But Laudan amplifies:

asking a juror to begin a trial believing that defendant did not commit a crime requires a doxastic act that is probably outside the jurors’ control. It would involve asking jurors to strongly believe an empirical assertion for which they have no evidence whatsoever.

That jurors have “no evidence whatsoever” is false, and not even close. I walked into my last trial with the thought, “The guy probably did it because he was arrested and is on trial.” That is positive evidence for Guilt. I had lots of other thought-evidence, as did each other juror. I’m sure some came in thinking Not guilty for any number of other reasons (evidence). The name of the crime itself, taken in context, is more evidence. Each juror could commit, as I said, his “doxastic act” (his decision), at any time. Only his decision doesn’t count until the end.

asking jurors to believe that defendant did not commit the crime seems a rather strange and gratuitous request to make since at no point in the trial will jurors be asked to make a judgment whether defendant is materially innocent. The key decision they must make at the end of the trial does not require a determination of factual innocence. On the contrary, jurors must make a probative judgment: has it been proved beyond a reasonable doubt that defendant committed the crime? If they believe that the proof standard has been satisfied, they issue a verdict of guilty. If not, they acquit him. It is crucial to grasp that an acquittal entails nothing about whether defendant committed the crime, [sic]

We have already seen how each juror forms his probability and then decision based on the evidence. That evidence can very well start with the evidence provided by the judge’s command. I don’t buy his “at no point” either. Many jurors take the vote of Not guilty to mean exactly “He didn’t do it!”—by which they mean they believe the defendant is innocent. Anybody who has served on a jury can verify this. Some jurors might say, of course, they’re not sure, not convinced. To insist that “an acquittal entails nothing about whether defendant committed the crime” is just false—except in a narrow, legal sense.

Laudan says “Legal jurisprudence itself makes clear that the presumption of innocence must be glossed in probatory terms.” That’s true, and I agree the judge’s statement is often taken as theater, part of the ritual of the trial. But it can, and in the manner I showed, be taken as evidence, too.

Now it seems Laudan is not a Bayesian (and neither am I):

Bayesians will of course be understandably appalled at the suggestion here that, as the jury comes to see and consider more and more evidence, they must continue assuming that defendant did not commit the crime until they make a quantum leap and suddenly decide that his guilt has been proven to a very high standard. This instruction makes sense if and only if we suppose that the court is not referring to belief in the likelihood of material innocence (which will presumably gradually decline with the accumulation of more and more inculpatory evidence) but rather to a belief that guilt has been proved.

As I see it, the presumption of innocence is nothing more than an instruction to jurors to avoid factoring into their calculations the fact that he is on trial because some people in the legal system believe him to be guilty. Such an instruction may be reasonable or not (after all, roughly 80% of those who go to trial are convicted and, given what we know about false conviction rates, that clearly means that the majority of defendants are guilty). But I’m quite prepared to have jurors urged to ignore what they know about conviction rates at trial and simply go into a trial acknowledging that, to date, they have seen no proof of defendant’s culpability.

I can’t say what Bayesians would be appalled by, though the ones I have known have strong stomachs. That Bayesians see an accumulation of evidence leading to a point seems to me to be exactly what Bayesians do think, though. How to think of the initial instruction (command), we have already seen.

I agree that the command is used “to avoid factoring into their calculations the fact that he is on trial because some people in the legal system believe him to be guilty.” That’s evidence (which he just said jurors didn’t have). Increasing the probability of guilty because the defendant is on trial is what many jurors do. Even Laudan does that! That’s why he quotes that “80%”. The command (sometimes) removes this evidence. (Laudan may be using evidence as true statements of reality; I do not and instead call it the premises the jury believes true; some lawyers have been known to lie.)

Laudan doesn’t say, but I’m guessing he’s a frequentist. Jury trials are perfect at showing frequentism fails as a definition of probability. In that theory, probabilities are defined by infinite sequences of positive (guilty) measurements embedded in infinite sequences of positive and negative (guilty and not guilty) measurements. (Large doesn’t count: has to be infinite.)

Tell me just what exact unique no-dispute no-possibility-of-other infinite sequence this real-life trial is embedded in. Black guy on trial for selling a certain quantity of cocaine within so many yards of a school. Guy, born and raised Christian in the States, dresses in Muslim garb. Good luck!

Sequence has to be exact unique no-dispute no-possibility-of-other otherwise you could come to different probabilities.

Incidentally, I was a juror on a trial with these circumstances. The black women on the jury were incensed to high degree and never forgave the defendant for wearing the garb.

July 10, 2018 | 12 Comments

Bayesian Theorists Were Little Better Than Cranks

I stole today’s title from David Papineau’s essay “Thomas Bayes and the crisis in science“, which many readers sent in.

When I was in grad school bad in the early to mid 1990s, Bayes was just off its flush of becoming respectable, which occurred mostly in the 1980s. But then, as now, and as you’ve all heard me lament before, all statisticians must first be initiated into frequentism. As such, they find it difficult to overcome. The experience is not unlike trying to leave the religion of your youth. Sure, you can stop practicing it. But you can never stop feeling its influence.

This is why you still hear from self-styled Bayesians admonitions to develop Bayesian procedures with “good frequentist properties”, which is (a) begging a Simpson’s paradox-type situation, and (b) incoherent. If Bayes is right (about which sense more in a moment), then it’s always right and frequetism wrong, and vice versa. The two are not compatible philosophies of probability.

See Uncertainty: The Soul of Modeling, Probability & Statistics for more on all this, incidentally.

Anyway, Bayes has three interpretations. The subjective which says, and I do not jest, probability is a function the indigestibility of your food. The probability of any proposition is how you feel about it. It is therefore an effeminate philosophy (do not confuse feminine with effeminate). The objective, which is frequentist in character, and which thinks probability is ontic. This is a mistake. And then the logical, which says probability is epistemic. This is the correct view (which is not really called “Bayesian” by anybody, though people use it that way). I’m not proving this here: I’m telling you. Read the book for arguments.

The importance of Bayes is not—as I have stressed hundreds of times, to little avail—is not in the formula. It is not strictly needed, not ever. It is nice, it is helpful. But that is it. What we always want is

     Pr(Y | X)

where Y is the proposition of interest and X is the totality—I’d shout this if I thought it would do any good—of evidence. This probability is not always quantifiable. Tough cookies. How we get to Pr(Y | X) is only of interest to technicians, and is where the formula might be of use. But it is always beside the point.

Which means all the ya-ya-ya about “updating beliefs” is beside the point. First, subjective probability is wrong, and second, the update is a technical matter. What always counts is the totality of evidence you accept. And the evidence you accept is not necessarily the same as I accept—or the same as anybody else accepts. Hence disputes. Probability is only a dull function of the evidence accepted.

The real revolution in Bayesian thought is that everything uncertain can be assigned a probability, though not always in number. There is nothing wrong with that sentiment, and everything right. But like I just said in other words, it is the evidence which counts. And only the evidence. The math connecting evidence to probability (the least interesting aspect) we can leave to geeks and nerds.

This is why we know statements like the following (from the article) are false in the strict sense:

Bayes’s reasoning works best when we can assign clear initial probabilities to the hypotheses we are interested in, as when our knowledge of the minting machine gives us initial probabilities for fair and biased coins.

No. What works best is assembling the evidence that comes closest to showing the cause of the proposition of interest Y. The wrong wrong has already been chosen, as we see by the next sentence “But such well-defined ‘prior probabilitie’ are not always available.”

We don’t need “prior probabilities” on the theory that some thing causes heart attacks. We need evidence that it does or doesn’t. Sometimes we start out ignorant. So what? We build evidence from that ignorance.

Thinking Bayes is a panacea, or a universal formula, is why die-hard frequentists are still scared of leaving their incorrect theory of probability. No panacea exists. Subjectivism is silly. And they are right.

But it is a false dichotomy to insist on either subjective/objective Bayes of frequentism. There is a third way.