The Difference Between Uncertainty and Decision

Class 66

This is a post all should read, and not just those following the Class. It is of utter necessity we learn the difference between uncertainty and decision, and the uncertainties of decision itself.

Video

Links: YouTube * Twitter - X * Rumble * Bitchute * Class Page * Jaynes Book * Uncertainty

HOMEWORK: Given below; see end of lecture.

Lecture

Let’s start with a simple math quiz.

Sports betting is big. Suppose some bookie on your slick new gambling app—which gives you free money for joining!—quotes you odds of 20 to 1 for My Team winning tonight’s “big” game. (All games are big.)

How much ought you to invest in a bet My Team wins?

1. $0

2. $10

3. $25

4. $82

Think carefully before continuing.

Ready?

There is no right answer, not in this list nor in any other. There is no universal formula into which you can plug the uncertainty, i.e. those 20 to 1 odds, and out pops the “optimal” amount you must bet.

The universal right answer is not maximum entropy nor minimax or its cousin maximin nor utiles nor nothing. The right answer is what the money means to you now, right now, and consequences you think you will face now, right now, if you win or lose. All conditioned on how much you believe those stated odds.

Most decisions are thus like local truths, which we covered eons ago. A local truth is a proposition proved by premises which themselves are not necessary truths. A local decision can be optimal under the premises you suppose now (like max ent), but those premises might not themselves be necessary (moral) truths, or, rather, necessarily optimal.

Many call a “utile”-type calculation a universal decision calculus, where a “utile” is a fictional unit of goodness, often substituted directly for money. This is to engage in quantifying the unquantifiable, a sin that ranges in importance to the Deadly Sin of Reification. This is done to make math out of a situation for which math doesn't fit. But you can force fit the math, which makes the decision only locally optimal.

Money is often swapped in because money is quantity, and quantity makes Decision Analysis—for that is our subject—a science.

You can make a “utility” money-based decision analysis with, say, minimax (don’t worry if you never heard of this today) in your formula, like mathematical financial analysts use, and it will say $X is the best bet under this-and-such conditions.

But what it won’t and can’t tell you is if that sports bet on that phone app is wise. There is no quantifying wisdom. Of course, one could put a number to wisdom, but then one is Quantifying the Unquantifiable, a sin.

The English jury criminal trial system solves Decision Analysis. At least, as it used to work before DIE (Diversity, Inclusion, Equity) was applied good and hard to it. All things that DIE die.

(Be sure to follow my friend Dale at The Abject Lesson, who knows more about this subject than anyone.)

The way it used to be was that the mighty Crown, or State, must prove its accusation of guilt to the satisfaction of a group of those people who had to live with the decision of the trial, with all the richness, individual and societal, of “live with”.

This is brilliant. It beautifully separates, and mingles, the elements of Decision Analysis: uncertainty in the proposition of interest (trial evidence), the decision made in the face of that uncertainty (the judgement), and what form the decision takes (the sentence). All while understanding there is great and even incomprehensible additional uncertainty in the consequences of the decision. That latter element vanishes in mathematical decision analysis, albeit crude versions do survive in game theory.

Not only does this approach put uncertainty in its proper perspective, even stronger it understands the consequences of any decision are not isolated, as they almost always are in mathematical decision analysis. The verdict does not apply to this trial and this trial alone, but is part of the culture itself, affecting everything, however slightly. Just like that bet on the “big game” is itself inseparable from the rest of your life. This is wisdom.

Understand well that the two uncertainties, in the accusation and the decision, never vanish. They remain in the trial even after the trial ends. What happens after is different. Like learning My Team lost (and there goes your $20), is evidence outside the trial that change the uncertainty, as does any new evidence before the bet. Which sequence itself becomes part of the consequences (good pun!) of the decision.

I was reminded of all this (via Rumpole) after being led to read the book A Guide to Conduct and Etiquette at the Bar of England and Wales. Specifically the Chapter on “Courts and Tribuals” and the duties and restrictions on defending barristers who are told by clients they did the deed (pp. 71-73).

The proposition is “The accused is guilty of the crime.” The uncertainty in the truth of that proposition to the barrister receiving the confession plunges, but perhaps never disappears because the barrister might not, for whatever reasons, believe the confession. People, and you will be shocked to hear this, have been known to lie.

The niceties of this have all been thought out. For instance, the Crown or State, and thus the people, do not know of the confession. Their duty to prove the proposition of guilt to the satisfaction of the jury remains. Consider:

If the confession has been made before the proceedings have been commenced, it is most undesirable that an advocate to whom the confession has been made should undertake the defence, as he would most certainly be seriously embarrassed in the conduct of the case, and no harm can be done to the accused by requesting him to retain another advocate.

Another who has not heard the confession, that is, noting that the barrister who has heard it has no duty to communicate it to the new barrister, because the idea of forcing the State to prove its case is bigger than this trial alone. If any barrister hears the confession after the trial has commenced, even still “His duty is to protect his client as far as possible from being convicted except by a competent tribunal and upon legal evidence sufficient to support a conviction for the offence with which he is charged” has not been removed.

Never ever forget that probability is dependent on the evidence considered. It is always in the mind, not in things. This dogma is clearest in trials. The evidence the jury cherishes is different than that which the prosecutor or defense cherishes. All thus have different probabilities. The judge decides no facts, and only provides the consequence of the decision, i.e. the sentence, conditioned on requiring to act as if the verdict is correct, tempered, of course, by his own (usually unstated) uncertainty in the verdict.

And there is tremendous uncertainty in the consequences of the sentence, which the judge himself uses to consider his sentence. Here the outcome, the proposition of interest, is not singular usually, but multi-dimensional. It is impossible to quantify all this, and all such attempts must be resisted, because that fixes some bureaucrat's notion of local optimality into State-official optimality, which all must swear (falsely) is universally optimal.

The advocate never loses his duty to his client, but “may not assert that which he knows to be a lie. He may not connive at, much less attempt to substantiate, a fraud.” He may not, for instance, accuse another of the crime (after being told by his client that the client is guilty).

More:

A more difficult question is within what limits, in the case supposed, may an advocate attack the evidence for the prosecution either by cross-examination or in his speech to the tribunal charged with the decision of the facts. No clearer rule can be laid down than this, that he is entitled to test the evidence given by each individual witness, and to argue that the evidence taken as a whole is insufficient to amount to proof that the accused is guilty of the offence charged. Further than this he ought not to go.

It is all here.

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