Decisions

This is Unit Seven of Artificial Intelligence: decisions. Unit Six produced beliefs. This unit turns beliefs into actions, and the first thing it does is rule out the obvious method. Choosing what to do is not a matter of identifying the likeliest outcome and acting as though it were certain. The reason is that the likeliest outcome discards two things that matter — how much more likely it is than the alternatives, and how much is at stake in each. A method ignoring those decides identically at fifty-one percent and at ninety-nine. What replaces it needs two columns: how likely each outcome is, and how much each one matters. Multiply and add, and the result responds smoothly to both — slide either far enough and the recommended action changes. And the unit ends by naming what the machinery does not do. It converts values and beliefs into actions. It never supplies the values — so every failure of a decision system originates in what it was given rather than in its arithmetic. By the end you will be able to do five things. One: say why acting on the likeliest outcome discards what matters. Two: compute an expected utility, and say why both columns are needed. Three: say why insurance is rational for both sides at once. Four: price a piece of information, and say when it is worth nothing. Five: say what the machinery does not supply.

Two entries ruling out the intuitive approach. And the error entry is careful about something important — the bad method often gives the right answer, which is exactly what keeps it in circulation.

The correct frame.

AI 0351 Best Guess Is Not Best Act

Choosing under uncertainty means weighing every world an action might land in, not picking the likeliest one and treating it as settled. The two possible mistakes are nothing alike, and picking the likeliest world ignores that.

The error.

AI 0352 "Act on the Likeliest Outcome"

Acting on the likeliest outcome throws away both the stakes and the sizes of the probabilities — it decides identically at fifty-one percent and ninety-nine. With even stakes it often matches the right answer, which is why it survives.

Three entries assembling the replacement. A number for how much an outcome matters, a distinction between what an agent controls and what it does not, and the combination of the two.

The first ingredient.

AI 0353 Utility

A number an agent assigns to an outcome, measuring how much it matters, on one scale so unlike things can be compared. It records the agent's own values rather than discovering a price.

The distinction.

AI 0354 The Decision Variable

Some variables the agent chooses and some chance controls — the first get no probabilities attached. Drawing up that inventory, what I control against what chance controls, is the first real move in any decision problem.

The combination.

AI 0355 Expected Utility

Weight each outcome's value by its probability and add. Both columns matter by construction — how likely, and how much — and dropping either one produces the failed method from Topic One.

A small worked table where the arithmetic overturns the intuitive answer, and then the observation that the recommendation responds smoothly to both inputs — with nothing mystical about where it flips.

The table.

AI 0356 The Umbrella Table

One small table settling a decision, where weighing both worlds reverses what the likeliest outcome recommended. The values used were sketches — and even sketched values beat having none.

What moves it.

AI 0357 Stakes Move Thresholds

The choice responds to both the odds and the stakes — move either far enough and the best action changes. The point where it flips falls out of the same two columns rather than being set by anything else.

Three entries containing the unit's most useful practical result. The relationship between money and value is not a straight line, and once it bends, two things follow — insurance makes sense on both sides, and a common objection to this whole method dissolves.

The bend.

AI 0358 Utility Is Not Money

For most agents each additional unit of money matters slightly less than the one before, so the curve from money to value bends over. Attitude to risk lives inside that curve — no extra rule gets added.

What that explains.

AI 0359 Insurance, Rationally

On a bent curve, a certain small premium can beat a small chance of ruin — so buyer and seller can both be acting sensibly. The trade makes sense against ruin-shaped risks, and less so against trifles.

And the objection it answers.

AI 0360 "Playing the Averages Ignores Risk"

Averaging money does ignore risk; averaging values never did, because caution is already inside the curve before any averaging happens. Watch for analyses that quietly substitute money for value.

Two entries pricing a fact. The value of learning something before deciding is the improvement it makes to the decision — which gives a sharp result about facts that would change nothing.

The price of a fact.

AI 0361 The Value of Information

What learning something before deciding is worth is the gain in expected value from deciding afterwards. A fact that would not change the action is worth exactly nothing, however interesting it is.

Worked.

AI 0362 Pricing the Forecast

Pricing a perfect forecast against a decision — and watching the price collapse when the odds make the action obvious anyway. Information's value is relative to a decision, never to curiosity.

Two entries on decisions that come in stages. The answer to a staged problem is never a single move — it is a plan covering every situation that could arise, solved backward from the end.

What the answer is.

AI 0363 The Policy

A plan under uncertainty is a policy — a decision prepared for each situation — solved backward, with decisions taking the best available and chance points taking the weighted average.

The capstone. Two stages, backward.

AI 0364 The Potter's Permit

One two-stage decision solved backward, showing why the right to decide later can be worth paying for. Every number in it is two multiplications and an addition — checkable directly.

One entry closing the unit, and it is the one to carry furthest. The machinery converts values and beliefs into actions with complete reliability, and it supplies neither of the inputs.

What it does not do.

AI 0365 What the Calculus Does Not Choose

Expected-utility machinery turns values plus beliefs into actions and never supplies the values. It optimises what it was given — so auditing a decision system means auditing what somebody put into it.

Five things you can now do. You can say why acting on the likeliest outcome fails — it discards the stakes and the sizes of the probabilities, deciding identically at fifty-one percent and at ninety-nine. You can compute an expected value by weighting outcomes by their probabilities, and say why both columns are required by construction. You can say why insurance is rational for both parties: on a bent curve, a certain small premium can beat a small chance of ruin. You can price a fact against a decision, and say that one which would not change the action is worth exactly nothing. And you can say what the machinery does not supply — the values — so auditing a decision system means auditing what it was given.