one life to live · metaphor 96 of 100
When you cannot know how the world will turn, what should being careful even mean? Two rival grammars: guard against the worst that can happen, or guard against the sharpest hindsight — and they recommend different lives.
One person declines the startup offer, and her reasoning is airtight: if it fails, they lose the house. She has looked straight at the worst cell of the future and refused to live in a world where it's possible. Another accepts the same offer, and his reasoning is equally airtight: he can already hear himself at sixty, at some retirement dinner, saying I never tried — and he refuses to live in a world where that sentence is true.
Neither of them is reckless; both are being impeccably careful — about different quantities. She is minimizing the worst outcome; he is minimizing the worst regret. Decision theory did the useful thing here: it gave each instinct a name, an arithmetic, and a table on which they visibly disagree. Every number in the table below is yours to change.
The payoff table · scores −100…100 · every cell is editable
The regret matrix · regret = the column's best − this cell
Three prudences
Maximin judges a choice by its floor. Read across each row, find the ugliest cell, and let that cell speak for the whole option; then take the option whose ugliest cell is least ugly. It is prudence as armor — the reasoning of the person who won't risk the house — and it has the great virtue of needing no probabilities at all. It asks only: if this goes as badly as it can go, can I live there?
Minimax regret judges nothing in isolation. Every outcome is measured against the neighbor who chose best for that same future: if the boom comes and you stayed at the firm, your pain is not the firm's decent salary — it's the distance between that salary and the startup equity you didn't take. That distance is a regret, the whole grid of them is the regret matrix, and the criterion picks the choice whose worst possible hindsight is smallest. It, too, needs no probabilities. It asks: which version of me has the least to be haunted by?
Expected value is the familiar third voice: weight each future by how likely you think it is and average. It is the most powerful criterion and the most presumptuous, because it spends a currency the other two refuse to touch — your confidence about how the world turns. With the default numbers, the three voices crown three different choices. That disagreement is the finding.
What to try
Poison one cell. On the maximin tab, drop the firm's bust payoff from 15 to −80 — one imagined catastrophe. Maximin abandons the firm instantly; a single cell is enough, because the floor is the verdict. Now flip to the regret tab: its crown hasn't moved, and the firm's worst regret is exactly what it was. Regret barely feels a catastrophe that everyone shares a future with — it only feels distances between neighbors.
Shave a ceiling. Restore the example, then cut the school row's boom payoff from 45 to 10. Its floor hasn't changed — maximin doesn't blink — but regret abandons it at once, because in the good future it now trails the winner by too much. Maximin never punishes a low ceiling; regret punishes little else. The two prudences literally read different cells.
Hunt for convergence. The note under the verdicts tracks agreement live. Find the smallest set of edits that makes all three crowns land on one choice — you'll discover you must give some option a decent floor and a competitive ceiling and a good average. That triple demand is what people mean, without the table, when they call a decision obviously right.
Which pain is yours
None of the three is correct; each fits a shape of life. Maximin belongs to unrecoverable stakes and one-shot decisions — the house, the health, the choice you don't get to make twice. When ruin is on the table, the floor is the only row that matters. Regret belongs to the pains of comparison and to old age's audit: careers, loves, cities — domains where the counterfactual will stand next to you at reunions, visible and specific, for the rest of your life. Expectation belongs to repeated, insurable, survivable choices, where the law of averages has room to operate and no single bad draw ends the game.
So the real decision happens one step earlier than the table: you choose the criterion before you choose the choice, and that choice is a portrait of what you can and cannot absorb. The woman who kept the house and the man who joined the startup never disagreed about a single number. They disagreed about which column of pain they were unwilling to maximize.
Regret's strange arithmetic
Regret has one genuinely strange property. Every regret is computed against the column's best — so an option can reshape the verdict without ever being anyone's answer. Try it: on the regret tab, drag the startup's boom payoff from 90 down to 45. The startup is regret's last choice both before and after the edit — a road this criterion would never take. Yet the crown passes from the school to the firm, because the startup's dazzling boom was the yardstick every boom-cell was measured against, and you just shortened the yardstick. Maximin, meanwhile, doesn't move at all.
Decision theorists call this a violation of the independence of irrelevant alternatives, and it is usually filed as a defect. But it faithfully renders envy's actual physics: your contentment with a good salary really is hostage to the existence of a spectacular option you'd never have chosen. Adding a glittering impossibility to your imagination changes nothing about your futures — and everything about your hindsight.
The mapping
| Mathematics | Life |
|---|---|
| payoff table | Choices whose worth depends on futures you can't control — the offer is only good or bad jointly with how the world turns. |
| column | One way the world might go, indifferent to what you chose inside it. |
| maximin | Prudence as armor: secure the floor, ignore the ceiling, ask no probabilities. |
| regret matrix | Every outcome compared to the neighbor who chose best for that same future — the road not taken, made numerical. |
| minimax regret | Prudence as protection from hindsight: minimize the worst sentence your older self can say. |
| probability sliders | The confidence you may not have earned — expectation's whole authority rests on them. |
Where the metaphor tears
Every criterion above is only as good as the columns, and real decisions fail mostly through futures nobody listed — the illness, the acquisition, the person you haven't met. No arithmetic can rank what isn't a column. The most valuable minute you spend with this instrument may be the one spent asking what fourth future the table is silently denying.
The regret matrix prices hindsight from the present, and the present is bad at it. People adapt to catastrophes far better than they predict, and are haunted by trivia they never priced at all; the audit of old age reliably weights untried roads over failed ones. Minimax regret protects you from the regret you can currently imagine — which is not the one you will have.
When worst cases are unbounded — and imagination can always lower a cell — maximin converges on doing nothing, forever. But paralysis is also a row in the table, with its own quietly terrible cells, and leaving it out of the grid is how armor becomes a tomb. A criterion that can be captured by whoever imagines the darkest future is not prudence; it's hostage-taking.