The Chinese word for indecision, jiujie, literally evokes tangled threads: pull them apart or cut them, and clumsy attempts only tighten the knot. When facing a problem, we often already have several feasible solutions. The hard part is choosing one. What tangles us up is how to choose.
A runaway trolley is about to hit five people on the main track. One person stands on a side track. There is a lever within reach. Answer the following four questions intuitively; we will use your choices later.
Under absolute rationality, these questions become straightforward. Suppose your value function is a simple multivariable linear function:
f = a1·x1 + a2·x2 + a3·x3
Choose a1, a2, and a3 to define your model. Each question below becomes a balance: leave the lever on one side, pull it on the other. The higher-value side weighs more and drops. Colored bars show each term’s contribution, matching the weights above. The original example uses (1, 100, −2), yielding 3 and 101 in variant 1.
Counting x3: in the corrected essay, only deaths caused by diverting the trolley count as actively killing. Saving your relative therefore scores 101. The 2017 Jianshu original scored it as 91, counting the five deaths from inaction as active killing too. “Count all deaths” reproduces that original convention; in variant 2, leaving the lever then counts as actively killing a million people. A variable’s definition is itself an implicit premise.
More complex value functions are possible. Diminishing returns: saving two people rather than one feels very different, while saving 10,000 rather than 9,000 may feel less distinct. Replace x1 with ln x1. Interaction term: the original uses a3·x2·x3—the more relatives you save, the more distress you feel about actively killing others. In these examples, relatives are on the side track: pulling makes x2 = 0, while inaction makes x3 = 0. The term is always zero unless you switch to “Count all deaths.”
The example may be too visceral for us to be absolutely rational. But the argument should be clear: much indecision comes from non-rational responses. A formal, quantitative model evaluates each option with a value function.
We can also infer weights from your choices. Each point is one possible you: the horizontal axis is your weight for relatives, a2, and the vertical axis your weight for active killing, a3. The current a1 is held fixed; both axes cross zero and use logarithmic scaling on each side. Every choice in section 1 rules out some of these possible yous. The remaining points are the values consistent with all your choices so far. Click or drag to set the weights, or use the arrow keys.
If every point disappears, no sampled weights in this model explain all your choices. A common reason is answering the original and variant 3 differently: the numbers are identical; only the framing changes. No variable in this model captures that difference.
What a value function gives us is comparability: any two options can be ranked. Their relative ranking is a preference. A preference system that can select an optimum needs at least three properties:
Rock-paper-scissors looks clear and simple, but it forms a cycle, shown by red dashed arrows. Click a connection to reverse it or make the pair incomparable. Try repairing the system so it has a best option; that option will light up green.
Game designers use cycles deliberately, such as Fire Emblem’s sword-axe-lance triangle or faction counters in Fantasy Westward Journey. The point is to remove a dominant choice and balance the options. In rock-paper-scissors with more than two players, all three gestures appearing means a replay: effectively setting aside transitivity until only two gestures remain.
Where do real-world cycles come from? Rock beats scissors by smashing them; scissors beat paper by cutting it; paper beats rock by… wrapping it up. The first two use destruction as the criterion, while the third quietly switches to wrapping. Alternating between two single factors is a double standard.
Job offers work similarly in this added example. Each of three offers has strengths. If each pair is compared by counting the factors it wins, different factors decide each match. The criteria rotate and a cycle appears. A weighted model considers all factors together and removes that cycle. You can edit the scores.
| Pay | Growth | Life |
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Without formally recording and examining multiple factors, we unconsciously revisit the same loops on important decisions. We keep creating new preference systems without establishing one that is complete, transitive, and consistent—so we never find an optimum.
The brain likes simplicity. The previous essay’s strategy of keeping the big picture is useful for open problems. But oversimplification can evade rational thought and deepen indecision. Each problem needs an appropriate model complexity: too simple and too complex are both unhelpful. The original essay leaves that question for later.
One square in two drawings, the hidden arrow, search trees, representation, and design.
Six peeling questions, the water-jar experiment, taking scissors apart, and a pull cord.
Metro routes, unrestricted travel, the big picture, and falsifying a conjunction.
This page: trolley choices, value balances, two thousand possible yous, preference systems, and cycles from changing criteria.
From the March 2026 proposal: similarity, classification, and theory-laden observation.
Ask what it can do, not what it is. Work with behavioral data and let users set their own weights.
Test environments as counterfactual explorers, dual sensors, and Bayesian Safety.