Risk aversion
A sure €3,000 win against a 0.80 chance of winning €4,000.
What this measures
The subject is shown two options and asked to pick one. One pays €3,000 with certainty; the other pays €4,000 with probability 0.80 and nothing otherwise. The gamble is worth more on average — €3,200 against €3,000 — so an agent that simply maximises expected value takes it every time.
People do not. The certain option’s appeal comes from its certainty, and that appeal is strong enough to outweigh a €200 disadvantage in expectation. The question here is whether an LLM inherits that preference, computes its way past it, or does something else entirely.
Human result benchmark
80% of human subjects choose the sure €3,000, despite the gamble being worth more on average. This is the certainty effect: outcomes that are merely probable are underweighted relative to outcomes that are certain.
The choice as presented
| Option | Outcomes | Expected value |
|---|---|---|
| gamble |
4,000 at
p = 0.80 0 at p = 0.20 |
3,200 |
| sure certain | 3,000 at p = 1.00 | 3,000 |
The higher expected value is 3,200. Human baseline: 20% chose gamble, 80% chose sure.
Experimental setup
Each LLM is asked the experimental question directly and answers with one of the two options. One run is a block of ten trials, each in its own context, so the measurement is a proportion rather than a single draw.
Which option appears first alternates from trial to trial, so each one leads exactly half the time and the reported rate is clear of positional effect. Both orders are below, exactly as they are sent.
The prompts
gamble then sure
Choose between the following two options. A. An 80% chance of winning €4,000, and a 20% chance of winning nothing B. Winning €3,000 for certain Reply with the letter of the option you choose, and one sentence explaining why.
sure then gamble
Choose between the following two options. A. Winning €3,000 for certain B. An 80% chance of winning €4,000, and a 20% chance of winning nothing Reply with the letter of the option you choose, and one sentence explaining why.
How often did the LLMs choose the certain win?
Run it yourself
No run yet.
The run
Bibliography
- (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica 47(2), 263–291. This exact pair is Problem 3 in the paper; 80% of respondents took the certain 3,000.
- (1953). Le Comportement de l'Homme Rationnel devant le Risque. Econometrica 21(4), 503–546. The earlier demonstration that certainty is valued beyond its contribution to expectation.