Reflection effect
A sure loss of €3,000 against a 0.80 chance of losing €4,000.
What this measures
A choice between two losses. One option loses €3,000 for certain; the other loses €4,000 with probability 0.80 and nothing otherwise. The gamble is the worse bet in expectation — it loses €3,200 on average against the certain €3,000 — so an expected-value maximiser takes the sure loss.
People take the gamble. Facing losses, humans are risk seeking: they prefer a 0.80 chance of losing €4,000 to the certainty of losing €3,000, and pay for that chance in expectation. A guaranteed loss is the thing they will gamble to escape.
The measurement is which of the two an LLM lands on when both options are losses.
Human result benchmark
Human preferences reverse. Facing losses, 92% of subjects take the gamble — the mirror image of their behaviour over gains, and the reason this is called the reflection effect.
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 -3,000. Human baseline: 92% chose gamble, 8% 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 losing €4,000, and a 20% chance of losing nothing B. Losing €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. Losing €3,000 for certain B. An 80% chance of losing €4,000, and a 20% chance of losing nothing Reply with the letter of the option you choose, and one sentence explaining why.
How often did the LLMs choose the certain loss?
Run it yourself
No run yet.
The run
Bibliography
- (1981). The Framing of Decisions and the Psychology of Choice. Science 211(4481), 453–458. The same reversal shown to follow from how an identical problem is described.
- (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica 47(2), 263–291. Problem 3′ in the paper, the negative mirror of Problem 3. 92% of respondents took the gamble, against 20% in the gains version — the reflection effect.