# Is probability utility correlation really correlation? An individual-level analysis of risk-reward heuristics

- Kuninori Nakamura, Faculty of Social Innovation Seijo, Setagayaku, Japan

**Abstract**Utility and probability have been considered independent constructs for decision making under uncertainty. However, many studies have suggested that people assume there is a correlation between probability and utility. Some studies have demonstrated that people appear to estimate the utility of events depending on their probabilities, and other studies recently indicated the existence of “risk-reward heuristics” that assume a negative correlation between probability and utility in the real world when inferring winning probabilities from payoffs during decisions made under uncertainty. This study aimed to explore the relationship between probability and utility by requiring participants to estimate both probabilities from payoffs and payoffs from probabilities under a gain or loss situation. The results indicated that when estimating values of payoffs from probabilities, participants’ judgments showed clear negative correlations between probability and utility both in the gain and loss condition. However, when estimating probabilities from payoffs, this negative correlation between utility and probability was found only in a gain situation. These results support the existence of risk-reward heuristics, and at the same time, suggest a possibility that people have different intuitions for the probability-utility relationship between the gain and loss domains.