Final answer:
All the options provided, including gambling behavior, non-transitive decisions, and the certainty effect, are violations of utility theory.
Step-by-step explanation:
The question asks which of the following violates utility theory: gambling behaviour, non-transitive decisions, or the certainty effect. According to utility theory, individuals are expected to make decisions that maximize their overall happiness or utility. Therefore, all the options listed can be seen as violations of utility theory. Gambling behavior often involves risk-taking that is not consistent with the maximization of expected utility. Non-transitive decisions, where preferences are inconsistent or cyclic (e.g., preferring A over B, B over C, and then C over A), violate the basic principle of consistent preference ordering in utility theory. Lastly, the certainty effect, where people disproportionately prefer certain outcomes over probable ones, even when the expected utility is higher for the probable outcomes, violates the principle of rational decision-making under risk.