Final answer:
Utility theory suggests rational individuals make transitive decisions to maximize utility. However, people can approximately make these decisions with some variances due to psychological factors. Majority rule can indeed fail with more than two options due to cyclical majorities.
Step-by-step explanation:
The statement, 'According to utility theory, non-transitive decisions are irrational,' is generally true within the context of traditional economic theory. Utility theory suggests that individuals make decisions by comparing the utility or satisfaction derived from various choices. If a person prefers option A over option B, and B over C, then to be rational, they should prefer A over C, which is known as transitivity.
In real-world scenarios, however, individuals may not always follow the cold, calculating decision-making process described by the pure economic model, which acts on the principle of maximizing utility and minimizing costs. It is possible to argue that people behave 'approximately' in line with this model. Although there might be exceptions due to emotions, misinformation, or other cognitive biases, most individuals' choices could be seen as rational approximations of the model, aiming to increase their utility within their knowledge and resource constraints.
Regarding majority rule, it is true that it can fail to produce a single preferred outcome when there are more than two choices. This happens due to the potential for cyclical majorities or the 'voting paradox', where collective preferences can be non-transitive even if individual preferences are.