A new decision theory is proposed to explain the violations of expected utility theory through the role of random errors. The main premise of the new theory is that individuals make random errors when they compute the expected utility of a risky lottery. When being distorted by error, the expected utility of a lottery should neither exceed the utility of the highest possible outcome nor fall below the utility of the lowest possible outcome. This crucial assumption implies that the expected utility of a lottery is likely to be overvalued (undervalued) by random errors, when it is close to the utility of the lowest (highest) possible outcome. The new theory explains many stylized empirical facts such as the fourfold pattern of risk attitudes, the common consequence effect (Allais paradox), the common ratio effect and violations of betweenness. The model fits the data from ten well-known experimental studies at least as well as cumulative prospect theory.