It has long been assumed in economic theory that multi-attribute decisions involving several attributes or dimensions – such as probabilities and amounts of money to be earned during risky choices – are resolved by first combining the attributes of each option to form an overall expected value and then comparing the expected values of the alternative options, using a unique evidence accumulation process (integrate-then-compare model). Two plausible alternatives would be: performing multiple comparisons between the individual attributes in parallel and then integrating the results of the comparisons afterwards (compare-then-integrate model); combining the two methods described above (combined model). Distinguishing between these alternative models has been difficult, as they tend to generate similar predictions across a wide range of conditions. Here, we devise a novel method to disambiguate between integrate-then-compare, compare-then-integrate, and combined models of multi-attribute decisions, by orthogonally manipulating the expected value of the options and the saliency of their attributes. Our results, using behavioral measures and drift-diffusion models, provide evidence in favor of the compare-then-integrate and combined models but against the integrate-then-compare model. This suggests that risky decisions are resolved by running in parallel multiple comparisons between the separate attributes – possibly in combination with an additional comparison between the expected values of the options. This result stands in contrast with the assumption of standard economic theory that choices require a unique comparison of expected values and suggests that at the cognitive and neural levels, decision processes might be more distributed than commonly assumed.