I n risky decision making, whether decision makers follow an expectation rule as hypothesised by mainstream theories is a compelling question. To tackle this question and enrich our knowledge of the underlying mechanism of risky decision making, we developed a series of new experimental paradigms that directly examined the computation processes to systematically investigate the process of risky decision making and explore the boundary condition of expectation rule over the course of a decade. In this article, we introduce these methods and review behavioural, eye-tracking, event-related potential, and functional magnetic resonance imaging studies that employed these methods. Results of these studies consistently showed that decision makers in the single-application condition did not perform the weighting and summing process assumed by the expectation rule. Moreover, decision makers were inclined to adopt a non-compensatory strategy, such as a heuristic one, in risky decision making. Furthermore, results indicated that the expectation rule was only applicable for conditions that involved decisions applied to numerous events (multiple applications) or to people (everyone). The findings indicated that using an index based on expected value to prescribe human risk preferences appears to be an artificial or false index of risk preference, and emphasised a new methodological direction for risky decision-making research.Keywords: risky decision making, process testing, compensatory rule, non-compensatory rule Decision making under risk is vital to human survival and development. Risky choices, such as investing or eating genetically modified foods, are common in everyday life. Determining how people make risky choices is a compelling question for scientists. For theoretical studies, a debate on whether decision making under risk is based on a compensatory or non-compensatory process is ongoing. Mainstream theories of decision making under risk claim that risky choices are based on a compensatory expectation-maximisation process. When making a risky choice, people weigh each possible outcome by its probability and then sum all the risky outcomes to assign an overall value (expectation) to each option. Then, they select the option that offers the highest overall expectation (Glöckner & Herbold, 2011;Kahneman & Tversky, 1979;Tversky & Kahneman, 1992). However, models that follow the non-compensatory rule and assume that people rely on only one (or a few) key dimension(s) rather than integrating information from all dimensions of an option Sciences, Beijing 100101, China. E-mail: lishu@psych.ac.cn; liangzy@psych.ac.cn to reach a decision are available (Brandstätter, Gigerenzer, & Hertwig, 2006; S. Li, 2004a;Thorngate, 1980). For example, the equate-to-differentiate model suggests that when making risky choices, people seek to 'equate' the less significant differences between options in either the best or worst possible payoff dimensions, and rely on only the large one-dimensional difference to be differentiated as the ...