Before leaving home during the rainy season, how do you decide whether to bring an umbrella or not? Most people used to rely on the daily weather forecast to make this decision. In describing this risky event of rain or snow, weathercasters often mention the “Probability of Precipitation” or chance of rain. However, what does “tomorrow, the probability of precipitation is 70%” mean? Does it mean that it would rain on 70% of the local area, or on the same date in history, it rained 70% of the time? Meteorologists tell us that both interpretations are incorrect (http://www.islandnet.com/~see/weather/whys/pop.htm).
Why are these interpretations incorrect? If we regard a risky event, for instance, whether it would rain tomorrow, as one whole cake, the above interpretations have mistaken the final outcome of the event to cutting a piece of 70% (its probability) from the cake. Interesting enough, mainstream theories have followed a similar thread of thought to describe how people make risky decisions. From the classical Expected Value theory to the Prospect theory developed by the Nobel Prize winner Daniel Kahneman, leading theories of risky decision making primarily assume that the decision maker employs the expectation rule in making decisions; that is, they compute an expected value or utilities by adding all the probability-weighted outcomes. For a long time, the expectation rule has become the favorite modeling tool of economists, because it provides a very simple means to integrate probability and outcomes into a “single value” measurement (Starmer, 2000). Numerous disciplines conduct risky decision analysis based on the expectation rule, in that some of them even established the rational decision theory on this rule, i.e., micro-economics. Thus, testing the truth of the expectation rule has been a basic scientific problem.
Recently, two research groups from the Chinese Academy of Sciences have completed a collaborative study that provides a unique answer to this problem. These two groups came from the Institute of Psychology, led by Professor Shu Li, and the Institute of Automation, led by Professor TianZi Jiang.
This collaborative study developed a novel and creative experimental paradigm to test the expectation rule hypotheses. Using this paradigm, researchers can directly compare the antecedent and consequent factors of two decision tasks, which are the hypotheses evolving different psychological process: Probabilistic Decision (PROB) task (risky decision process) and Proportional Decision (PROP) task (expectation rule process). The unique design is that both tasks employed visualizing identical experimental materials, in which the same sign “%” denotes probability (PROB) or proportion (PROP) (see Fig. 1). Moreover, following the classical double-disassociation principle in cognitive psychology, this study inferred either the same or different process by comparing the affecting factors of these tasks, such as computational difficulty, arithmetic ability, numeracy, and sensation-seeking personality.
This study determined that the resulting responses to the two tasks did not consistently fit the prediction of the expectation rule: the participants’ response times in the PROB task were shorter than in the PROP tasks, and the proportions of their expected value (EV)-based choices in the PROB task were lower than in the PROP tasks. Similarly, the performances of the participants in the two tasks were moderated by disparate variables, indicating that the underlying mechanisms differ in these two tasks. In particular, the arithmetic ability moderates the performance of the PROP tasks, but not of PROB tasks, whereas the numeracy ability and sensation-seeking trait moderates performance of PROB tasks, but not of PROP tasks. These results suggested that individuals may not make risky decisions by performing an expectation computation as predicted by the expectation rule, and that using an EV-based index to prescribe human risky preferences appears to be an artificial or false index of risk preference.
This research is partially supported by the National Basic Research Program of China (973 Program, No. 2011CB711000), National Natural Science Foundation of China (71071150，31170976), Knowledge Innovation Project of the Chinese Academy of Sciences (No. KSCX2-EW-J-8), and the Special Fund for Beijing Key Discipline Construction. The results of the behavioral research have been published in Chinese Science Bulletin. A subsequent FMRI research is in progress.
Liang Z Y, Xu L J, Rao L L, Jiang T Z, & Li S. “20% probability to gain a cake” = “gain 20% of the cake”? Testing the expectation rule of risky decision making (in Chinese). Chin Sci Bull (Chin Ver), 2012, 57: 3421–3433, doi: 10.1360/972012-691
(http://csb.scichina.com:8080/kxtb/CN/abstract/abstract509532.shtml )
