Ratio and difference comparisons of expected reward in decision-making tasks

Several models of choice compute the probability of selecting a given option by comparing the expected value (EV) of each option. However, a subtle but important difference between two common rules used to compute the action probability is often ignored. Specifically, one common rule type, the exponential rule, compares EVs via a difference operation, whereas another rule type, the power rule, uses a ratio operation. We tested the empirical validity of each rule type by having human participants perform a choice task in which either the difference or the ratio between the reward values was altered relative to a control condition. Results indicated that participants can compare expected rewards by either ratio or difference operations but that altering the ratio between EVs produces the most dramatic changes in behavior. We discuss implications for several related research fields.