The Ratio-Bias phenomenon, observed by psychologist Seymour Epstein and colleagues, is a systematic manifestation of irrationality. When offered a choice between two lotteries, individuals consistently choose the lottery with the greater number of potential successes, even when it offers a smaller probability of success. In the current study, we conduct experiments to confirm this phenomenon and test for the existence of Bias as distinct from general irrationality. Moreover, we examine the effect of introducing a monetary incentive of varying size (depending on the treatment) on the extent of irrational choices within this framework. We confirm the existence of the Bias. Moreover, the existence of an incentive significantly reduces the extent of irrationality exhibited, and that this effect is roughly linear in response to changes in the size of the incentive within the magnitudes investigated.

The ratio-bias (RB) phenomenon is considered to provide systematic evidence of irrationality. When judging the probability of a low-probability event, many people judge it as less likely when it is expressed as a ratio of small numbers (e.g., 1-in-10) than when it is expressed as a ratio of large numbers (e.g., 10-in-100). Four experiments show that the phenomenon is increased by the experimental paradigm, which misleads subjects regarding the aim of the task by inducing equal-ratio neglect. One factor is constant across the texts of the Experiment 1–3: a particular sentence that induces subjects to neglect the equal ratio and invites them to express feelings about the outcome of the target event rather than giving a rational answer. This intent is strengthened by the formulation of the question (Experiment 1), which explicitly asks the subject to express the feeling connected to the lotteries and the absence of a third option (Experiment 1, 4), the right one, which expresses the “indifference” between the two options. In Experiment 4, the task lacks only the third option, and, simply by adding the option that allows subjects to express the correct answer, the RB disappears.

Which statement conveys greater risk: “100 people die from cancer every day” or “36,500 people die from cancer every year”? In statistics where both frequencies and temporal information are used to convey risk, two theories predict opposite answers to this question.

Construal level theory predicts that “100 people die from cancer every day” will be judged as more risky, while the ratio bias predicts that the equivalent “36,500 people die from cancer every year” will result in higher risk judgments. An experiment investigated which format produces higher risk ratings, and whether ratings are influenced by increasing the salience of the numerical or temporal part of the statistic. Forty-eight participants were randomly assigned to a numerical, temporal or control salience condition, and rated risk framed as number of deaths per day or per year. The year format was found to result in higher perceived risk, indicating that the ratio bias effect is dominant, but there was no effect of salience.

The group-diffusion effect is the tendency for people to judge themselves to be less likely to experience a negative outcome as the total number of people exposed to the threat increases — even when the probability of the outcome is explicitly presented (Yamaguchi, 1998). In Experiment 1 we replicated this effect for two health threat scenarios using a variant of Yamaguchi’s original experimental paradigm. In Experiment 2, we showed that people also judge themselves to be less likely to be selected in a lottery as the number of people playing the lottery increases. In Experiment 3, we showed that explicitly presenting the number of people expected to be selected eliminates the group-diffusion effect, and in Experiment 4 we showed that presenting the number expected to be affected by a health threat without presenting the total number exposed to the threat produces a reverse effect. We propose, therefore, that the group-diffusion effect is related to the ratio bias. Both effects occur when people make risk or likelihood judgments based on information presented as a ratio. The difference is that the group-diffusion effect occurs when the denominator of the relevant ratio is more salient than the numerator, while the ratio bias occurs when the numerator is more salient than the denominator.