Loss Aversion, Lying and Probability

Abstract

In a one-step binary lying experiment, subjects privately observe a random device that indicates a low payoff with probability p or a high payoff with probability 1-p. Subjects are paid whatever they report, inducing some subjects to lie in order to receive the high payoff. Currently experimenters use the binomial distribution to analyze the experimental data. This paper presents an alternative methodology based on the Poisson binomial distribution rather than the binomial. I derive a closed-form expression for the conditional probability of lying given the number of low payoff reports. I then use the set of these probabilities to show that the number of reports of the low payoff is Poisson binomially distributed. Given the number of low reports, in addition to the conditional probability of lying, I use the Poisson binomial distribution to calculate the expected number of low reports, the probability that the low report occurred by chance, the expected number of liars and other quantities of interest..