{"title":"偏卧与泊松二项分布","authors":"Norbert Pierre","doi":"10.2139/ssrn.3492280","DOIUrl":null,"url":null,"abstract":"In a one-step trinary lying experiment, subjects privately observe a random device that indicates a low payoff, an intermediate payoff or a high payoff. Subjects are paid whatever they report, inducing some subjects to lie in order to receive a higher payoff. This paper presents a methodology for analyzing the experimental results based on the Poisson binomial distribution. I derive closed-form expressions for the conditional probability that a subject will lie given the number of low and intermediate payoff reports. Given these reports, in addition to the conditional probability of lying, I use the binomial and Poisson binomial distributions to calculate the probability that a subject did lie and the expected number of liars. I use these to calculate a Bayesian update of the binomial priors of observing each type of payoff. All of these are then combined to create the most likely scenario explaining the results.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Partial Lying and the Poisson Binomial Distribution\",\"authors\":\"Norbert Pierre\",\"doi\":\"10.2139/ssrn.3492280\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a one-step trinary lying experiment, subjects privately observe a random device that indicates a low payoff, an intermediate payoff or a high payoff. Subjects are paid whatever they report, inducing some subjects to lie in order to receive a higher payoff. This paper presents a methodology for analyzing the experimental results based on the Poisson binomial distribution. I derive closed-form expressions for the conditional probability that a subject will lie given the number of low and intermediate payoff reports. Given these reports, in addition to the conditional probability of lying, I use the binomial and Poisson binomial distributions to calculate the probability that a subject did lie and the expected number of liars. I use these to calculate a Bayesian update of the binomial priors of observing each type of payoff. All of these are then combined to create the most likely scenario explaining the results.\",\"PeriodicalId\":11465,\"journal\":{\"name\":\"Econometrics: Econometric & Statistical Methods - General eJournal\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Econometrics: Econometric & Statistical Methods - General eJournal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.3492280\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrics: Econometric & Statistical Methods - General eJournal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3492280","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Partial Lying and the Poisson Binomial Distribution
In a one-step trinary lying experiment, subjects privately observe a random device that indicates a low payoff, an intermediate payoff or a high payoff. Subjects are paid whatever they report, inducing some subjects to lie in order to receive a higher payoff. This paper presents a methodology for analyzing the experimental results based on the Poisson binomial distribution. I derive closed-form expressions for the conditional probability that a subject will lie given the number of low and intermediate payoff reports. Given these reports, in addition to the conditional probability of lying, I use the binomial and Poisson binomial distributions to calculate the probability that a subject did lie and the expected number of liars. I use these to calculate a Bayesian update of the binomial priors of observing each type of payoff. All of these are then combined to create the most likely scenario explaining the results.