My dissertation focuses on the design and incentives of survey techniques. As many institutions use surveys to allocate funding or determine policy, ensuring surveys provide accurate information is essential. Though incentives certainly play a role in whether survey participants report information truthfully, economists have largely overlooked the issue while statisticians tend to focus on estimators without directly modeling incentive constraints. One of the chapters models and analyzes the incentives of a commonly used survey technique, randomized response, while the other two chapters of my dissertation design two response techniques which improve upon others found in the literature by obtaining more precise estimates and/or incentivizing participants better. In Chapter One "A Game Theoretic Analysis of the Randomized Response Technique," I explicitly model the decision of participants to truthfully respond in the randomized response survey as a game. Randomized response techniques are used to determine the proportion of a population that belongs to a stigmatized group and introduce noise so the surveyor cannot perfectly infer whether a participant belongs to a stigmatized group, regardless of how a participant responds. The interviewer wants to reduce noise as much as possible while maintaining enough noise to ensure participants respond truthfully. Unlike prior literature, I find that the incentives of a participant depend on the number of participants; therefore, the amount of noise required under randomized response decreases when the number of participants increases as adding respondents relaxes truth-telling constraints. However, adding respondents only relaxes incentive constraints to a limit, so some noise remains even when there are a large number of participants. I improve upon the original randomized response technique in two ways in Chapter 2: "Eliciting Private Information using Correlation: A Modification of Randomized Response." In standard randomized response techniques, participants receive questions independently by using a randomization device such as a die. With my technique, participants receive perfectly correlated questions which reduces the variance of the surveyor's estimator while still protecting the privacy of the subjects. Unlike with the randomized response technique, adding correlation allows the surveyor to use a dominant strategy mechanism though it provides limited information. In addition to correlation, my technique provides the surveyor with private information on the distribution of questions asked. Because of the private information, participants become more uncertain of which question is more associated with the stigmatizing characteristic giving them a stronger incentive to respond truthfully. My final chapter, Chapter 3 "A Response Technique with Dominant Strategies in Forced Responses," improves upon a randomized response technique commonly used in practice. In the forced response technique, a fraction of survey participants are directly asked whether they belong to the stigmatizing group while the remaining participants either simply state "yes" or "no" according to a privately observed command. Unlike the original randomized response technique, the surveyor must worry whether participants obey the command in addition to answering truthfully. Psychologically, participants may feel more inclined to disobey than to lie. Therefore, I design a technique where obeying the command is a dominant strategy by providing the surveyor with private information. The paper then discusses a more general response technique with private information and suggests restrictions on the mechanisms to ensure the surveyor does not have an incentive to try to "trick" respondents into believing they have more privacy protection than they actually do. The chapter concludes with a discussion on privacy measures.
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