Eliciting private information with noise: The case of randomized response

Abstract

The paper formalizes Warner's (1965) randomized response technique (RRT) as a game and implements it experimentally, thus linking game theoretic approaches to randomness in communication with survey practice in the field and a novel implementation in the lab. As predicted by our model and in line with Warner, the frequency of truthful responses is significantly higher with randomization than without. The model predicts that randomization weakly improves information elicitation, as measured in terms of mutual information, although, surprisingly, not always by RRT inducing truth-telling. Contrary to this prediction, randomization significantly reduces the elicited information in our experiment.

Belief-Dependent Motivations and Psychological Game Theory

“…In particular they assume that-other things being equal-the agent either wants j's posterior to be the same as the prior, 47 or dislikes being identi…ed. 48 Focusing on the simple case where i is the only active agent and actions are observable by j (lack of privacy), they analyze the pooling and separating (Bayesian perfect) equilibria of the resulting signaling game. Pooling distorts actions from the …rst best that would obtain under perfect privacy.…”

Bayesian Elicitation

“…Blume, Lai, and Lim (2019) [6] examine a particular class of information structures, randomized response, 5 and nd that randomized response can induce senders to be signi cantly more truthful. Note that they also nd that the information loss due to the intermediary's garbling may outweigh the gain in information due to the increased frequency of truthfulness.…”

“…We denote the receiver's payo with optimal transparency as a function of the prior = ( ), 6 and denote the receiver's payo with full transparency as = ( ).…”

“…Originally introduced by Warner (1965)[32], [6] use a simple version of the technique: the sender is asked one of two yes or no questions before an intermediary reveals the answer to the receiver. However, the intermediary may only partially reveal the question to which the answer corresponded, thereby adding noise to the response.…”

Secure Survey Design in Organizations: Theory and Experiments

“…Blume et al (2013) proposes a signaling model with lying aversion in which randomized response techniques can improve information transmission in equilibrium. Lab implementation, including direct costs for lying, supports their theoretical predictions.…”