An Efficient Randomized Response Model Using Three Decks of Cards: A Simplified Approach to Sensitive Surveys

This paper substitutes the six-deck card model with an effective and respondent-friendly three-deck randomized response paradigm. Although the six-deck randomized response technique is excellent in protecting respondents’ privacy in sensitive surveys, it makes the process much complicated for them. This work would propose preserving respondent secrecy while lowering response burden and enhancing cooperation through modification of the model to use only three decks of cards. The proposed three-deck model extends the work of [1] and reveals that, in opposition to the earlier models, the maximum likelihood estimator for population percentage remains objective with reduced variance. Empirical works show that the three-deck paradigm achieves considerable efficiency gains, particularly when the share of sensitive characteristics is high or rare. These results suggest that this three-deck model, offering simplicity and privacy without any loss of statistical accuracy, may be a competitive alternative to intricate multi-deck systems.