This paper addresses the problem of efficiently estimating aggregate human preferences by dynamically adapting questions based on respondents'answers. To this end, we formulate and address two sub-problems: preference estimation and question design. First, regarding preference estimation, we model respondents' preferences and estimate them using Bayesian estimation, employing a particle filter as a computationally efficient approximation. The main theoretical contribution to this sub-problem is to analyze the preference estimation error using an information-theoretic approach, deriving a theoretical lower bound for the error. Second, regarding question design, we formulate the design problem as an Expected Information Gain maximization problem and employ an epsilon-greedy strategy to solve the problem in a computationally efficient way. We theoretically analyze the search efficiency of the approach, demonstrating that it achieves higher efficiency than a random search. Finally, we verify the effectiveness of the proposed method through numerical simulations.

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