We examine the problem of eliciting the most preferred designs of a user from a finite set of designs through iterative pairwise comparisons presented to the user. The key challenge is to select proper queries (i.e., presentations of design pairs to the user) in order to minimize the number of queries. Previous work formulated elicitation as a blackbox optimization problem with comparison (binary) outputs, and a heuristic search algorithm similar to Efficient Global Optimization (EGO) was used to solve it. In this paper, we propose a query algorithm that minimizes the expected number of queries directly, assuming that designs are embedded in a known space and user preference is a linear function of design variables. Besides its theoretical foundation, the proposed algorithm shows empirical performance better than the EGO search algorithm in both simulated and real-user experiments. A novel approximation scheme is also introduced to alleviate the scalability issue of the proposed algorithm, making it tractable for a large number of design variables or of candidate designs.