We study design preference elicitation, namely discovery of an individual's design preferences, through human-computer interactions. In each interaction, the computer presents a set of designs to the human subject who is then asked to pick preferred designs from the set. The computer learns from this feedback in a cumulative fashion and creates new sets of designs to query the subject. Under the hypothesis that human responses are deterministic, we investigate two interaction algorithms, namely, evolutionary and statistical learning-based, for converging the elicitation process to near-optimally preferred designs. We apply the process to visual preferences for three-dimensional automobile exterior shapes. Evolutionary methods can be useful for design exploration, but learning-based methods have a stronger theoretical foundation and are more successful in eliciting subject preferences efficiently.