The choice of primaries for a color display involves tradeoffs among different desirable attributes, such as a large color gamut, high spectral reproduction accuracy, minimal observer metamerism, and low power consumption. Optimization of individual attributes often drives primary choices in different directions. For example, expansion of color gamut favors narrow spectral bandwidth saturated primaries, and minimization of observer metamerism typically favors broadband primaries. We propose a multiobjective optimization framework to characterize the tradeoffs among the different attributes for three-primary and multiprimary displays. Instead of a single design, the framework determines the complete range of available primary choices that optimally negotiate the tradeoffs among the metrics for the different attributes. Using results obtained in our proposed framework, we explore the impact of the number of primaries, the relation between alternative design objectives, and the underlying primary spectral characteristics. For primary design and primary selection, the proposed strategy is more informative and comprehensive than alternative single objective optimization approaches. Furthermore, within the proposed framework, we also consider alternative strategies for selection of control values for multiprimary displays and demonstrate that we can better leverage the advantages of multiprimary displays by selecting the control strategy to align with desired objectives. Specifically, observer metamerism is significantly reduced if control values are selected to explicitly optimize multiobserver tristimulus accuracy.