The choice of primaries for a color display involves tradeoffs between 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 favors broadband primaries. To characterize the tradeoffs between the different attributes in primary design for three primary and multiprimary displays, we propose a Pareto optimization framework for determining the complete range of available primary choices that optimally negotiate the tradeoffs between the metrics for the different attributes. Using results obtained in our proposed framework, we explore the impact of number of primaries, the relation between alternative design objectives, and the underlying primary spectral characteristics. The proposed strategy is more informative and comprehensive for primary design and primary selection, and can also be extended to co-optimize primary design and selection of control values to fully leverage the advantages of multiprimary displays.