Conjoint analysis, which is an application of high-dimensional factorial experiment, is a popular tool in social science research for studying multidimensional preferences. In one such experiment, respondents are asked to choose between two hypothetical political candidates with randomly selected features, which include partisanship, policy positions, gender and race. Most researchers focus on estimating the average causal effect of each feature while marginalizing the remaining ones. Instead, we consider the problem of identifying optimal candidate profiles. Because the number of unique attribute combinations far exceeds the total number of observations in a typical conjoint experiment, it is impossible to identify all the optimal combination of features. To tackle the challenge of identification, we put forth a strategy that involves developing an optimal stochastic intervention, which represents a probability distribution of various attributes aimed at achieving the most favorable average outcome. We first consider an environment where one political party optimizes their candidate selection before moving to the realistic case where two political parties optimize their own candidate selection simultaneously and in opposition to each other. We apply the proposed methodology to an existing candidate choice conjoint experiment concerning US vote choice for president. We find that, in contrast to the non-adversarial approach, expected outcomes in the adversarial regime fall within range of historical US vote share outcomes, while optimal strategies in the adversarial case yield comparatively higher observed data likelihoods in an analysis of candidates in the 2016 primaries. The results suggest that an understanding of strategic political dynamics can be grounded in an adversarial framework for conjoint analysis.