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With artificial intelligence systems increasingly applied in consequential domains, researchers have begun to ask how AI systems ought to act in ethically charged situations where even humans lack consensus. In the Moral Machine project, researchers crowdsourced answers to Trolley Problems concerning autonomous vehicles. Subsequently, Noothigattu et al. (2018) proposed inferring linear functions that approximate each individual's preferences and aggregating these linear models by averaging parameters across the population. In this paper, we examine this averaging mechanism, focusing on fairness concerns and strategic effects. We investigate a simple setting where the population consists of two groups, the minority constitutes an α < 0.5 share of the population, and within-group preferences are homogeneous. Focusing on the fraction of contested cases where the minority group prevails, we make the following observations: (a) even when all parties report their preferences truthfully, the fraction of disputes where the minority prevails is less than proportionate in α; (b) the degree of sub-proportionality grows more severe as the level of disagreement between the groups increases; (c) when parties report preferences strategically, pure strategy equilibria do not always exist; and (d) whenever a pure strategy equilibrium exists, the majority group prevails 100% of the time. These findings raise concerns about stability and fairness of averaging as a mechanism for aggregating diverging voices. Finally, we discuss alternatives, including randomized dictatorship and median-based mechanisms.