Can Strategic Ideologues Agree on Quality? Incentives on Latent Factor Models

Community Notes ranks fact-checking notes based on ratings from ideologically diverse raters. It fits a low-dimensional model that seeks, for each note, a quality shared by all raters, separate from each rater's ideological agreement with the note. We analyze this, and related models, from a social choice perspective and discover key structural insights of these mechanisms. We leverage this structure to study both the outcomes compared to different objectives as well as incentive properties. Highlights of our results include: 1) privileging the perspective of the average rater maximizes social welfare, but is subject to simple manipulation strategies; 2) privileging the perspective of the median rater satisfies the Condorcet criterion, and is the only identifiable viewpoint robust to the same manipulations, even by coalitions; 3) more ideologically extreme agents have a larger incentive to participate.