Fig. 6: The area under the preference curve (AUC) is greatest when multiple options receive high ratings.

Left panel: Illustration of the preference profiles of all participants, with the rows representing three distinct voting methods and columns referring to the legitimacy ratings. The options are sorted in such a way that the highest-rated option is on the right, and the lowest-rated option is on the left. The blue curve is estimated via Local Polynomial Regression Fitting; its shaded area represents the 95 percent confidence interval. Right panel: Illustration of the average area under the preference profile curves (AUC) across questions for each participant, rescaled within each voting method. The AUC is plotted against the legitimacy rating for each voting method, providing a visual representation of the relationship between the AUC and the perceived legitimacy of the voting methods.