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In the setting where a group of agents is asked a single subjectivemulti-choice question (e.g. which one do you prefer? cat or dog?), we areinterested in evaluating the quality of the collected feedback. However, thecollected statistics are not sufficient to reflect how informative the feedbackis since fully informative feedback (equal affection of the choices) and fullyuninformative feedback (random selection) have the same uniform statistics.  Here we distinguish the above two scenarios by additionally asking forrespondents' predictions about others' choices. We assume that informativerespondents' predictions strongly depend on their own choices whileuninformative respondents' do not. With this assumption, we propose a newdefinition for uninformative feedback and correspondingly design a family ofevaluation metrics, called f-variety, for group-level feedback which can 1)distinguish informative feedback and uninformative feedback (separation) evenif their statistics are both uniform and 2) decrease as the ratio ofuninformative respondents increases (monotonicity). We validate our approachboth theoretically and numerically. Moreover, we conduct two real-world casestudies about 1) comparisons about athletes and 2) comparisons about stand-upcomedians to show the superiority of our approach.

Equal Affection or Random Selection: the Quality of Subjective Feedback from a Group Perspective