Biased perceptions of public opinion don't define echo chambers but reveal systematic differences in political awareness.

Echo chambers are widely acknowledged as a feature of online discourse and current politics: a phenomenon arising when people selectively engage with like-minded others and are shielded from opposing ideas. Various studies have operationalized the concept through studying opinions, interactions, reinforcement or group identity. Echo chambers both feed and are fed by the false consensus effect, whereby people overestimate the degree to which others share their views, with algorithmic filtering of social media also a contributing factor. Although there is strong evidence that meta-opinions - that is, people's perceptions of others' opinions - often fail to reflect reality, no attempt has been made to explore the space of meta-opinions, or detect echo chambers within this space. We created a new, information-theoretic method for directly quantifying the information content of meta-opinions, allowing detailed exploratory analysis of their relationships with demographic factors and underlying opinions. In a gamified survey (presented as a quiz) of 476 UK respondents, we found both the liberal left, and also people at both extremes of the left/right scale, to have more accurate knowledge of others' opinions. Surprisingly however, we found that meta-opinions, although displaying significant false consensus effects, were not divided into any strong clusters representative of echo chambers. We suggest that the metaphor of discrete echo chambers may be inappropriate for meta-opinions: while measures of meta-opinion accuracy and its influences can reveal echo chamber characteristics where other metrics confirm their presence, the presence or absence of meta-opinion clusters is not itself sufficient to define an echo chamber. We publish both data and analysis code as supplementary material.