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Social media companies have struggled to provide a democratically legitimate definition of "Fake News". Reliance on expert judgment has attracted criticism due to a general trust deficit and political polarisation. Approaches reliant on the ``wisdom of the crowds'' are a cost-effective, transparent and inclusive alternative. This paper provides a novel end-to-end methodology to detect fake news on X via "wisdom of the synthetic & representative crowds". We deploy an online survey on the Lucid platform to gather veracity assessments for a number of pandemic-related tweets from crowd-workers. Borrowing from the MrP literature, we train a Hierarchical Bayesian model to predict the veracity of each tweet from the perspective of different personae from the population of interest. We then weight the predicted veracity assessments according to a representative stratification frame, such that decisions about ``fake'' tweets are representative of the overall polity of interest. Based on these aggregated scores, we analyse a corpus of tweets and perform a second MrP to generate state-level estimates of the number of people who share fake news. We find small but statistically meaningful heterogeneity in fake news sharing across US states. At the individual-level: i. sharing fake news is generally rare, with an average sharing probability interval [0.07,0.14]; ii. strong evidence that Democrats share less fake news, accounting for a reduction in the sharing odds of [57.3%,3.9%] relative to the average user; iii. when Republican definitions of fake news are used, it is the latter who show a decrease in the propensity to share fake news worth [50.8%, 2.0%]; iv. some evidence that women share less fake news than men, an effect worth a [29.5%,4.9%] decrease., Comment: 50 pages, 6 figures, 2 tables