Interesting read. Regarding the relationship between volume and accuracy, there need not be one in limit-order-book markets like Kalshi and Polymarkets. In theory, as long as quotes are accurate and adjust quickly to new information, there is no need (and no incentive) to trade since prices are efficient. This is the case in US equity markets: most price discovery occurs through quote updates, not through trades.

Studying prediction markets is one of my current research areas. In my latest paper (preprint at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6443103), we find that on Polymarkets, markets are, on average, quite accurate and unbiased. We did see a similar non-pattern between trade volume and accuracy, past a certain threshold.