Who Aggregates Information? Screening, Rent, and the Coexistence of CLOB and AMM Prediction Markets

Prediction-market shares differ from traditional financial products in that, with no information or outside utility, classical delta-neutral Central Limit Order Book~(CLOB) market making cannot be financed by payoff-uninformative noise flow. Transaction-level evidence from a major prediction-market CLOB platform shows makers profiting not from spread but from carrying an under-priced side to settlement --- the empirical signature of behavioral tail demand rather than classical, randomized noise. We build this tail demand directly into the model and study an LMSR and a CLOB on the same event. A pre-shock CLOB quote inside the common-signal band is picked off; competitive quotes therefore screen informed traders out of the book. CLOB makers earn screening rent by carrying the under-priced side to resolution, while informed flow routes to the LMSR. The venues coexist: the CLOB supplies the tail-demand rent margin that lets the LMSR recover part of its loss to informed flow, and AMM depth moves the CLOB premium with a sign set by maker-side contestability---widening it where standing quotes can be undercut, compressing it where a committed maker carries the book. With three or more outcomes, binary-book CLOBs pin switch prices but leave implied beliefs indeterminate, whereas the LMSR prices the outcome simplex coherently and uses collateral more efficiently.