We create a formal framework for the design of informative securities in prediction markets. These securities allow a market organizer to infer the likelihood of events of interest as well as if he knew all of the traders' private signals. We consider the design of markets that are always informative, markets that are informative for a particular signal structure of the participants, and informative markets constructed from a restricted selection of securities. We find that to achieve informativeness, it can be necessary to allow participants to express information that may not be directly of interest to the market organizer, and that understanding the participants' signal structure is important for designing informative prediction markets.
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