  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.
