An n-candidate election in which the electorate views n-1 of the candidates as equivalent alternatives to the nth.  But they need to solve the coordination problem of which one to vote for.  A prediction market allows speculators to drive up the price of any one of them, convincing the voters that he is the focal point and winning, or conversely to jam the signal by equalizing their share prices while at the same time going long on the nth.  Of course the voters know this, but they may not know that all of the voters know (etc) this.

How informative can prediction markets be in such a scenario?  I think Justin Wolfers might be interested in the answer.

See Rajiv Sethi for related thoughts.