A multiagent Turing test based on a prediction market

In a Turing test, a single agent (the judge, generally a human) chats with two mysterious conversation partners [1]. One of the two mystery conversationalists is a human, while the other is a computer program (a chat bot, or just bot). The bot is the entity who is actually taking the test: If the judge cannot (accurately) tell which mystery conversation partner is the human and which is the bot, then the bot passes the test (and otherwise it fails). It is easy to see that a Turing test can also be run with only a single mysterious conversation partner (whom we will call the target). To do so, the test organizer chooses a human target with probability 50% and a computer target with probability 50%. Then, after a conversation with the target, the judge is asked to report how probable she thinks it is that the target is a human--if she reports 50% or higher when talking to a bot, then that bot passes the test.