A student and a colleague of mine, Colleen Berndt and Larry Iannaccone, have an interesting paper on the Oracle at Delphi. It turns out that the Oracle’s prophecies tended to be pretty accurate:
The long journey some made to reach Delphi, combined with the long waits for a consultation, indicate a greater opportunity for information to make its way to the priests and pythias. In addition to the information circulated at the local watering holes, the priestesses were able to aggregate information gleaned from petitioner.
On political subjects, it was especially important for Delphi to be independent of political influence:
When Delphi gained its independence from the Phocians, it began to benefit greatly from a perception of fairness. Lack of control by any one state meant that Delphi could operate free from any political pressure.
Since the Oracle charged by the question, it was important to think carefully about the questions one asked. This is also good advice for those creating prediction markets today. The cost of creating a market is largely independent of the topic, while the value varies greatly by topic. So for the best cost-benefit, ask the biggest questions.