Many psychology experiments show that individually judged probabilities of the same event can vary depending on the partition of the state space (a framing effect called "partition-dependence"). We show that these biases transfer to competitive prediction markets in which multiple informed traders are provided economic incentives to bet on their beliefs about events. We report results of a short controlled lab study, a longer field experiment (betting on the NBA playoffs and the FIFA World Cup), and naturally-occurring trading in macro-economic derivatives. The combined evidence suggests that partition-dependence can exist and persist in lab and field prediction markets