We study a scenario where an adjudication task (e.g., the resolution of a binary dispute) is outsourced to a set of agents who are appointed as jurors. This scenario is particularly relevant in a Web3 environment, where no verification of the adjudication outcome is possible, and the appointed agents are, in principle, indifferent to the final verdict. We consider simple adjudication mechanisms that use (1) majority voting to decide the final verdict and (2) a payment function to reward the agents with the majority vote and possibly punish the ones in the minority. Agents interact with such a mechanism strategically: they exert some effort to understand how to properly judge the dispute and cast a yes/no vote that depends on this understanding and on information they have about the rest of the votes. Eventually, they vote so that their utility (i.e., their payment from the mechanism minus the cost due to their effort) is maximized. Under reasonable assumptions about how an agent's effort is related to her understanding of the dispute, we show that appropriate payment functions can be used to recover the correct adjudication outcome with high probability. Our findings follow from a detailed analysis of the induced strategic game and make use of both theoretical arguments and simulation experiments.