I'm thinking maybe the task provider could send a key that should be somehow mixed with the response. But, if the worker simply uses the key to encrypt the result, the message could still be corrupted. Is homomorphic encryption any helpful?
Another way is voting, but requires at least 3 different workers to solve the same task, which becomes expensive. Crypto falls in this category.
Yet another way is validating whether the results are in a expected range or format, but this could be difficult since the task provider shouldn't solve it to know. Zero knowledge proof?
Homeomorphic encryption is the middle ground. Solutions still need to be verified, but because only you can understand the encrypted tasks, it is in principle impossible for the other participants to cheat. In practice I think it is still entirely an academic exercise; I don’t think anyone actually uses homeomorphic encryption for anything real.
There's no generic answer to this, your controls and incentives need to be matched to the type of problem you're trying to solve and the interests of network participants.
For example, seti@home "worked" despite waste, mainly IMHO because you got an awesome looking screensaver out of it and you got to tell people your computer was searching for alien life. The leaderboard rankings also were also a great incentive for the types of people who had control over a lot of compute.