We don’t need there to be a benefit to a low amount of fraud to optimize for it. Optimization is a purely mathematical exercise [1]. Once we construct the problem with a chosen set of constraints then we apply mathematical techniques to solve it. Of course, many types of optimization problems (especially non-linear or non-convex) can be extremely difficult to solve optimally without relaxing some constraints or settling for approximations to the optimal solution.
But, besides that, the task of interpreting the results and of potentially selecting new constraints or even a new objective function is a separate matter. Perhaps we should be seeking to maximize trust rather than minimize fraud in society. But then we have to ask ourselves: “what would that look like?”
There does not need to be a set of constraints for optimisation to be defined. You can talk about optimisation on an unconstrained domain, for example all of ℝ⨯ℝ. But there DOES need to be a measure function that measures what you are optimising for. The benefit of fraud would be one such function you could optimise for, and that seems to be what GP is after. The pure amount of fraud is a different one, which seems to be what you are interested in.
But, besides that, the task of interpreting the results and of potentially selecting new constraints or even a new objective function is a separate matter. Perhaps we should be seeking to maximize trust rather than minimize fraud in society. But then we have to ask ourselves: “what would that look like?”
[1] https://en.wikipedia.org/wiki/Mathematical_optimization