In the above example, attempts to produce a most accurate estimate of the sum do a better job than attempts to produce most complete sum.

In general what you learn from applied mathematics is that plenty of methods that are in some abstract sense more distant from the perfect method have a result closer to the result of the perfect method.

E.g. the perfect method could evaluate every possible argument, sum all of them, and then decide. The approximate method can evaluate a least biased sample of the arguments, sum them, and then decide, whereas the method that tries to match the perfect method the most would sum all available arguments. If you could convince an agent that the latter is 'most rational' (which may be intuitively appealing because it does resemble the perfect method the most) and is what should be done, then in a complex subject where agent does not itself enumerate all arguments, you can feed arguments to that agent, biasing the sum, and extract profit of some kind.