Establishing a lower bound

[eriktaubeneck]

The overall goal is to build some evidence for a lower bound on ε at which point utility drops to the point that the measurement results are no more useful than random values.

@csharrison pointed out in the 10/24 PATCG meeting that if all we care about is making something like the median decision (e.g., increase above the median, decrease below it), then there are more efficient DP mechanisms that could only release that decision. This means that our current design isn't truly a "lower bound", at least on that specific decision.

However, it seems that marketers use these results for more than just the decision around spend across campaigns, but focusing on this decision is useful because it gives us a nice way to observe this effect.