Suppose you’re deciding between two statistical methods. You pick the one that has more power. This increases your chances of making a correct decision in theory while possibly lowering your chances of actually concluding the truth. The subtle trap is that the meaning of “in theory” changes because you have two competing theories.
When you compare the power of two methods, you’re evaluating each method’s probability of success under its own assumptions. In other words, you’re picking the method that has the better opinion of itself. Thus the more powerful method is not necessarily the method that has the better chance of leading you to a correct conclusion.
Comparing power alone is not enough. You also need to evaluate whether a method makes realistic assumptions and whether it is robust to deviations from its assumptions.