Double-blind trials aren't the gold standard, they're the best available standard. They still don't replicate far too often, because they don't remove bias (and I'm not just referring to publication bias). Which is why, when considering how to interpret a study, you look at the history of what scientific positions the experimenter has supported in the past, and then update away from that to compensate for bias which you have good reason to think will show up in their data.
In the example, past results suggest that, even if the trial was double-blind, someone who is committed to achieving a good result for the treatment will get more favorable data than some other experimenter with no involvement.
And that's on top of the trivial fact that someone with an interest in getting a successful trial is more likely to use a directionally-slanted stopping rule if they have doubts about the efficacy than if they are confident it will work, which is not explicitly relevant in Eliezer's example.
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Romer goes on to write:
He should reread Kuhn. Kuhn says that the cause of persistent disagreement is usually the lack of a relevant and workable scientific paradigm which can identify important problems, resolve disputes, and thereby mandate researchers to come to consensus. Romer's use of the phrase "the norms of science" indicates that he believes in a singular, universal, monolithic set of principles which is valid for all types of scientific inquiry. But economists obviously cannot use the same principles as physicists, simply because they cannot run experiments. What Romer is really complaining about is that there is no good paradigm for economics, but that's not anyone's fault - the discovery and articulation of a paradigm is as difficult as doing the science that the paradigm supports. A more valid criticism of the field would be "We are trying to do science without a strong enough paradigm, and the weakness of the paradigm is preventing us from resolving our disagreements definitively. Instead of trying to do more research along the same old lines, we should go back to the philosophical foundations and re-examine what it means to do economics."
This is a field in which the discoverer of the theorem that rational agents cannot disagree was given the highest possible honours...