I don't think that the kind of case you are describing here is a strong consideration against using Period Independence in cases that don't involve exact repetition.
What if we assume Period Independence except for exact repetitions, where the value of extra repetitions eventually go to zero? Perhaps this could be a way to be "timid" while making the downsides of "timidity" seem not so bad or even reasonable? For example in section 6.3.2, such a person would only choose deal 1 over deal 2 if the years of happy lives offered in deal 1 are such that he would already have repeated all possible happy time periods so many times that he values more repetitions very little.
BTW what do you think about my suggestion to do a sequence of blog posts based on your thesis? Or maybe you can at least do one post as a trial run? Also as an unrelated comment, the font in your thesis seems to be such that it's pretty uncomfortable to read in Adobe Acrobat, unless I zoom in to make the text much larger than I usually have to. Not sure if it's something you can easily fix. If not, I can try to help if you email me the source of the PDF.
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I'd like to see effect sizes, and perhaps the result of running the reviewed studies through the p-curve tool accompanying such claims.
I agree that this would be good, but didn't think it was worthwhile for me to go through the extra effort in this case. But I did think it was worthwhile to share what I had already found. I think I was very clear about how closely this had been vetted (which is to say, extremely little).