It seems to me that this blog has just reached it's first real crisis.
Three people are announcing three apparently opposed beliefs with substantial real expected consequences and yet no-one has yet spoken, or it seems to me implied, the key slogan... "LETS USE SCIENCE!" or, as hubristic Bayesian wannabes, not invoked Bayes as an idol to swear by, but rather said "LETS USE HUMANE REFLECTIVE DECISION THEORY, THE QUANTITATIVELY UNKNOWN BUT QUALITATIVELY INTUITED POWER DEEPER THAN SCIENCE FROM WHICH IT STEMS AND TO WHICH OUR COMMUNITY IS DEVOTED".
IF RDS was applied to our current situation, people would be analyzing Yvain's, Davis' and Eby's proposals, working out exactly what their implications are, and trying to propose, in the name of SCIENCE, hypotheses which will distinguish between them, and in the name of BAYES, confidence estimates of their analyses and of the quality with which the denotations of their words have cleaved reality at the joints enabling an odds ratio of updating to be extracted from a single data point. People would be working out what features of which of the models used by Yvain, Davis and Eby constitute evidence against what other features. They would be trying to evaluate non-verbally, through subjectively opaque but known-to-be-informative processes vulnerable to verbal overshadowing, what relative odds to place on those different features of the models. Finally, they would be examining the expected costs entailed by experiments being proposed and selecting those experiments which promise to provide the most information for the least cost be performed. The cost estimate would include both the effort required to perform the experiments, probably best assessed with an outside view in most cases like these, and the dangers to the minds of the participants from possible adverse outcomes, taking into account, as well as possible, the structural uncertainty of the models.
I sincerely hope to see some of that in the comments section soon, either under this post or the "Applied Picoeconomics" post.
My first response to this was "Wait, I have a model?"
Right now I don't think we're even at a point where it's valuable to think of three different "theories" or what they imply. We have three different techniques, all of which are kind of supported by picoeconomics but also kind of hand-wave-y. And ZM's objection to my post seems to be more philosophical than a simple "your method won't work" (and I still don't entirely understand Pjeby).
Once we have some more discussion, if it becomes clear that we have actually have three different but comparable willpower techniques and we really want to know which will work best, then we can start wishing we could test them. I'm doubtful we can actually do so, since I doubt we could get more than about 30 volunteers, and 30 divided by 3 groups does not a legitimate sample size make for a complicated psych experiment. But if you have some ideas, I'd be happy to help.
The sample size issue etc is why I talk about Bayes. You get important info from single data points all the time in life. There's just a fetish against doing so in science due to bad epistemology trying and failing to counter other bad epistemology.
You certainly derived your belief that your procedure would work from a theory. You hadn't actually even seed it work, so nothing but a theoretical basis could explain your attempt.