Well, as you may see it’s also is not helpful

My reasoning explicitly puts instrumental rationality ahead of epistemic. I hold this view precisely to the degree which I do in fact think it is helpful.

The extra category of a “fair bet” just adds another semantic disagreement between halfers and thirders.

It’s just a criterion by which to assess disagreements, not adding something more complicated to a model.

Regarding your remarks on these particular experiments:

If someone thinks the typical reward structure is some reward structure, then they’ll by default guess that a proposed experiment has that reward structure.

This reasonably can be expected to apply to halfers or thirders.

If you convince me that halfer reward structure is typical, I go halfer. (As previously stated since I favour the typical reward structure). To the extent that it’s not what I would guess by default, that’s precisely because I don’t intuitively feel that it’s typical and feel more that you are presenting a weird, atypical reward structure!

And thirder utilities are modified

duringthe experiment. They are not just specified by a betting scheme, they go back and forth based on the knowledge state of the participant—behave the way probabilities are supposed to behave. And that’s because they are partially probabilities—a result of incorrect factorization of E(X).

Probability is a mathematical concept with very specific properties. In my previous post I talk about it specifically and show that thirder probabilities for Sleeping Beauty are ill-defined.

I’ve previously shown that some of your previous posts incorrectly model the Thirder perspective, but I haven’t carefully reviewed and critiqued all of your posts. Can you specify exactly what model of the Thirder viewpoint you are referencing here? (which will not only help me critique it but also help me determine what exactly you mean by the utilities changing in the first place, i.e. do you count Thirders evaluating the total utility of a possibility branch more highly when there are more of them as a “modification” or not (I would not consider this a “modification”).

So had some results I didn’t feel were complete enough in to make a comment on (in the senses that subjectively I kept on feeling that there was some follow-on thing I should check to verify it or make sense of it), then got sidetracked by various stuff, including planning and now going on a

~~trip~~sacred pilgrimage to see the eclipse. Anyway:all of these results relate to the “main group” (non-fanged, 7-or-more segment turtles):

Everything seems to have some independent relation with weight (except nostril size afaik, but I didn’t particularly test nostril size). When you control for other stuff, wrinkles and scars (especially scars) become less important relative to segments.

The effect of abnormalities seems suspiciously close to 1 lb on average per abnormality (so, subjectively I think it might be 1). Adding abnormalities has an effect that looks like smoothing (in a biased manner so as to increase the average weight): the weight distribution peak gets spread out, but the outliers don’t get proportionately spread out. I had trouble finding a smoothing function* that I was satisfied exactly replicated the effect on the weight distribution however. This could be due to it not being a smoothing function, me not guessing the correct form, or me guessing the correct form and getting fooled by randomness into thinking it doesn’t quite fit.

For green turtles with zero miscellaneous abnormalities, the distribution of scars looked somewhat close to a Poisson distribution. For the same turtles, the distribution of wrinkles on the other hand looked similar but kind of spread out a bit...like the effect of a smoothing function. And they both get spread out more with different colours. Hmm. Same spreading happens to some extent with segments as the colours change.

On the other hand, segment distribution seemed narrower than Poisson, even one with a shifted axis, and the abnormality distribution definitely looks nothing like Poisson (peaks at 0, diminishes far slower than a 0-peak Poisson).

Anyway, on the basis of not very much clear evidence but on seeming plausibility, some wild speculation:

I speculate there is a hidden variable, age. Effect of wrinkles and greyer colour (among non-fanged turtles) could be a proxy for age, and not a direct effect (names of those characteristics are also suggestive). Scars is likely a weaker proxy for age and also no direct effect. I guess segments likely do have some direct effect, while also being a (weak, like scars) proxy for age. Abnormalities clearly have a direct effect. Have not properly tested interactions between these supposed direct effects (age, segments, abnormalities), but if abnormality effect doesn’t stack additively with the other effects, it would be harder for the 1-lb-per-abnormality size of the abnormality effect to be a non-coincidence.

So, further wild speculation: so age affect on weight could also be smoothing function (though, looks like high weight tail is thicker for greenish-gray—does that suggest it is not a smoothing function?

unknown: is there an inherent uncertainty in the weight given the characteristics, or does there merely appear to be because of the age proxies being unreliable indicators of age? is that even distinguishable?

* by smoothing function I think I mean another random variable that you add to the first one, this other random variable takes on a range of values within a relatively narrow range. (e.g. uniform distribution from 0.0 to 2.0, or e.g. 50% chance of being 0.2, 50% chance of being 1.8).

Anyway, this all feels figure-outable even though I haven’t figured it out yet. Some guesses where I throw out most of the above information (apart from prioritization of characteristics) because I haven’t organized it to generate an estimator, and just guess ad hoc based on similar datapoints, plus Flint and Harold copied from above:

Abigail 21.6, Bertrand 19.3, Chartreuse 27.7, Dontanien 20.5, Espera 17.6, Flint 7.3, Gunther 28.9, Harold 20.4, Irene 26.1, Jacqueline 19.7