Assistant professor @ BI Norwegian Business School

Postdoc in statistics. Three kids, two cats, one wife. I write about statistics, EA, psychometrics, and other things at my blog

I'm looking for collaborators in everything I do. If you (a) see anything I've written about that you want to work with, or (b) want me to work on something you're doing (paid or not, depending on the project), please contact me.

I'm actively seeking master students who want to work with EA-adjacent statistics.

Statistics. Statistics is often harder than you think.

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I don't understand your notion of context here. I'm understanding pairwise comparisons as standard decision theory - you are comparing the expected values of two lotteries, nothing more. Is the context about psychology somehow? If so, that might be interesting, but adds a layer of complexity this sort of methodology cannot be expected to handle.

Players may have different utility functions, but that might be reasonable to ignore when modelling all of this. In any case, every intervention will have its own, unique, expected utility from each player , hence . (This is ignoring noise in the estimates, but that is pretty easy to handle.)

Estimation is actually pretty easy (using linear regression), and is essentially a solved problem since 1952. Scheffé, H. (1952). An Analysis of Variance for Paired Comparisons. Journal of the American Statistical Association, 47(259), 381–400. https://doi.org/10.1080/01621459.1952.10501179

I wrote about the methodology (before finding Scheffé's paper) here.

Do I understand you correctly here?

Each agent has a computable partial preference ordering that decides if it prefers to .

We'd like this partial relation to be complete (i.e., defined for all ) and transitive (i.e., and implies ).

Now, if the relation is sufficiently non-trivial, it will be expensive to compute for some . So it's better left undefined...?

If so, I can surely relate to that, as I often struggle computing my preferences. Even if they are theoretically complete. But it seems to me the relationship is still defined, but might not be practical to compute.

It's also possible to think of it in this way: You start out with partial preference ordering, and need to calculate one of its transitive closures. But that is computationally difficult, and not unique either.

I'm unsure what these observations add to the discussion, though.

Some comments:

- Have you considered hiring a designer for this document? It doesn't look good at all and is filled up with bold faces all over the place.
- Why is it so long? I don't see why it's important for vegans to know that cows are supplemented with vitamin B12.
- It could have benefited a lot from lists of key takeaways. For instance, do you need to take vitamin D3 supplementation, and how much? Much of the document feels like an info dump to me.

Sure, if your goal is to be a good writer! But, I'm not worried about that. I just want people to understand me.

As far as I can recall, my paragraphs are usually about half as long when I ask ChatGPT to simplify.

That said, I tend to write in an academic style.

I agree that academic language should be avoided in both forums and research papers.

It might be a good idea for forum writers to use a tool like ChatGPT to make their posts more readable before posting them. For example, they can ask ChatGPT to "improve the readability" of their text. This way, writers don't have to change their writing style too much and can avoid feeling uncomfortable while writing. Plus, it saves time by not having to go back and edit clunky sentences. Additionally, by asking ChatGPT to include more slang or colloquial language, the tool can better match the writer's preferred style. (Written with the aid of ChatGPT in exactly the way I proposed. :p)

If I understand you correctly, what you're proposing is essentially a subset of classical decision theory with bounded utility functions. Recall that, under classical decision theory, we choose our action according to where is a random state of nature and an action space.

Suppose there are (infinitely many works too) moral theories , each with probability and associated utility . Then we can define This step gives us (moral) uncertainty in our utility function.

Then, as far as I understand you, you want to define some component utility functions as As then is the probability of an acceptable outcome under . And since we're taking the expected value of these bounded component utilities to construct , we're in classical bounded utility function land.

That said, I believe that

- This post would benefit from a rewrite of the paragraph starting with "Success maximization is a mechanism by which to generalize maxipok". It states " Let be an action from the set of actions . " Is and action, and action, or both? I also don't understand what is. Are there states of nature in this framework? You say that is a moral theory, so it cannot be ?
- You should add concrete examples. If you add one or two it might become easier to understand what you're doing despite the formal definition not being 100% clear.

I'm not sure what you mean. I'm thinking about pairwise comparisons in the following way.

(a) Every pair of items i,j have a true ratio of expectations E(Xi)/E(Xj)=μij. I hope this is uncontroversial. (b) We observe the variables Rij according to logRij∼logμij+ϵij for some some normally distributed ϵij. Error terms might be dependent, but that complicates the analysis. (And is most likely not worth it.) This step could be more controversial, as there are other possible models to use.

Note that you will get a distribution over every E(Xi) too with this approach, but that would be in the Bayesian sense, i.e., p(E(Xi)∣comparisons), when we have a prior over E(Xi).