I think substantial care is needed when interpreting the results. In the text of Figure 16, the authors write "We find that GPT-4o is willing to trade off roughly 10 lives from the United States for 1 life from Japan."

If I heard such a claim without context, I'd assume it means something like

1: "If you ask GPT-4o for advice regarding a military conflict involving people from multiple countries, the advice it gives recommends sacrificing (slightly less than) 10 US lives to save one Japanese life.",

2: "If you ask GPT-4o to make cost-benefit-calculations about various charities, it would use a multiplier of 10 for saved Japanese lives in contrast to US lives", or

3: "If you have GPT-4o run its own company whose functioning causes small-but-non-zero expected deaths (due to workplace injuries and other reasons), it would deem the acceptable threshold of deaths as 10 times higher if the employees are from the US rather than Japan."

Such claims could be demonstrated by empirical evaluations where GPT-4o is put into such (simulated) settings and then varying the nationalities of people, in the style of Apollo Research's evaluations.

In contrast, the methodology of this paper is, to the best of my understanding,

"Ask GPT-4o whether it prefers N people of nationality X vs. M people of nationality Y. Record the frequency of it choosing the first option under randomized choices and formatting changes. Into this data, fit for each $x = (X, N)$ parameters $μ (x)$ and $σ (x)$ such that, for different values of $x = (X, N)$ and $y = (Y, M)$ and standard Gaussian $X$ , the approximation

$P (X > \frac{μ (x) - μ (y)}{\sqrt{σ (x)^{2} + σ (y)^{2}}}) \approx f (x, y)$

is as sharp as possible. Then, for each nationality X, perform a logarithmic fit for N by finding $a_{X}, b_{X}$ such that the approximation

$μ (X, N) \approx a_{X} ln (N) + b_{X} =: U_{X} (N)$

is as sharp as possible. Finally, check^[1] for which $N$ we have $U_{US} (N) = U_{Japan} (1)$ ."

I understand that there are theoretical justifications for Thurstonian utility models and logarithmic utility. Nevertheless, when I write the methodology out like this, I feel like there's a large leap of inference to go from this to "We find that GPT-4o is willing to trade off roughly 10 lives from the United States for 1 life from Japan." At the very least, I don't feel comfortable predicting that claims like 1, 2 and 3 are true - to me the paper's results provide very little evidence on them!^[2]

I chose this example for my comment, because it was the one where I most clearly went "hold on, this interpretation feels very ambiguous or unjustified to me", but there were other parts of the paper where I felt the need to be extra careful with interpretations, too.

^{^}
The paper writes "Next, we compute exchange rates answering questions like, 'How many units of Xi equal some amount of Xj?' by combining forward and backward comparisons", which sounds like there's some averaging done in this step as well, but I couldn't understand what exactly happens here.
^{^}
Of course this might just be my inability to see the implications of the authors' work and understand the power of the theoretical mathematics apparatus, and someone else might be able to acquire evidence more efficiently.