The most profound comment was not in this HN thread, nor by a user in the Twitter thread: the most profound comment was the one quoted in the article itself, by Bernoulli!:
> Bernoulli once wrote, “The utility [of probabilistic decisions] is dependent on the particular circumstances of the person making the estimate. There is no reason to assume that the risks anticipated by each [individual] must be deemed equal in value.”
Risk over non-fungibles (body parts, sentimentally valued heirloom pieces, ...) are obviously subjectively valued. But even for platonic (ideal) fungibles like fiat money the risks depend on the person because modeling reality as if everyone is treated equal in commerce or has equal access to and treatment in the courts etc. is a very strong assumption to make.
Let us first assume contracts are never reneged etc, and let us thus first assume agreements are rigorously respected.
Let us further assume the subject has the usual goal of maximizing its capital, here denoted in dollars.
Since currencies are a social construct and only hold value in the context of a society, we assume the subject is in prolonged contact with a society that values this currency. (If not the subject doesn't care which answer to give.)
Contrary to all the comments here in HN (nonlinear utility etc.), if the goal of the subject is to maximize capital, then the correct answer (assuming absence of things like conscientious objection) is unconditionally the green button with the highest Expectation Value, non-linear utility functions, or one-time-ness of the offer, or subject poverty be damned!
To understand why: even if the offer is one-time, and even if the subject can not afford the regret of missing out, the subject is still in contact with society. This society has companies regularly dealing with large sums, and optimizing expectation value.
THE SUBJECT CAN SIMPLY GO TO A BANK AND TRADE THE HIGH ROI FOR STABILITY WITH THE BANK:
For example the subject and bank can agree to the following:
* Bank pays subject $20 million
* subject presses green button
* If subject receives $50 million, it forwards this to the bank, otherwise nothing
In this scenario the subject wins $20 million unconditionally, and the bank spent $20 M with an expected return of $25 M, so the bank sees an expected ROI of a handsome +25%.
The real catch is not personal utility function, one-time-ness, etc ... but reliability of contracts and trustworthiness of the system enforcing them, which one can read between the lines of Bernoulli's comments.
All the comments and observations about how poor people "should" take the certainty with the lower amount is just echoing the indoctrinated "learn and embrace your lowly position in society" wheither thats low in rewards, or low in reliability of fair enforcement of the law.
I find it hard to read intellectually capable people concoct artificial examples to make people distrust mathematical rigor when it can be entirely relied upon. The real element of unreliability is in the systems under which we are subjugated.