I think one confusing aspect is the fact that the person being critical about the structure of the post is also the target of the post, therefore it is difficult to assume good intent.
If another well respected user had written a similar comment about why the post should have been written differently, then it would be a much cleaner discussion about writing standards and similar considerations. Actually, a lot of people did, not really about the structure (at least I don’t think so), but mostly about the tone of the post.
As for EY, it is difficult not to assume that this criticism isn’t completely genuine, and is some way to attack the author. That being said, maybe we should evaluate arguments for what they are, regardless of why they were stated in the first place (or is it being too naive?)
In that regard, your post is very interesting because it addresses both questions: showing that EY hasn’t always followed this stated basic standard (i.e. claiming that the criticism is not genuine), and discussing the merit of this rule/good practice (i.e. is it a good basis for criticism)
Anyway, interesting post, thanks for writing it!
I think there’s actually one way to set relative responsibility weight which makes more mathematical sense than the others. But, first, let’s slightly change the problem, and assume that the members of the group arrived one by one, that we can order the members by time of arrival. If this is the case, I’d argue that the complete responsibility for the soup goes to the one who brought the last necessary element.
Now, back to the main problem, where the members aren’t ordered. We can set the responsibility weight of an element to be the number of permutations in which this particular element is the last necessary element, divided by the total number of permutations.
This method has several qualities : the sum of responsibilities is exactly one, each useful element (each Necessary Element of some Sufficient Set) has a positive responsibility weight, while each useless element has 0 responsibility weight. It also respects the symmetries of the problem (in our example, the responsibility of the pot, the fire and the water is the same, and the responsibility of each ingredient is the same)
In a subtle way, it also takes into account the scarcity of each ressource. For example, let’s compare the situation [1 pot, 1 fire, 1 water, 3 ingredients] with the situation [2 pots, 1 fire, 1 water, 3 ingredients]. In the first one, in any order, the responsibility goes to the last element, therefore the final responsibility weight is 1⁄7 for each element. The second situation is a bit trickier, we must consider two cases. First case, the last element is a pot (1/4 of the time). In this case, the responsibility goes to the seventh element, which gives 1⁄7 responsibility weight to everything but the pots, and 1⁄14 responsibility weight to each pot. Second case, the last element is not a pot (3/4 of the time), in which case the responsibility goes to the last element, which gives 1⁄6 responsibility weight to everything but the pots, and 0 to each pot. In total, the responsibilities are 1⁄56 for each pot, and 9⁄56 for each other element. We see that the responsibility has been divided by 8 for each pot, basically because the pot is no longer a scarce ressource.
Anyway, my point is, this method seems to be the good way to generalize on the idea of NESS : instead of just checking whether an element is a Necessary Element of some Sufficient Set, one must count how many times this element is the Necessary Element of some permutation.