May I ask what your impression of "the sum" is? Namely, what is "the sum of a game" to you? The question may sound slightly opaque (and, sure, maybe even pedantic), but here are examples of some aspects I am trying to garner:
• Do you see it as a single number (e.g., representable by a single floating-point value)? If not, how alike to a number is it? To what degrees does it lend itself to ordering (higher/lower/equal) and aggregation?
• Do you think the concept of "the sum" has a consensus interpretation (consensus across people, say)? For a particular game, do you think its sum has a consensus determination?
I'm less settled on precisely those aspects, and I think they tend to mask aspects that are worth clarifying/examining. Please do not see this as my claim that my stance is absolutely the only valid one. However, without a unified stance on these aspects, it feels hard to contribute further to the discussion.
My contention is that "a game" cannot be condensed down to a single number. (More specifically, I think that it should only be done so in a way that is unequivocally universal and objective. If this doesn't exist, any discussion should begin on more general premises, rather than the premise that a game can be condensed down to a single number.) From the perspective of evaluating whether capitalism installs incentives that result in a better world, I view it as overly simplistic to think about "a sum" and then consider whether that sum is zero/nonzero/positive/negative.
Of course, these are models, and I judge the merits of a model based on its ability to be useful. But here I really consider that such a simplistic model is a hindrance. I don't mean hindrance in the sense that it necessarily results in poor decisions being made (partially because the model seems to come with an intrinsic notion of "poor"). It's a hindrance in that it seems too ubiquitously adopted, to the extent that discussions on the alternative are hard to initiate/sustain/come by.
As a result, I think there is a lot more elaboration needed before landing on this dichotomy:
> But to argue that externalities make capitalism zero-sum is to argue externalities always exactly match whatever value was gained by capitalist transactions. Which is even harder to prove than the already dubious argument that externalities are larger than the value of capitalism.
Namely, I don't readily see that there is a dichotomy in the form of either (1) "externalities always exactly match whatever value was gained by capitalist transactions" or (2) "externalities are larger than the value of capitalism". The dichotomy doesn't easily stand to me because it seems attached to an oversimplified way to compare outcomes/merits of a game ("exactly match whatever value", "larger than the value of").