I think “zero/positive/negative sum” is just fine for the common term if everyone knows it’s not referring to game theory, since “zero sum” seems just fine for describing an interaction which neither produces or destroys resources. I like the suggestion of “zero sum in X” to help make this clear (for example, theft is zero sum in property, at least if there’s no property damage, even though it might be far from zero sum in terms of happiness or other things).
What I object to is the association between these common terms and game theory. In particular, I think the most common mistaken reasoning is to infer that minmax reasoning is appropriate in situations which have been described as zero sum.
Personally, I don’t particularly mind “zero sum” as the common term, interchangeable with “constant sum”, and I’ll only have to care about the misconception when someone’s making an erroneous inference based on it.
I believe that the mistake in using the term “zero-sum” for games like “theft” or “elections” is NOT that the term zero-sum is limited, but that it throws out incredibly important information in the mapping.
I think there are a few insurmountable problems to using the term for game theory:
It’s too tempting to think “zero sum” contrasts with “positive sum” and “negative sum”. These temptations are perfectly good concepts if we just use them for interactions which lose/gain resources, but can be given no sensible interpretations in game theory.
As I outlined in the post, even “constant sum” isn’t the right generalization. If you try to identify completely adversarial games this way, you’ll miss examples where the utilities have to be re-scaled. So it’s better to at least say “zero sum really means linear game of negative slope” or something along those lines, rather than “constant sum”.
Granted, linear games of negative slope can be re-scaled to be zero-sum.
I think “zero/positive/negative sum” is just fine for the common term if everyone knows it’s not referring to game theory, since “zero sum” seems just fine for describing an interaction which neither produces or destroys resources. I like the suggestion of “zero sum in X” to help make this clear (for example, theft is zero sum in property, at least if there’s no property damage, even though it might be far from zero sum in terms of happiness or other things).
What I object to is the association between these common terms and game theory. In particular, I think the most common mistaken reasoning is to infer that minmax reasoning is appropriate in situations which have been described as zero sum.
I think there are a few insurmountable problems to using the term for game theory:
It’s too tempting to think “zero sum” contrasts with “positive sum” and “negative sum”. These temptations are perfectly good concepts if we just use them for interactions which lose/gain resources, but can be given no sensible interpretations in game theory.
As I outlined in the post, even “constant sum” isn’t the right generalization. If you try to identify completely adversarial games this way, you’ll miss examples where the utilities have to be re-scaled. So it’s better to at least say “zero sum really means linear game of negative slope” or something along those lines, rather than “constant sum”.
Granted, linear games of negative slope can be re-scaled to be zero-sum.