Let's assume you are talking about sharing, as that's what the original point was about. Specifically the sharing of 19 bones among 20 dogs, by dividing up the bones.
Assumign by 'naive' you mean wrong, are you saying that it is simply a more optimal situation for one dog to go hungry?
Does the one dog always go hungry, or does one dog (but a different one each time) go hungry?
Do we just let the one dog go hungry each time intentionally, so that in future no dog goes hungry? What if then one day there are only 18 bones for 19 dogs? Do we let that dog die too?
What if a group of 18 dogs is required to take down an animal that provides enough bones, but we let the two other dogs die because sharing is naive?
Well, that pretty fundamentally calls into question rather a lot of all the principles civilisation is founded upon and which permeate nature, even (nature!).
So you better provide some amazing scientifically backed proof of that statement. No, Atlas Shrugged is not scientific proof.
The dog can die. It isn't my problem.
Once there are only 19 dogs left, the number of bones will simply be reduced to (slightly more than) 18, because the prevailing ideology is that there must be 5% unemployment. (This is greatly simplified, of course, but that's the gist of it.)
Eventually you'll stop being lucky. And in any case, it's not always the same dog who gets unlucky. So yes, it is your problem, or at least it will be.
What am I saying people should do?