On a Curved Manifold?

Here’s something curious about lawyers. Locally they fight negative-sum games — effectively, expending resources fighting over the division of a non-increasing good.

  • lawyer 1: OK, I get x%
  • lawyer 2: and I get 1−x %
  • lawyer 1: Yes. Now, I vote that x be increased
  • lawyer 2: But that would mean that my share, 1−x, would decrease
  • lawyer 1: Exactly.
  • lawyer 2: But…
  • lawyer 1: Exactly.

Globally, however, the effect of lawyers is positive-sum. Without a justice system, grievances would not be heard, property rights would not be enforced, and the world would be worse off.

So … a space with locally negative curvature and globally positive curvature … hmm, how can that work?


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