Opponent Indifference in Rating Systems: A Theoretical Case for Sonas
summary
Defines an axiom called opponent indifference and proves any one‑dimensional, memoryless, zero‑sum rating satisfying it has a constant K and a separable skill curve, which cannot represent arbitrarily long skill chains (no full scale). Shows the stronger notion (strong opponent indifference) forces linear bisectors and trivial systems. Introduces thresholding to get P-opponent indifference: restricting indifference to P-close opponents lets nontrivial systems regain full scale, and matches the Sonas linear‑threshold fit to high‑level chess, so the construction actually works in practice.
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chapters (13)
- 0:00Introduction
- 0:12Our Rating System
- 3:52Prior Work
- 5:24Volatility Hacking
- 6:55Opponent Selection
- 8:53Useful Notions
- 10:28Opponent Indifference
- 11:12Skill Chains
- 13:25Full Scale
- 15:17Generalizing Opponent Indifference
- 15:56Strong Opponent Indifference
- 17:06Thresholding
- 20:43Conclusion
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