Normative principles in Rationality

Here are a number of proposed normative principle about how to 'reason well' and/or 'decide well'.

• Kelly betting: Given a wager pick the one that maximizes your growth rate. In many-cases this coincides with log-wealth.
  • Maximize growth rates. Ole Peters' Principle. 
  • Maximize Geometric mean. 
  • Maximize log-wealth. 
• Efficient Market hypothesis (/No Arbitrage/Garrabrant criterion) infinite:
  • Efficient Market Hypothesis (finite cut-off): when betting/trading in a market, we cannot multiply our initial capital $C$ with a large fraction $\alpha$ over the risk-less rate $r$.
• Maximum Entropy Principle (MaxEnt): given constraints $R_i$ on an unknown probability probability distribution $p$, your 'best' estimate is $p^{\ast }$ that maximizes the entropy under the constraints $R_i$.
  • Maximum Caliber (MaxCal): given dynamical (time-dependent) constraints $f_i\left(t\right)$ on an unknown stochastic process the 'best' estimate for the underlying distribution on paths or 'law' $\mu$ is the path distribution that maximizes path entropy under constraints. 
  • Maximum Causal Entropy
• Minimum Description Length Principle
  • Solomonoff Induction
  • Minimize Kolmogorov complexity
  • Minimize Bernouli-Kolomogorov complexity (statistical complexity). 
• Bayesian Updating

How might these be related?

Kelly betting or log-wealth betting is generalized by Ole Peters' Principle of Maximizing Growth Rates.

MaximumCaliber is a straightforward generalization of MaxEntropy. MaxCausalEnt

Bayesian updating is a special case of MaxEnt. 

MaxEnt is a special case of Ole Peters.

Note that Maximum Caliber is different in the following sense: