Efficient Market Hypothesis (finite cut-off): when betting/trading in a market, we cannot multiply our initial capital C with a large fraction α over the risk-less rate r.
Maximum Entropy Principle (MaxEnt): given constraints Ri on an unknown probability probability distribution p, your ‘best’ estimate is p∗ that maximizes the entropy under the constraints Ri.
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 α over the risk-less rate r.
Maximum Entropy Principle (MaxEnt): given constraints Ri on an unknown probability probability distribution p, your ‘best’ estimate is p∗ that maximizes the entropy under the constraints Ri.
Maximum Caliber (MaxCal): given dynamical (time-dependent) constraints fi(t) on an unknown stochastic process the ‘best’ estimate for the underlying distribution on paths or ‘law’ μ 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: