Well-defined probability space

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JC bloviates about statistics and probabilities a lot on this site, especially as regards their essential unsuitability for dealing with the future behaviour of non-linear, complex systems like normal human organisations.

Probabilities typically only work in limited circumstances: what I would call a “well-defined probability space”.

Classic examples include dice rolling coin flipping, and card games and gambling scenarios not involving physical aptitude: though they are bounded, fixed-rule, zero-sum games sports, generally, are not well-defined probability spaces, because they depend on relative physical skill, and this is not constant or measurable.

Well-defined probability spaces are situations in which:

1. Bounded:
   1. All possible outcomes must be known
   2. Probabilities must be well-defined and sum to 1
   3. Each outcome must have a quantifiable value/payoff
2. Independent: Events are independent so that previous outcomes cannot affect probabilities of future outcomes.
3. Static: The system and “rules” are static and can’t be changed, and probabilities and payoff values remain constant over time.

Notably, these conditions do not prevail in almost any case involving humans with moral agency outside the confines of finite, zero-sum games.

See also

• Expected value
• Future-state and present-state uncertainty