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## Ignore words

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Completeness, Transitivity, Continuity, Independence
Von-Neuman Morgenstern 4 Axioms
Transitivity
If A is better than B, B is better than C, then A is better than C
Rubinstein on violations of Transitivity
car example, prefer certain options to other based on a set of three preferences (speed, price, safety). but transitivity is breached because three preferences are similar but two are better (majority rule decision process)
Achimedean (betweeness)
you can always make a probability mixture of a better and a worse bundle to get a bundle in between
Independence
If you prefer A to B, then you prefer A mixed with something over B mixed with that same thing
normativity
how the world SHOULD be (think EUT)
descriptive
define and describe, count (who what when where)
Given these assumptions
your preferences can be represented with numbers
Luca Pacioli: The Problem of Points (1494)
50-50 game where winner takes all and both contribute equally to the pot. If the game is interrupted early... who takes what amount of the pot?
Pascal's solution
Sum (the probability of outcomes * their value)
EV
will take bet with highest expected value
limitations of EV
can only be used for numeric outcomes