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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

St. Petersburg Paradox

bernouli looked at this- fair coin flipped until it comes up heads. payoff is $2^n where n is the number of flips

Money pumps

if your decision process is inconsistent or irrational then you can in theory be exploited endlessly for profit

bernoulli's solution?

utility- value of money in terms of its usefulness as to what it can buy you

water vs. diamonds

prices determined by the next marginal unit (not the total value of the good)

bernoulli and st. petersburg

log(prize) converges at around .602 utiles or about $4.

Modern utility

does away with the concept of derived pleasure. will only worry about what you prefer among the set of things you can choose