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Rational Utility & Expected Utility


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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