LEC 3 - ANOMALIES IN EXPECTED UTILITY THEORY Flashcards
what is a prospect
a number of possible outcomes along with their associated probabilities
what axiom does Allais violate
Independence/substitution axiom
Also called Common consequence effect
Sure-thing principle
Your decision should not be influenced by sure things
whats the axiom completeness mean
always have a preference
how would you write a prospect r with a 50% chance of winning 100 and 50% chance of not winning anything
how would you write the prospect S: certainty of winning 45
S=(45)
what does the EUT axiom for completeness mean for all q, r
either q>r or r>q or q∼r (indifferent)
what’s the EUT axiom for transitivity mean
what does the EUT axiom continuity say
can write r as a combination of q and s
what’s the independence EUT axiom and example
for all prospects q r s
if q>r then (q, p;s, 1-p)> (r, p; s, 1-p), for all p
can make probability tree for example
allais problem (common consequence effect), independence problem, example, how to set it up
common ratio effect
difference between allais and Ellsberg paradox
Allais Paradox; objective probabilities
were known
Ellsberg (1961); no objective
probabilities
what’s the Ellsberg paradox
The Ellsberg paradox is a paradox of choice in which people’s decisions produce inconsistencies with subjective expected utility theory
how does the Ellsberg paradox violate SEU
we don’t think in terms of these probabilities. just don’t like the probabilities are not given
in subjective expected utility how can we tell if x is preferred to y
x is preferred to y if SEU(x) is larger than SEU(y)
subjective EU
what does risk mean
when a person is not sure which state will occur but knows the probabilities of each state
what does certainty mean
when a person knows one state will occur with certainty
what does ambiguity mean
when a person is not sure what the distribution of probabilities is
what is ambiguity aversion
Unwillingness to take on gambles with ambiguous probabilities
3 colour problem Ellsberg paradox. need to learn. recap nov16 9mins
important.
summarise the fox and tversky paper 1995
aim: does ambiguity aversion exist in the absence of a contrast between clear and ambiguous
comparative - max wtp to play bag A and bag B, both bags presented - found strong ambiguity aversion - wtp more on clear bet then vague
non comparative - max wtp to play either bag A or B, each subject sees one bag - no evidence of ambiguity aversion - wtp less on clear bet then vague
difference between within and between subject design
Between-subjects (or between-groups) study design: different people test each condition, so that each person is only exposed to a single user interface.
Within-subjects (or repeated-measures) study design: the same person tests all the conditions (i.e., all the user interfaces).
For example, if we wanted to compare two car-rental sites A and B by looking at how participants book cars on each site, our study could be designed in two different ways, both perfectly legitimate:
Between-subjects: Each participant could test a single car-rental site and book a car only on that site.
Within-subjects: Each participant could test both car-rental sites and book a car on each.
