Once upon a time, I took a course in Decision Theory at ETH. Here are some notes:
normative theory vs descriptive theory (maths vs psychology)
prospect theory
options vs choices
money pump
bond vs shares
Main notions:
- Slide
- Normative: Perfect rationality, optimality, payoff maximality
- Descriptive: How real people think and make decisions.
- bias: persistent and systematic deviation from rationality
- Prescriptive: How can we help people to make better decisions. How can we structure the choice environment to minimize decision errors and biases.
- People use limited heuristics in making decisions
- Decision maker
- individual, couple, family, firm, country
- any monolithic cognitive agent
- Goals, preferences, wants, desires
- options, alternatives, courses of action
- beliefs
- Decision under
- certainty
- all options and outcomes are completely known to the DM (military diet, ups example)
- risk
- When all the choices and options are known but there are well defined stochastic nodes (gambling, insurance, investing)
- uncertainty
- options are not well defined, or probabilities are not defined (or both) (examples most of life)
- certainty
- Preferences
- Revealed, Complete, Transitive, Independent, Stable
- People often satisfice instead of optimize
- People guess, estimate and try to do “well enough’’ rather than optimally.
- Rationality is bounded in two ways.
- Information from the environment
- cognitive capacity
- Sometimes close enough is fine, sometimes not
- Cognitive illusions: Monty hall problem
- Limitations in attention and memory. There are tools which compensate for that.
- Multi Attribute Evaluation (MAUT)
- identify options
- define goals
- quantify subjective evaluations
- weight and scale different evaluations so they can be aggregated meaningfully.
- make reasonable and justifiable decisions
- Problem, Objectives, Alternatives, Consequences, Tradeoffs (PrOACT)
- Comparative, multiple stakeholders (probably not equally important), multiple goals (maybe not equally important), multiple choices with multiple attibutes, judgements are necessary, quantify!
- Identify the decision maker
- Identify the alternatives
- the relevant attributes
- assign values to the attributes of each alternatives
- determine a weight for each attribute
- for each alternative, compute a weighted mean
- make a provisional decision
- get feedback and run a sensitivity analysis
- compensatory vs noncompensatory
- sometimes some alternatives are not acceptable (minimum requirements)
- minor changes may cause a change in the resulting decision
- “fair’’ method and easy to develop political support
- analytic hierarchy process: binary comparison of pairs of attributes in terms of their importance and then assign a weight (how much better is on alternative compared to the other)
- built in check for transitivity and consistency
- a well defined process to turn subjective judgements into more objective ratings
- Secretary problem
- What makes a good decision (good outcome or good reasons?)
- expected value
- probability (classical, frequency, subjective)
- it can be hard for people to reason about probabilities correctly (monty hall, other pitfalls)
- birthday problem
- bayes rule
- st petersburg gamble
- Moral worth: Bernoulli: the worth of something is not the same as its value → Definition of utility (utility = value^a)
- Expected utility does not work always
- Allais gambles. The result is a contradiction to EUT.
- Feelings about risk: People will accept 1000 times greater risks if they are their own volition, rather than involuntary
- O.J. SImpson example
- People are generally risk averse, but to varying degrees
- EVT defines rationality if the goal of the DM is to maximize value in the long run
- EUT defines rationality if the goal of the DM is to maximize utility (moral worth) in the long run
- Risk seeking in the domain of losses, risk averse in the domain of gains
- Decision framing
- Money trump
- Sequential investment problem
- Persistent cognitive noise
- systematic departures from EUT – biases
- Friedman-Savage utility function
- Prospect theory
- descriptive account of decision theory under risk
- aims to account for systematic deviations from eut and evt
- Coding — outcomes relative to the current state in terms of gains and losses
- combination — joining similar prospects
- segregation — isolation of sure things
- cancellation — discarding shared components
- simplification — rounding
- elimination of dominated options
- probability weighting function — the estimation that people do on probabilities (magnification of small values in the expense of larger values)
- 4 fold pattern of risk preferences
- risk seeking over low p gains — lotteries
- risk averse over low p losses — insurance
- risk averse over high p losses — certainty effect
- risk seeking over high p losses — end of the day effect
- certainty effect
- insurance which does not pay with a very small probability
- end of the day effect
- people make large bets on the last day to “break even’’
- Shortcomings
- average choices on average
- not for every one
- not even for someone over the domain of time
- no insight — just better predictions
- does not scale. (portfolio example, mulistage risky decisions)
- Dynamic decision contexts are defined by:
- sequential choices are made and they are interspersed with updated information about the environment
- the decision environment changes over time (depending on the choices of DM)
- normative approaches
- maximize expected payoff
- dynamic programming
- descriptive approaches
- case studies
- experimental methods (behavioral laboratories)
- human behaviour is compared to the normative approach
- identification of systematic departures from optimality — existent cognitive mechanisms can be accounted for
- ⇒ people predictably irrational (underlying assumption)
- optimal stopping
- example: secretary problem
- target: select a maximum value
- full information games
- perfectly known distribution
- draw a number from [0,20] — given the relative order of the number that you encountered so far but not the number
- partial information
- known distribution but not its parameters
- german tank problem
- no information
- iid random variables with unknown distribution
- secretary problem
- Sometimes called the Sultan’s Dowry Problem, the Marriage Problem, or the Fussy Suitor Problem
- optimal decision policy — threshold (e^{-1})
- generalized secretary problem
- persistent bias for stopping too soon
- probability distortion and not risk aversion is the (assumed) answer
- Other dynamic decision problem
- sell a good over a time interval where offers in a specific range arrive with a probability
- Kelly criterion
- always bet the same proportion (2p – 1)
- maximizes the expected geometric mean
- poor criterion in prediction decision makers behavior
- people have strong urge to adjust their investments
- evidence of learning to adjust less over rounds
- if we charge people when they adjust, we help them
- sequential investment problem
- optimal policy: bet max or not according to whether we are “above or below the expectation’’
- Heuristics as rule of thumb.
- gambler’s fallacy (law of small numbers)
- hot hand fallacy (law of small numbers)
- stars
- availability heuristics (how easy it is to recall a piece of information)
- anchoring and adjustment
- factorial where presented the larger number first or last
- use of early values to predict
- framing effect (the influence of questions)
- confirmation bias
- are people really irrational — heuristics evolved for some reason. Carefully designed corner case are examined.
- public goods game
- selfish players take no interest
- social optimal is far off
- many people are pro-social
- design vector according to the answers
- overconfidence quiz
- attentional
- selective memory/information search: confirmation bias
- selective encoding: excuses/rationalizations
- selective encoding : rewarded events are remembered better
- motivational
- need to appear competent and confident to tothers and oneself. confidence and optimism help to get things done.
- attentional
- bordeaux and regression
- wisdom of crowds
- risky decision theory and gambling
- rush of winning
- highly reinforcing