Two dimensions of rationality
Epistemic Rationality: The consistency of judgments and beliefs
Examples:
Wason 4-card problem
Linda problem
Instrumental Rationality: The consistency of behavior with goals and desires
Instrumental Rationality
A Medical Decision
Mortality rates: Majority of patients, physicians, and college students choose radiation
Survival rates: Now the choice is for surgery
The data are, of course, identical.
Is the contradiction a form of irrationality?
The Irrelevance of the Past: Arkes & Blumer (1985)
Season tickets to the university’s theater productions
Price of tickets was $15, $13, or $8.
Prices determined randomly for experimental subjects
Dependent variable: How many plays did each person attend
Honoring of Sunk Costs
Pay more, more likely to attend
The endowment effect is a related phenomenon
Is this behavior irrational?
Two Systems of Reasoning
System 1: Rapid, parallel, automatic, carried out without conscious awareness. Old in evolutionary terms
System 2: Slow, sequential, deliberate, inhibits the effects of System 1.
How does this explain the inconsistency of preferences, the honoring of sunk costs, and the endowment effect?
Two Versions of Rationality
For early humans, evolution may have provided problem specific solutions, leading to the development of System 1 reasoning
This has led some authors to deny that human reasoning is irrational
With the development of human culture there is a growing need for the context-free, generalized problem solving of System 2
Long-leash evolution
Stanovich & West (2000)
“The more we understand about evolutionary mechanisms, the more awed appreciation we have for them. But at the same time, it is not inconsistent … to be horrified at the fact that a multi-million dollar advertising advertizing industry is in part predicated on creating stimuli that will trigger System 1 heuristics that many of us will not have the cognitive energy or cognitive disposition to override. … It is no consolation that the heuristics so triggered were evolutionarily adaptive in their day”.
The Role of Two Systems in Cognitive Science
Where do these ideas fit within the broader context of cognitive science?
How might these ideas influence, or be explained by, physical symbol systems?
How might these ideas influence, or be explained by, neural network models?
How does dual process theory fit with the massive modularity hypothesis and the domain-general process hypothesis?
Where do the two systems fit within ACT?
Two Systems and the Three Levels of Theory
Where do these ideas fit within Marr’s and Stanovich’s frameworks for cognitive theories?
Where does the concept of rationality fit?
Two individual difference dimensions: Cognitive capacity, Thinking dispositions
Where do these fit?
Rationality and Social Dilemmas
Social Dilemma: Decisions involving two or more players, where the outcome depends on the joint decisions of both
Here the notion of rationality runs into difficulties
Prisoners Dilemma
Rational Game Theory
Developed by Von Neumann and Morgenstern (1944), and extended by John Nash (1951)
The Nash equilibrium: No player can benefit by changing strategy while others keep theirs unchanged.
To find a Nash equilibrium requires certain assumptions
“Common Knowledge” assumption: Each player is rational and knows the others to be rational
The High-Low Game: Rational game theory offers no solution!
There is no formal reason why one should choose H (I.e., no Nash equilibrium)
Ultimatum Game
What is the “rational” strategy for each player in the ultimatum game? Why is this a rational strategy (what does it achieve)?
The Nash equilibrium
Assume both players prefer a large amount to a small amount, and a small amount to nothing
The Proposer should offer as little as possible
The Responder should take it
Ultimatum Game: Assume P has to divide $100
Consider three offers, $1, $10, $50.
P cannot do better than to offer $1
R cannot do better than to acceptHow do people actually behave in this game? Would you behave the same way?
Several variables influence behavior, but the modal offer is around 40% of the stake
Offers less than 10% or 20% will be rejected
Players adopting the “rational” strategy will make less money than those who follow the typical strategyHow would you account for people's deviations from rationality? What role does a sense of “fairness” play in the game?
Most players use terms like “fairness” in explaining their behavior
According to Nowak et al, how might evolution theory account for the development of fairness?
As it stands, evolution favors “reason” over “fairness” – the Nash equilibrium
Any other strategy will be eliminated if reproductive value is related to payoff
Note how Nowak et al work with the expected benefits of strategies – one definition of rationalityThe optimal strategy changes if there is any basis for being able to predict the other player’s behavior
There is now a way for the Proposer to assign probabilities to the Responder’s actions
A Responder who accepts low offers is likely to get low offers in future
A Responder who refuses low offers is likely to encourage higher offers.There will be an increase in the optimum offer by Proposers, and in the optimum level at which Responders should reject
The increase depends on a parameter w, the proportion of people who know what happens
Thus the evolution of a sense of fairness depends on the notion of “reputation”
This assumes group knowledge of previous encounters, so repeated play with the same person is not necessaryDoes the Nowak et al theory explain behavior in the Ultimatum game?
Responders will reject low offers even if they know that their rejection will not become public knowledge, and they will never see the Proposer again
Is something else going on?
Remember Gintis’s choreographer: A set of social norms that have evolved among members of a speciesGintis’s Theory
More than reputation: A built-in norm for rejecting low offers
A willingness to punish an unfair Proposer, even at a cost to the Responder
Does not require any knowledge of Proposer’s prior behavior by the Responder, or prior knowledge of the Responder’s prior behavior by the Proposer
Why might this evolve?How did Jensen et al study the UG in chimpanzees?
Investigators use a mini-game: Proposer has to choose between two possible offers
Is it the same game as the full UG? Humans do exhibit fairness, as in the full gameChimps behave differently from people. What does this imply?
Are chimps more rational?
If chimps do not exhibit a sense of fairness, why not?
Why does this emerge only in humansCompare the ultimatum game with the prisoner's dilemma. How are they alike? How do they differ?
Similarities: Typical behavior does not obey the prescriptions of formal game theory. Players can do better by avoiding the Nash equilibria.
Differences: In the ultimatum game, the responder knows the proposer’s choice
“Fairness” and “cooperation” may reflect different sets of norms