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Riskless Choice: Presence of Multiple Attributes How aredecisions made? How doyoumakesuchchoices?
Riskless Choice: simplifying heuristics • Presence of multiple attributes, decision alternatives represented as vectors Simplifying heuristics: • Dominance principle: If alternative A is at least as preferred as alternative B on all attributes and strictly preferred on at least one attribute, we say that alternative A dominates alternative B • Sometimes violated. Why? Kahneman experiment with subjects putting their hand in cold water, implications for prison system • Satisficing heuristics: Set an acceptable or satisfactory level for each attribute. The attributes for each alternative are compared with these satisfactory levels. Alternatives with attribute levels that are not satisfactory are discarded and all alternatives that meet the satisficing levels are kept.
Riskless Choice … simplifying heuristics continued • Lexicographic model: Rank the attributes in terms of importance. Compare alternatives one at a time: starting with the most important attribute. If there are ties, look at the second most important attribute, the third most important attribute, etc. Note 1: This is a non-compensatory model. What does it mean? Note 2: Recall lexicographic semi-order. How does it differ? • Combination procedure: first use the dominance principle, then the satisficing principle, then use the lexicographic model
Tradeoff procedure, Franklin’s moral algebra • A compensatory model: allows poor performance on one (some) attribute(s) to be compensated by superior performance in other attributes. • When would you use a compensatory model? When not? • Benjamin Franklin’s “moral or prudential algebra” • describes how he made important choices – recommended the approach to a friend • When would you use each of the models?
Linear Value FunctionModel – A PopularModel Makepairwisecomparisons of alternatives Estimate the weights for the attributes Max epsilon s. t. Value difference in twoalternatives > epsilon Not a badmodel in predictingchoices …
Luce’s choice theory (1959) • Luce’s model: p(x; A) = u(x)/∑u(y) over all y in A Based on the independence principle: p(x; y) ≥ ½ iff p(x; A) ≥ p(y; A) (provided p(y; A) ≠ 0) The ordering of x and y, by choice probability, is independent of the considered set of alternatives Illustrate with an example!
Elimination by Aspects: A Theory of Choice Amos Tversky: Psychological Review 79,1972 Views riskless choice behavior as a probabilistic process (because of observed inconsistencies, uncertainty in choosing) Each alternative is viewed as a set of aspects (characteristics) This paper develops a probabilistic theory of choice, based on a covert elimination process – critique of the Luce model
Elimination by Aspects … motivating example Consider buying a record for your collection. There are three choices: a Debussy (D) and two different recordings of the same Beethoven symphony (B1, B2). Assume the two Beethoven recordings are of equal quality, and that you are undecided between adding a Debussy or a Beethoven to your collection. Hence p(B1; B2) = u(B1)/(u(B1)+u(B2))=1/2 and u(B1)=u(B2)=1/2; similarly: p(D; B1) = p(D; B2) = ½ and the corresponding utilities equal each other According to the Luce model, p(D;B1,B2)= u(D)/ (u(D)+u(B1)+u(B2))=1/3. Intuitively not right! One would expect it to be ½! Lesson: set A matters!
Elimination by Aspects (EBA): An outline • Describe each alternative using a set of aspects • At every stage, an aspect is selected with probability that is proportional to its weight (value, utility, importance) • The selection of an aspect eliminates all the alternatives that do not include the selected aspect, and the process is continued until a single alternative remains • Note: aspects which are common to all alternatives do not help in the elimination process • Example: purchase of a new car
EBA Model continued • Mathematical formulation (see paper) • Beethoven, Debussy example: The EBA modelgetsitright
Elimination by Aspects … Validation: • Some consequences of the EBA model previously tested (indirect test) • Difficulty of directly verifying the EBA model. Constructed a test for this purpose. See section in paper.
Elimination by Aspects … conclusions • Strategic implication: the EBA model provides a method for investigating questions concerning optimal design or location of alternatives in order to maximize/minimize choice probability (taking advantage of “irrelevant” alternatives). • The introduction of an additional alternative “hurts” similar alternatives more than dissimilar ones -- how to use in product design, political campaigns? • Theoretical flaw (normatively): failure to ensure that the alternatives retained are, in fact, superior to those which have been eliminated