34.6 Judgment and decision making and behavioral pricing
A. Tversky and Kahneman (1974)
3 heuristics that are used to assess probabilities and predict values:
Representativeness heuristic: “the degree to which A resembles B.” (p. 1124) (also known as similarity)
Insensitivity to prior probability (base rate) of outcomes: (neglected and only take into consideration similarity). With no specific evidence, prior prob is considered, with worthless (misleading) evidence, prior prob is ignored
Insensitivity to sample size: (1) smaller hospitals are more likely to stray from 50% prop of boys (hence, more likely to obtain more than 60% boys), (2) Even with smaller sample, if the proportion is greater, one can still infer posterior prob to be higher (unaccounted for equal prior prob), which is known as “conservatism.”
Misconceptions of chance: local representativeness (local characteristics represent global ones). Gambler’s fallacy: “chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium.” (p. 1125) Law of small numbers: “even small samples are highly representative of the populations from which they are drawn.” (p. 1125)
Insensitivity to predictability: predictions based on favorability of the description (or attributes), but it violates the normative statistical theory (predictability here is strictly related to information, the range of predictions and extremeness should depend on the range of information, not on uninformative info).
The illusion of validity: people are confidence in their prediction when they are presented with strong similarity between input and the selected outcomes), which persists even in cases that the judge understands factors that limit his predictions’ accuracy. This illusion can be caused by internal consistency (highly consistent patterns). Redundancy (or correlation) among inputs decreases accuracy while it increases confidence.
Misconceptions of regression: regression toward the mean (e.g., flight instructors praise or scold on previous landing can “predict” the next landing).
Availability heuristic: The ease at which instances or concurrences come to mind.
Biases due to the retrievability of instances: Factors affect retrievability are familiarity, and salience (p. 1127) (recent occurrence > remote, and more vivid instance > less vivid).
Biases due to the effectiveness of a search set: how easy it is for you to recall your search set matters. (e.g., abstract vs. concrete words (Galbraith and Underwood 1973))
Biases of imaginability: the ease with which an instance can be constructed. (evidence in constructing committee based on imagination).
Illusory correlation (frequency with which two events co-occur): “the associative connection between events are strengthened when the events frequently co-occur.” (p. 1128).
Adjustment and anchoring:
Insufficient adjustment: under anchoring effect, (e.g., African countries in UN, and long calculations based on insufficient calculation).
Biases in the evaluation of conjunctive and disjunctive events: people prefer conjunctive events over simple events (because overestimate of conjunctive events), and simple events over disjunctive events (because underestimate of disjunctive events), which might lead to underestimate the length in planning (because it usually involves successive events - conjunctive events). Similarly, evaluation of risk are conjunctive events, which we will underestimate. “The chain-like structure of conjunctions leads to overestimation, the funnel-like structure of disjunctions leads to underestimation.” (p. 1129).
Anchoring in the assessment of subjective probability distributions: regardless of expertise (e.g., sophisticated or native subjects), people usually overly narrow confidence intervals (which reflect more certainty), than is justified by knowledge about the assessed quantities (p. 1129). People have 2 ways to derive subjective probability distributions for a quantity:
Select values that correspond to specified percentiles of his probability distribution
Asses the probability that the true value of the quantity will exceed some specified values
Interestingly, the second procedure yields less extreme odds than the first procedure.
Thaler (1985)
Internal accounting
Let \(z= \{z_1, \dots, z_i, \dots, z_n \}\) be vector of goods at prices \(p = \{p_1, \dots, p_i, \dots, p_n \}\)
Consider consumer’s utility function
\[ \max_{z} U(z) \text{ s.t.} \sum p_i z_i \le I \]
where \(I\) is the individual’s wealth.
Using Lagrange multipliers
\[ \max_{z} U(z) - \lambda (\sum p_i z_i - I) \]
which is the original model of economic which takes into account of prices and products characteristics (normative prescriptions of economic theory), while ignoring the “framing” effects proposed by (A. Tversky and Kahneman 1981)
This paper proposes:
- Value function \(v(.)\) from prospect theory
- Price is changed into reference price
- Relax the principle of fungibility
Assumptions:
“People respond more to perceived changes than to absolute levels.” (p. 201). Hence, we have reference point to infer losses and gains.
Concave for gains (\(v''(x)<0,x>0\)) and convex for losses (\(v''(x) >0, x<0\))
Losses loom larger than gains (also known as endowment effect): loss function is steeper than the gain function \(v(x) < -v(-x), x>0\)
Joint outcome \((x,y)\) can be valued
- Jointly as \(v(x+y)\) known as integrated
- Separately as \(v(x) + v(y)\) known as segregated.
And the joint outcome \((x,y)\) can have 4 combinations:
| Outcomes | Math | Preference |
|---|---|---|
| Multiple gains | \(x>0,y>0\) \(v(x) + v(y) > v(x+y)\) (\(v\) is concave |
Segregation |
| Multiple losses | \(v(-x)+v(-y)<v(-(x+y))\) | Integration |
Mixed gain (cancellation) |
Consider \((x,-y)\) where \(x>y\) (net gain). \(v(x) + v(-y)<v(x-y)\) |
Integration |
Mixed loss (“silver lining” principle) |
Consider \((x,-y)\) where \(x<y\) (net loss) \(v(x) +v(-y) \ge \le v(x-y)\) (undetermined) |
Segregation if \(v(x)> v(x-y)-v(-y)\) |
To incorporate the notice of reference outcomes (or reference price), instead of \(y\), we will substitute it with \(\Delta x\) (which is changes in the expected outcome).
We label reference outcome as \((x+\Delta x:x)\)
When individuals encountered a decision (transaction) as a pleasure maximizing machine, they will
Stage 1: evaluate potential transactions (i.e., judgment process)
Stage 2: whether to approve each potential transaction (i.e., decision process)
Transactions
3 price concepts regarding good \(z\):
\(p\) = actual price
\(\bar{p}\) = value equivalent of \(z\) (i.e.., money that the individual would be indifferent between receiving \(\bar{p}\) or \(z\) as a gift)
\(p^*\) = reference price (i.e., expected or “just” price for \(z\)), determined by:
- Fairness
2 kinds of utility:
Acquisition utility: “value of the good received compared to the outlay”
Acquisition utility equals the net utility from the trade of \(p\) to obtain \(z\) (valued at \(\bar{p}\))
Compound outcome \((z,-p)= (\bar{p}, -p)\), with value function \(v(\bar{p}, -p)\) (usually coded as integrated, hence cost of good is not treated as a loss)
Transaction utility: perceived merits
Transaction utility equals price paid compared to reference price
Reference outcome \(v(-p: -p^*)\)
Total utility equals the sum of acquisition utility and transaction utility
\(w(z, p, p^*)= v(p, -p) + \beta v(-p:-p^*)\)
where \(\beta\) is the weight of transaction utility (can be thought of as consumer surplus in the standard theory). Hence, pathological bargain hunters have \(\beta >1\)
For multiple accounts (i.e., multiple goods categories), people will purchase iff
\[ \frac{w(z_i, p_i,p_i^*)}{p_i} \ge k \]
where \(k\) is a constant (similar to \(\lambda\) in the standard model)
High \(k\)’s are observed for seductive or additive goods (apply to luxury goods as gifts as well)
Low \(k\)’s are observed for goods that are desirable in the long run (e.g., exercise or education).
and individuals seek to maximize \(\sum w(.)\) subject to \(\sum p_i z_i \le I\)
Due to local optimization (i.e., constraint of time and category specific budget constraints, decision process is that people will buy good \(z\) at price \(p\) iff
\[ \frac{(w,p,p^*)}{p}> k_{it} \]
where \(k_{it}\) is the budget constraint for category \(i\) in time period \(t\)
Alternatively, global optimization would require \(k_{it}\) to be constant (but ppl don’t act this way).
3 implications:
Compounding rule
Transaction utility:
Sellouts and scalping
Methods of raising price:
Increase the perceived reference price
increase the min purchase required or tie the sale to something else
obscure reference price (hence, transaction disutility less salient)
Suggested retail price
Budgeting: Theory of gift giving (give something that recipients already consume in positive quantities)
Lichtenstein and Bearden (1989)
- Consistency and distinctiveness influence internal price standard and purchase evaluations.
Simonson and Tversky (1992)
Effect of context on choice:
Tradeoff contrast: preference for an alternative is enhanced based on the tradeoffs withing the set under consideration are favorable.
Extremeness aversion: the attractiveness of an option is increased if is an intermediate option, while decreased if it is an extreme option.
E. U. Weber and Johnson (2009)
- Summary of mindful judgment and decision making
Sokolova, Seenivasan, and Thomas (2020)
Left-digit bias (e.g., Difference between $4 and $2.99 is larger than between $4.01 and $3) is a cognitive bias we all have (independent of culture).
Left-digit bias is stronger in stimulus based price evaluation (people see focal and reference price at the same time) because people rely on perceptual representation of prices without rounding them
Left-digit bias is weaker in memory-based price evaluations (people can retrieve at least one price from memory) because people rely on conceptual representations, which makes them more likely to round the prices.
Perceptually, 2.99 is represented as a sequence of digits, so it’s represented as 2.99 itself.
Conceptually, 2.99 is coded as 3 (nearest accessible round number)