Behavioral Economics

Sources: Wikipedia (CC BY-SA 4.0) · Kahneman & Tversky (1979), Prospect Theory

People are not rational maximizers. Prospect theory replaces expected utility with a value function that is concave for gains, convex for losses, and steeper on the loss side. Behavioral economics catalogs the systematic ways humans deviate from the rational-agent model.

The value function

Kahneman and Tversky's value function has three properties. Reference dependence: outcomes are evaluated as gains or losses relative to a reference point, not absolute levels. Diminishing sensitivity: the function is concave for gains and convex for losses. Loss aversion: losses hurt roughly twice as much as equivalent gains feel good (the coefficient lambda is typically around 2.25).

Scheme

; Prospect theory value function
; v(x) = x^alpha           if x >= 0  (gains)
; v(x) = -lambda * |x|^beta if x < 0  (losses)
; Typical: alpha=0.88, beta=0.88, lambda=2.25

(define alpha 0.88)
(define beta 0.88)
(define lambda-param 2.25)

(define (value x)
  (if (>= x 0)
      (expt x alpha)
      (* (- lambda-param) (expt (abs x) beta))))

; Compare symmetric gains and losses
(define amounts (list 10 50 100 500))

(display "Amount | Gain value | Loss value | Ratio") (newline)
(display "-------+------------+------------+------") (newline)
(for-each
  (lambda (x)
    (let ((g (value x))
          (l (value (- x))))
      (display x) (display "    | ")
      (display (/ (round (* g 100)) 100)) (display "      | ")
      (display (/ (round (* l 100)) 100)) (display "     | ")
      (display (/ (round (* (/ (abs l) g) 100)) 100))
      (newline)))
  amounts)

Loss aversion and framing

Loss aversion means people reject gambles that a rational agent would accept. A 50-50 bet to win $110 or lose $100 has positive expected value, but most people decline. Framing changes decisions by relabeling the same outcome: "90% survival rate" versus "10% mortality rate" triggers different choices despite identical information.

Scheme

; Loss aversion: reject positive-EV gambles

(define lambda-param 2.25)
(define alpha 0.88)
(define beta 0.88)

(define (value x)
  (if (>= x 0) (expt x alpha)
      (* (- lambda-param) (expt (abs x) beta))))

; 50-50 bet: win $110 or lose $100
(define ev-monetary (* 0.5 (+ 110 (- 100))))
(define ev-prospect (+ (* 0.5 (value 110)) (* 0.5 (value (- 100)))))

(display "Monetary EV: $") (display ev-monetary) (newline)
(display "Prospect value: ") (display (/ (round (* ev-prospect 100)) 100)) (newline)
(display "Accept under EU theory? yes") (newline)
(display "Accept under prospect theory? ")
(display (if (> ev-prospect 0) "yes" "no")) (newline)

; Framing effect
(newline)
(display "--- Framing ---") (newline)
(display "Frame A: 200 of 600 people saved (certain)") (newline)
(display "Frame B: 1/3 chance all 600 saved, 2/3 chance none saved") (newline)
(display "Same expected outcome (200 saved).") (newline)
(display "Most choose A when framed as gains, B when framed as losses.")

Anchoring and nudges

Anchoring: initial exposure to a number biases subsequent estimates toward that number, even when it is irrelevant. Asking "Is the population of Chicago more or less than 10 million?" yields higher estimates than anchoring at 1 million. Nudges exploit these biases for good: changing default options (opt-out vs opt-in for retirement savings) dramatically changes behavior without restricting choice. This is libertarian paternalism.

Scheme

; Nudge: default effect on retirement savings
; Opt-in: only ~40% of employees participate
; Opt-out (auto-enrollment): ~90% participate
; Same options, same freedom, different outcome

(define employees 1000)
(define opt-in-rate 0.40)
(define opt-out-rate 0.90)
(define annual-contribution 3000)
(define years 30)
(define rate 0.07)

(define (future-value pmt r n)
  ; Annuity FV = pmt * ((1+r)^n - 1) / r
  (* pmt (/ (- (expt (+ 1 r) n) 1) r)))

(define per-person-fv (future-value annual-contribution rate years))

(display "Per-person retirement savings (30yr): $")
(display (round per-person-fv)) (newline) (newline)

(define total-optin (* employees opt-in-rate per-person-fv))
(define total-optout (* employees opt-out-rate per-person-fv))

(display "Opt-in system (40%): $")
(display (round total-optin)) (newline)
(display "Opt-out system (90%): $")
(display (round total-optout)) (newline)
(display "Difference from one default change: $")
(display (round (- total-optout total-optin)))

Neighbors

Cross-references

Cogsci Ch.6 — decision making: the cognitive architecture behind biases

Foundations (Wikipedia)

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