Prospect Theory

Posted by fiddlemath on November 1, 2012

This was a bunch of lecture notes I made before a quick talk explaining the basics of prospect theory to the Madison Less Wrong meetup. I haven’t even tried to make this readable, yet.

The Allais Paradox

From WP:

Gamble 1:

  • Option A: Gain $1M.
  • Option B: Gain $1M at 89% or gain $5M at 10%.

Gamble 2:

  • Option A: Gain $1M at 11%.
  • Option B: Gaim $5M at 10%.

Alternately, from LW:

Gamble 1:

  • Option A: $24K at 100%
  • Option B: $27K at 33/34

Gamble 2:

  • Option A: $24K at 34%
  • Option B: $27K at 33%

The Endowment Effect:

“Pure tokens”, tradeable for between $10 and $20 dollars at the experiment’s end: markets worked.

Mugs: Some of the group (Sellers) are given a nice mug (worth about $6), Buyers had to use their own money to by mugs if they wanted them. Average selling price was about double the average buying price. Later, “Choosers” could accept either a mug or money, at whatever point they found themselves indifferent.

Averages: Sellers: $7.12, Choosers: $3.12, Buyers: $2.87.

Prospect Theory: Evaluation

Values of gains or losses. (losses about double slope of gains; range between 1.5 and 2.5)

Decision weights. (almost-logistic curve; crosses x=y between .2 and .6; usually)

Exact curves vary from person to person!

Prospect Theory: Editing

The full “prospect theory” actually has a few more moving parts. Decisions, it says, are broken into two parts, “Editing” and “Evaluation”

From here:


  • Coding: outcomes become gains or losses
  • Combination: simplify prospects by combining probabilities with identical outcomes
  • Segregation: riskless components of prospects are separated from risky components. (300 @ p 200 @ (1-p)) becomes 200 + 100@p.
  • Cancellation: discard common outcome-probability pairs between choices.
  • Simplification: prospects are likely to be rounded off; very unlikely outcomes are discarded.
  • Detecting dominance: strictly-dominated outcomes are scanned and rejected.

Evaluation: The edited prospects are evaluated by summing the products of decision weights of probabilities, and the values of gains or losses.

“Cumulative Prospect Theory”: is described online, but I’m not going to explain it.

Mental Accounting

The frames by which we ascribe “gains” and “losses” are complicated. You can fiddle with these, but the defaults can be hard to see.

(Richard Thaler, “Mental Accounting”)

What Do We Do About This?

  • You will regret negative outcomes less than you expect. Do not try too hard to minimize regret.
  • Avoid “What You See Is All There Is”, by evaluating relevant, similar scenarios. In particular:
    • Make a story where losses are neutral but gains are more positive, or vice versa, to balance risk aversion and the endowment effect.
    • Imagine buying or selling your options to someone else. How would you value them?
    • Make a story where your decision is reversed. “Would you take 1 year’s extra labor to have your current, worse system?”
    • Don’t play stopping problems; comparison shop.
  • Find better frames. (gpm vs mpg, say: example, Adam goes 12->14mpg; Beth goes 30->40mpg. Who saves more gas? (note that, starting next year, new cars will have gpm info on their sticker))
  • Shift goalposts: goals are reference points, and we can view losses and gains in terms of the goals we’ve already set.