Prospection

“Think” –Aretha Franklin Prospection “Think” –Aretha Franklin

“Forever Is Tomorrow Is Today” –David Gray Prospection “Forever Is Tomorrow Is Today” –David Gray

“things that have not yet come to pass” PERCEPTION PRESENT LEARNING & MEMORY “things that are” “things that were” “things that have not yet come to pass” PAST FUTURE ∞ TIME

Prospection is the human ability to think flexibly about possible, often “far-future” events

Expected Utility Theory John von Neumann Oskar Morgenstern

Expected Utility Theory Expected Value =

Odds of Gain x Value of Gain Expected Utility Theory Expected Value = Odds of Gain x Value of Gain

= $4 = $5 Expected Value = Odds of Gain x Value of Gain (1) x ($4) Expected Utility Theory If it comes up heads I’ll give you $10. Should you pay $4 to play? Expected Value = Odds of Gain x Value of Gain (1) x ($4) = $4 (1/2) x ($10) = $5

= $4 = $1.67 Expected Value = Odds of Gain x Value of Gain (1) x ($4) Expected Utility Theory If it comes up 2 I’ll give you $10. Should you pay $4 to play? Expected Value = Odds of Gain x Value of Gain (1) x ($4) = $4 (1/6) x ($10) = $1.67

Odds of Gain x Value of Gain Expected Utility Theory If you pick all 6 numbers, I’ll give you $50 million. Should you pay $1 to play? Expected Value = Odds of Gain x Value of Gain Jackpot must be $175 million before the expected value = $1 (1/175,711,536) x ($50,000,000) = $0.23

Expected Utility Theory

Odds of Gain x Value of Gain Expected Utility Theory Errors of odds Errors of valuation Expected Value = Odds of Gain x Value of Gain

Errors of odds Errors of valuation Today’s gameplan sample size neglect gambler’s fallacy availability bias planning fallacy

Today’s gameplan

Errors of odds TTHTHHHTHTHHHHHHHHTTTHHHHHHHHTHHHHTTHHHHHTTTTTTHTHTHHHHHTTTHHTHHHHTHTTTTTTTTHTTTHHHHTTTTTHHHTHHHTHHTT

Most people say “They are the same” Errors of odds 45 babies are born each day in a large hospital and 15 in a small hospital. Each hospital records the days on which more than 60% of the babies born were boys. Which hospital recorded more such days in 2009? Most people say “They are the same”

Sample Size Neglect Errors of odds Proportion of “heads” 40 flips 0.52 0.53 0.48 0.50 0.51 0.47 400 flips 0.50 0.49 0.51 4,000 flips 0.50 40,000 flips 0.53 0.40 0.50 0.33 0.62 0.45 0.42

Gambler’s fallacy Errors of odds A fair coin is flipped 9 times. In which series is a HEAD more likely than a TAIL on the 10th flip? T T T T T T T T T ____ H H H H H H H H ____

Gambler’s fallacy Errors of odds The belief that the likelihood of a chance event is influenced by the nature of the events that preceded it.

Gambler’s fallacy Errors of odds An .800 free-throw shooter shoots 9 free throws. In which series is a HIT more likely than a MISS on the 10th shot? H H H H H H H H H ____ M M M M M M M M M ____

So How Do We Calculate Odds? Errors of odds So How Do We Calculate Odds? Are you more likely to see a dog or a pig on a leash in Cambridge?

_ _ R _ R _ _ _ Availability bias So How Do We Calculate Odds? Errors of odds So How Do We Calculate Odds? Are there more 4-letter English words with R in the 3rd or 1st place? Availability bias _ _ R _ R _ _ _ BARE, FORT, PARK... RING, ROPE, ROOT...

Errors of odds Availability bias

Errors of odds Availability bias

The Planning Fallacy Errors of odds Big Dig estimated to cost $2.8 billion in 1985, but has cost $14.6 billion as of 2006.

Errors of odds The Planning Fallacy

Errors of odds Errors of odds Errors of valuation Errors of valuation Today’s gameplan Errors of odds Errors of odds Errors of valuation Errors of valuation sample size neglect gambler’s fallacy availability bias planning fallacy

Categorical perception in phonology

Errors of odds Errors of odds Errors of valuation Errors of valuation Today’s gameplan Errors of odds Errors of odds presentism relative valuation gain/loss nonlinearity temporal discounting Errors of valuation Errors of valuation sample size neglect gambler’s fallacy availability bias planning fallacy

Errors of valuation Presentism

Errors of valuation Presentism

Errors of valuation Presentism

Relative valuation Errors of valuation $135K $150K Year 3 $55K $40K

Gain/Loss nonlinearity Errors of valuation Gain/Loss nonlinearity Daniel Kahneman Amos Tversky

Gain/Loss nonlinearity Errors of valuation Gain/Loss nonlinearity OBJECTIVE VALUE +$10 + -$10 SUBJECTIVE VALUE The Domain of Gain of Loss

Gain/Loss nonlinearity Errors of valuation Gain/Loss nonlinearity SUBJECTIVE VALUE + +$10 -$10 + OBJECTIVE VALUE +$10 -$10

Gain/Loss nonlinearity Errors of valuation Gain/Loss nonlinearity SUBJECTIVE VALUE + It curves! -$10 + OBJECTIVE VALUE +$10

The curves asymptote Errors of valuation You want to buy a car stereo. The dealer near your house sells it for $248, but if you take the T to Wonderland, you can get it for $148. Would you spend two hours on the T to save $100?

The curves asymptote Errors of valuation You want to buy a car with a stereo. The dealer near your house sells it for $38,948, but if you take the T to Wonderland, you can get it for $38,848. Would you spend two hours on the T to save $100?

The curves asymptote + + Errors of valuation SUBJECTIVE VALUE OBJECTIVE VALUE

The curves asymptote + + Errors of valuation -$38948 -$38848 -$248 SUBJECTIVE VALUE + -$248 -$38948 -$38848 -$148 + OBJECTIVE VALUE

The curves asymptote + + Errors of valuation -$248 -$38948 -$38848 SUBJECTIVE VALUE + -$248 -$38948 -$38848 -$148 + OBJECTIVE VALUE -$148 -$248 -$38,848 -$38,948

It’s steeper for losses than gains Errors of valuation Losses loom larger than gains SUBJECTIVE VALUE + It’s steeper for losses than gains -$10 + +$10 OBJECTIVE VALUE

Losses loom larger than gains Errors of valuation Losses loom larger than gains

Losses loom larger than gains Errors of valuation Losses loom larger than gains The Endowment Effect Objective Value = $5.00 Sellers Offer = $7.12 Buyers Bid = $2.57

Losses loom larger than gains Errors of valuation Losses loom larger than gains The Endowment Effect SUBJECTIVE VALUE + Objective Value = $5.00 Sellers Offer = $7.12 Buyers Bid = $2.57 +$2.57 +$5.00 + -$5.00 OBJECTIVE VALUE -$7.12

Errors of valuation Temporal discounting

> > ? $12 $10 now in 1 week $10 now $12 in 1 week Errors of valuation > $12 $10 more is better than less > now in 1 week sooner is better than later $10 now $12 in 1 week ?

$12 in 1 week $10 now $12 in 53 weeks $10 in 52 weeks Errors of valuation Temporal discounting $12 in 1 week $10 now $12 in 53 weeks $10 in 52 weeks vs.

Errors of valuation Temporal discounting

Odds of Gain x Value of Gain Whence errors? Errors of odds Errors of valuation Expected Value = Odds of Gain x Value of Gain

Whence errors?

Whence errors?