Thinking Fast and Slow Nots (Part 4)
Jan. 9, 2020
Thinking: Fast and Slow
Daniel Kahneman, 2011 Thinking Fast And Slow The following are sections and ideas in condensed form that I found particularly salient.
Part 4 - Choices
Mathematical Psychology by Amos - A Function to relate psychological intensity to the physical magnitude of the stimulus.
Gustav Fechner’s Logarithmic function.
Would you rather...
1. Have an 80% chance to win $100, and 20% chance to win $10?
Expected Value = (0.8x100)+(0.2x10) = $82 2. Have $80 for sure.
Based on expected value, people should prefer the gamble, but most people choose the certain $80 option.
Bernoulli’s psychophysics - People’s choices are not based on dollar values, but on psychological values of their outcomes (utilities).
Bernoulli’s Utility Function:
W=Weath in Millions U=Utility Units
W 1 2 3 4 5 6 7 8 9 10 UU 10 30 48 60 70 78 84 90 96 100
Expected Utility aka “moral expectation”
Adding 1 Million to 1 Million yields increment of 20 utility units Adding 1 Million to 9 Million yields increment of 4 utility units
Now would you rather...
1. Have equal chances to win $1M or $7M?
Expected Value = (0.5x1) + (0.5x7) = 4
Utility Value = (0.5x10) + (0.5x84) = 47 2. Have $4M for sure
Expected Value = 4
Utility Value = 60
Same expected value but the option with $4M for sure give a utility of 60 over the uncertain option utility of 47. Bernoulli’s Utility Theory attempts to assign value to people’s aversion to risk, and inclination to choose the sure thing.
The poor pay for insurance, and the rich sell it to them.
$1M loss for someone with $10M is a loss of 4 utility points, versus a loss of 18 utility points for somebody who starts with $3M.
But Bernoulli’s Theory does not take a reference point into account.
Today Jack and Jill each have $5M.
Yesterday Jack had $1M and Jill had $9M.
Are they equally happy? (Do they still have the same utility?)
No, Jack is elated with the gain, Jill is crushed. Even if Jack only went from $1M to $2M, he would still be much happier than Jill who went from $9M to $5M.
Anthony has $1M. Betty has $4M.
Both are offered one of two choices:
1. Gamble: Equal chances to own $1M or $4M. 2. Sure Thing: Own $2M for sure.
Anthony likes the sure thing - it doubles his wealth!
Betty hates the sure thing - she loses no matter what! With the gamble, she may be able to keep what she has.
Bernoulli’s Expected Utility Theory fails to explain risk-seeking behavior (Betty, entrepreneurs, generals who decisions only include poor options)
You dislike losing MORE than you like winning.
Three Principles of Prospect Theory
1. Evaluation is relative to a neutral reference point (aka “adaptation level)
2. Diminishing sensitivity applies to sensory dimensions and changes in wealth.
- Turning on a weak light in an already bright room vs. a dark room.
- $1M to somebody with $10 vs. somebody with $1M. 3. Losses are felt more dramatically than gains.
Consider a coin toss gamble 1. Tails - Lose $100
2. Heads - Gain $150
So, “What is the smallest gain I need to balance a loss of $100?”
For many people, the answer is about $200.
The Loss Aversion Ratio - between 1.5 to 2.5 depending on the person.
Richard Thaler’s Endowment Effect = The cost of giving up something.
Buy a concert ticket to your favorite band for $200, you would have paid up to $500.
They are going for $3000 on the internet, but you still will not sell it - Endowment Effect.
Bad Events - We are driven more strongly to avoid losses than to achieve gains.
Putt to avoid bogie (loss) VS. putt to achieve birdie (gain) - Study showed that golfers did
3.6% better when putting to avoid bogie. Not insignificant: If Tiger Woods putt for birdie like he did to get par, he would have improved his score by one stroke, and earnings by $1M.
“This reform will not pass, those who stand to lose will fight harder than those who stand to gain.”
P = Probability (%) DW = Decision Weight
P% 0 1 2 5 10 20 50 80 90 95 98 99 100 DW 0 5.5 8.1 13.2 18.6 26.1 42.1 60.1 71.2 79.3 87.1 91.2 100
A 2% probability to win has utility = 8 (0+8.1)
A 2% probability to NOT win has utility = 13 (100-87.1)
1. 2% chance to win $1M tomorrow
2. almost certain to win $1M tomorrow, but 2% chance to NOT win.
The Anxiety of the second situation outweighs the hope in the first. (Higher utility)
The Fourfold Pattern (top right quadrant is new and unexpected) GAINS LOSSES
HIGH PROBABILITY (certainty effect)
95% chance to win $10,000 Fear of disappointment
95% chance to loss $10,000 Hope to avoid loss
LOW PROBABILITY (possibility effect)
5% chance to win $10,000 Hope of large gain
5% chance to lose $10,000 Fear of large loss
Top Left = Bernoulli
Bottom Left = Lotteries
Bottom Right = Insurance
Top Right = Desperate gambles in the face of only bad options (Dig the hole deeper...)
In Court: Plaintiff with strong case (90% chance of victory): Risk-seeking defendant has upper hand over risk-averse plaintiff, who is willing to settle.
compare with role reversal...
Plaintiff with weak case (small chance of victory): Risk-seeking plaintiff is the gambler now, and defendant will settle to avoid complete loss.
If the city litigates all 200 cases, it will lose 10, for total loss of $10 million If the city settles all cases for $100,000, the total loss is $20 million
The Long View: For similar decisions, paying a premium to avoid a small risk is costly.
1) People overestimate the probabilities of unlikely events. (Tsunami, Earthquake, Nuclear accident)
2) People overweight unlikely events in their decisions.
Craig Fox’s Basketball Rankings: Asked people to rank the top 8 teams’ chances of winning the championship. Altogether, the probability judgements added up to 240% (it should be 100%).
When thinking about a team’s chances of winnings... focused attention, confirmation bias, cognitive ease causes overweighting.
“Money, Kisses, and Electric Shocks: On the Affective Psychology of Risk” assessed that people are less sensitive to probability when a choice involves emotion. This was later revised by the author on the basis of some experiments by a psychology team from Princeton, that probability is neglected in the face of a vivid outcome.
Power of Format
Probability Format: Patients similar to Mr. Jones are estimated to have a 10% probability of committing an act of violence against others during the first several months after discharge from prison.
Frequency Format: Of every 100 patients similar to Mr. Jones, 10 are estimated to commit an act of violence against others during the first several months after discharge from prison.
Professionals who saw the frequency format (not the probability format) were twice as likely to deny the discharge. (41% to 21%).
Format of data can evoke different emotions (can be used to sway opinion)
1. “approximately 1000 homicides a year are committed nationwide by seriously metally ill individuals who are not taking medication.”
2. “1000 of 273,000,000 Americans will die in this manner each year.”
3. “Annual likelihood of being killed by such an individual is approximately 0.00036%”
4. “1000 Americans will die in this manner each year. 1/30 of suicide deaths. 1⁄4 of laryngeal cancer deaths.”
DNA in court cases:
Wish to cast certainty over DNA evidence? “The chance of a false match is 0.1%”
Wish to cast doubt over DNA evidence? “A false match occurs in 1 of 1000 capital cases.”
You have two decisions to make: Decision 1
A) Sure gain of $240
B) 25% chance to gain $1000, 75% chance to gain nothing Decision 2
C) Sure loss $750
D) 75% chance to lose $1000, 25% chance to lose nothing
Most people prefer A over B (sure gain)
Most people prefer D over C (possibility of loss)
Now combine the choices...
AD) 25% chance to gain $240, 75% chance to lose $760. BC) 25% chance to gain $250, 75% chance to lose $750.
BC dominates AD! But most respondents do not combine the decision. Narrow Framing = sequence of two decisions, considered separately.
Broad Framing = one single comprehensive decision, consisting of four options.
Human tendency is to default to narrow framing, but the combination of
this thought process combined with loss aversion is dangerous.
Stock traders should resist the urge to micromanage stocks, and to check results daily. Once a quarter is enough. Commitment NOT to change one’s position for several periods improves financial performance.
“Are you on your deathbed? Is this the last offer of a small favorable gamble you will ever consider? Of course, you are unlikely to be offered exactly this same gamble again, but you will have many opportunities to consider attractive gambles with stakes that are small relative to your wealth. You will do yourself a large financial favor if you are able to see each of these gambles as part of a bundle of small gambles and rehearse the mantra that will get you significantly closer to economic rationality: You win a few, you lose a few. The main purpose of the mantra is to control your emotional response when you lose.”
Qualifications to this mantra:
1. Gambles are genuinely independent of each other. (Investments are not multiples in the same industry).
2. Possible loss does not cause you to worry about total wealth. Gamble is small in relation to overall wealth.
3. Do not apply to long shots with small probabilities of winning for each bet (lottery).
People prone to narrow framing would do better to have a risk policy rather than construct individual preferences for each risky choice. It will not win out in every situation, but consistency in the long view is what provides the advantage. Examples are:
- Never buy extended warranties
- Always take the highest deductible when buying insurance.
Disposition Effect - Massive preference from finance research for investors to sell winners rather than losers. An instance of Narrow Framing. When deciding which stock to sell, investors close out for gains. People remain committed to failed endeavours, resisting cancellation in effort to avoid a permanent negative stain on the record.
Sunk-Cost Fallacy keeps people too long in poor jobs, unhappy marriages, unpromising research.
Regret is “accompanied by feelings that one should have known better, by a sinking feeling, by thoughts about the mistake and opportunities lost, by a tendency to kick oneself.”
Comparison to the Norm.
In the following two scenarios, who feels more regret?
A) Mr. Brown almost never picks up hitchhikers. Yesterday he gave a man a ride and
B) Mr. Smith frequently picks up hitchhikers. Yesterday he gave a man and was robbed.
Mr. Brown in scenario A will feel more regret.
People expect to feel more intense regret for action than for inaction. Who feels more regret in the following two scenarios?
A) Paul owns shares in Company X. He considered switching to Company Y, but decided against it. He now learns he would have been better off by $1200 if he switched.
B) George owns shares in Company Y. He switches to Company X. He now learns he would have been better off by $1200 if he had NOT switched.
George in Scenario B feels more regret.
We use Mental Accounts keep score of ourselves. For example: Two avid sports fans must drive 40 miles to see a basketball game. One bought the ticket for $40, thoe other got his for free. A blizzard is announced the night of the game. Who is more likely to brave the drive?
The man who paid for his ticket closes his mental account of the game with a negative balance if he does not go. His “sunk cost” is larger.
Mental Accounting also helps to explain why we sell winning stocks and hold on to losers.
Credit vs. cash purchases can hold separate Mental Accounts. Remember: Money is money.
Reversals (of preference) - “When you see cases in isolation, you are likely to be guided by an emotional reaction of System 1.”
Chistopher Hsee’s Dictionaries
Dictionary A with 10,000 entries, like new
Dictionary B with 20,000 entries, cover torn otherwise like new. Evaluated singly, A is preferred. Evaluated jointly, B is preferred.
Losses evoke stronger negative feelings than costs
“Costs are Not Loses” ~Richard Thayler’s note
1) Would you accept a gamble for 10% chance to win $95 and 90% chance to lose $5?
2) Would you pay $5 for a lottery ticket that offers 10% chance to win $100 and 90% chance to win nothing?
The two situations are identical! (uncertain prospect to be $95 richer, or $5 poorer). Somebody with reality-bound outlook would assign equal preference to situation 1 and 2. However, most people prefer option two.
KEEP vs. LOSE
Gas station cash discount vs. credit surcharge. People more readily forego the discount than pay the surcharge.
Brain studies of Framing Effects
Amygdala - Region for emotional arousal (subject’s choice conforms to frame)
Anterior Cingulate - Region for conflict and self-control (subject choice does not conform
to frame. Subject does not do what comes naturally)
Frontal Area - Region that combines emotion and reason to guide decisions (“rational”
subjects who were least susceptible to Framing Effect) Two ways to present surgery outcome:
1) one month survival rate is 90%. (KEEP)
2) 10% mortality in the first month. (LOSE)
The two situation are identical, yet 84% preferred the first option. The “rational” subject would assign equal preference to each situation.
Most of us deal with decision problems as they are framed. Reframing requires cognitive effort from system 2.
Decision Makers tend to prefer the sure thing over the gamble when the outcomes are good (risk averse).
They tend to reject the sure thing and accept the gamble when the outcomes are bad (risk seeking).
Choice and Consequence by Thomas Schelling and arbitrary tax law. Defaults to childless family .
Mental Accounting and Sunk Cost Fallacy (in Context of Framing)
1) Woman goes to theater having bought two $80 tickets. When she gets to the theater, the tickets are not in her wallet. Will she buy two more $80 tickets?
2) Woman goes to theater expecting to buy two $80 tickets. When she gets to the theater, the tickets are actually $160. Will she buy the two $160 tickets?
Most believe the woman in situation one will go home, while the woman in situation 2 will pay.
“The MPG Illusion” by Larrick and Soll - Who will save more gas if...? Adam switches from 12 mpg to 14 mpg.
Beth switches from 30 mpg to 40 mpg.
System 1 solution: Adam only increased only 2 mpg (1⁄6). Beth increased by 10 mpg (1⁄3). Beth saves more gas.
System 2 solution: If both drive 10,000 miles, Adam reduces consumption from 833 gal to 714 gal (savings of 119). Beth reduces consumption from 333 gal to 250 gal (savings of 83 gal). Adam saves more gas!
The MPG frame is wrong, and should be replaced by the gallons-per-mile metric. MPG can lead car buyers and policy makers astray.
Nudge by Thayler and Sunstein - Basic manual to apply behavioral economics to policy. Opt-in vs. opt-out and the power of the Default Option.