Introduction to Limited Rationality

# Introduction to Limited Rationality
## EC404; Fall 2022
### Prof. Ben Bushong
### Last updated February 17, 2022

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# Some Thoughts

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class: MSU
# Introduction to Limited Rationality
We can think about the idea of "Limited Rationality" in two ways (both are inspired by tons of work in psychology and under-explored in economics):

1. Informally: "Ways that our probabilistic beliefs are wrong". We call these collected errors **Quasi-Bayesian**.

- [1.1] Errors in probabilistic judgments about things. e.g., base-rate neglect, gambler's fallacy.

- [1.2] Errors in statistical reasoning about volitional agents e.g., level-k reasoning, cursedness and inferential
  naivety, hindsight bias.

- [1.3] "Motivated cognition": preferences and emotions distorting probabilistic judgments e.g., cognitive dissonance, self-serving biases.

But category we do for next few weeks `$\dots$`

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class: MSU
# Introduction to Limited Rationality

### "Quasi-Maximization"

We will model the person as engaging in traditional constrained maximization at each moment in time.

- But specify exact mistake the person is making in which function she is maximizing, or in what choice set she is choosing from.

Does not correspond to maximizing **true** preferences because

- [1.1] Present bias: moment by moment, you maximize full intertemporal utility, but at each moment tend to overweight current utility (and may mispredict the propensity to do so in the future).

- [1.2] Utility misprediction: because of current tastes or current focus, you (actively or passively) mispredict utility of future situations.

- [1.3] " Decision neglect" and "narrow bracketing": maximizing true utility among each choice set you focus on, but don't focus globally

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class: MSU
# Introduction to Limited Rationality

### Quasi-Maximization Defined More Broadly

Person maximizes a particular " goal" given his choice set:

$$ \text{Max}_{x\in X} V(x).$$

But `$V$` not actual utility function **should** be maximizing.

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class: MSU
# Introduction to Limited Rationality

Lesson and theme for economics of quasi-maximization perspective:

-  Have we ever chosen our " life course" ?

`$\Rightarrow$` Our piecemeal maximization may lead to life course we never **chose**.

-  A smoker "decided" thousands of times to smoke ... but did she ever decide to become a smoker?

-  A person in $12,000 credit-card debt made all the choices leading to that debt  ... but did she ever decide to be $12,000 in debt?

All three quasi-maximization errors contribute.

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# Decision Neglect and Narrow Bracketing

### Life.

Life's a bitch \_\_\_\_\_\_\_\_, and then \_\_\_\_\_\_\_ you die.

-  Life's a bitch *of a complicated expected-utility maximization problem*, and then *millions of isolated decisions taken and billions of potential decisions untaken later* you die.

-  Economic models tend to operate as if we sit down and formulate a complete contingent plan of what we'll do. And then we implement that choice.

Of course, perfect planning followed by perfect execution of plans is not what people do. Two hard-to-distinguish departures:

1. **Decision Neglect:** We make choices in only infinitesimal percentage of infinity of choice sets we face.

2. **Narrow bracketing:** We don't fully integrate our decisions with other decisions even when we could increase utility from doing so.

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# Decision Neglect and Narrow Bracketing

Nobody (including economists) thinks people do the maximize-complete-contingent-lifetime-expected-utility thing.

But turns out our failure to do global maximization matters.

-  This limit to rationality is the closest to a complexity-based mistake that we'll discuss in this course. (There are, of course, others)

We'll show:

-  People narrowly bracket even in relatively simple settings.

-  The **way** people narrowly bracket is suboptimal within the class of narrow-bracketing rules of behavior.

-  `$\dots$` and worse than **simpler** rules.

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class: MSU
# Decision Neglect and Narrow Bracketing

Life is an infinite series of (potential) choice sets, `$X_{1}, X_{2}, \dots X_{N},$` .

When facing choice sets `$X$` and `$Y$`, the agent

### Should:

`$$\text{Max}_{x,y\in X\times Y} u(x,y).$$`

### Instead might:

- **Decision Neglect**: "choose" some `$\overline{x}\in X$` without
    thinking, or

- **Narrowly Bracket**: } `$\text{Max}_{x\in X} u(x),$` and `$\text{Max}_{y\in Y} u(y)$` separately.

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class: MSU
# Decision Neglect and Narrow Bracketing

Casey faces choice: 50/50 lose $80 / lose nothing over lose $35 for sure?

-  Per prospect theory, Casey may choose the 50/50 gamble.

-  This is throwing away expected value.

What if Casey has a coin in their pocket. Could take the sure loss $35, then play 50/50  $40 with person next to them.

- This generates 50/50 lose $75, gain $5.

-  Unambiguously better than what most people do.

**Deeper question:** what does it mean if *merely reminding you of a possibility* changes your choice?

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# Decision Neglect and Narrow Bracketing

# Social-preferences example

-  Suppose you are choosing between 15 apples for self and 0 for an anonymous other vs. 9 for self and 4 for that other person.

**Would you choose (15, 0), or (9, 4)?**

Could take the 15 apples and split them up any way you want.

-  Didn't prevent you from doing whatever you wanted afterwards.

-  (15,0) isn't your final allocation if you don't want it to be.

-  Why not turn (15,0) into (9,6)?

Huge literature in economics about so-called "Dictator Games".

-  How many $10 dictator games did person to left of you play yesterday?

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# Decision Neglect and Narrow Bracketing

These are cases of " Decision Neglect" .

-  Experimenters bring into focus relevant pies to pay attention to, and the relevant set of people to split it among.

-  But more generally in life such focus happens by accident, by the design of others, and occasionally by our own design.

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class: MSU
# Decision Neglect and Narrow Bracketing

Two general approaches to showing that people "narrowly bracket" :

-  Direct---show people don't combine problems they'd be better off combining.

-  Indirect---combine presumptive facts about "background noise" to argue calibrationally that observed choices are " too non-linear" to be consistent with integrating with unobserved other parts of life.

-  Note: "indirect" shows simultaneously that people don't even narrowly bracket in as wise a way as they could.

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class: MSU
# Decision Neglect and Narrow Bracketing

**Decision (i):** Choose between

> $240 for certain and (.25, $1000; .75, $0)

**Decision (ii):** Choose between

> $-750 for certain and (.75, -$1000; .25, $0)

What does Prospect Theory tell us about behavior in this setting?

-  84% A over B, 87% D over C.

### This is an error of narrow bracketing!

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class: MSU
# Decision Neglect and Narrow Bracketing

We can see the real problem when we look at the combination of choices.

Subjects' combined choices:

-  73% AD, 11% AC, 14% BD, 3% BC.

But:

-  AD is really a lottery composed of: (.75, -$760; .25, $240).

-  BC is really a lottery composed of: (.75, -$750; .25 +$250).

So prefering AD to BC inconsistent with any theory ever proposed in either psychology or economics.

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class: MSU
# Decision Neglect and Narrow Bracketing

### So What?

You might retort: Okay, so people don't do impossible and completely integrate life choices. And?

**Answer 1:** yes, impossible. And so we study it.

- Claim is not that people are stupider than they have to be given that they are subject to human constraints.

- Humans on average make the mistakes that humans on average make.

- The point is rather: people are less rational than economic models suppose, in ways that matter.

**Answer 2:** This situation is in your face, and still don't integrate.

- So we've learned something about how powerful it is.

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# Decision Neglect and Narrow Bracketing

**Answer 3:** This result is general; it's not about these preferences, or this pair of choices.

Rabin and Weizsacker argue the violation we just illustrated

-  can occur for arbitrarily small degrees of narrow bracketing

-  can be economically significant

-  appear in a wide range of experimental tasks

-  Almost surely is exhibited massively in non-campus life.