CategorizationCategorization

Lauren Munyan, 2/11/04Lauren Munyan, 2/11/04

A boy and his dad were involved in an automobile accident. The dad was killed instantly, but the boy was rushed to the emergency room to try to save his life. The on-duty physician took one look at the boy and refused to operate on him, saying, "I can't operate on that boy. That's my son."

How can that be?

Brainteaser:

The physician is the boy’s mother.

Reason you might have screwed up:

About 25 percent of doctors are women. You may have been assuming the physician was similar to a prototype in your brain’s “doctor category”, which is likely to be a man.

Answer:

Categorical Cognition: A Psychological Model of Categories and Identification in Decision Making

Roland G. Fryer, Jr. and Matthew O. Jackson

• “girl band” example

• Most psychologists believe that we must use categories to process information

• Limit to the number of categories --> stereotyping, prejudice

• Article contributes model of “optimal categorization” and shows that it implies differential treatment of groups based on size

• Mullainathan (2001) - categorization can lead to biased estimates of probabilities

• Barberis and Shleifer (forthcoming) - financial markets

• Alvarez and Brehm (2002) - uncertainty or inexperience w/ other groups can influence opinions and voting behavior

Related Work

Employers and workersWorkers: 90% white, 10% blackTwo equally likely human capital levels, high and lowRepresent types as follows:

(0, 0) black-low(0, 1) black-high(1, 0) white-low(1, 1) white-high

Suppose employer only has three categories available in memory and has interacted with workers roughly in proportion to presence in population

Labor Market Example

Employer sorts types so objects in each category are as similar as possible -- Take total variation about the mean in each category and minimize the sum across categories

Say employer has interacted with 100 workers in proportion to population presence: 5 black-lows (0, 0), 5 black-highs (0, 1), 45 white-lows (1, 0), and 45 white-highs (1, 1)

Minimize variance by putting (0, 0)’s and (0, 1)’s in one category, (1, 0)’s in another, and (1, 1)’s in the third. In other words, lump all black workers together.

Labor Market Example

Labor Market Example

Minimum variance

Knowing that she will be categorized only as “black,” a black person would have less incentive to invest in high levels of human capital (education, etc.) since employers would only see type (0, 1/2) as opposed to (0, 1).

This leads to more black-low types in the black population, which can affect others’ categorizations.

(Low types will be seen as higher type than they really are, which could also be problematic.)

Labor Market Example

But why do people keep track of race? Why would employer want to categorize in a way that minimizes total variation?

Suppose two types of interactions: social and economicIn social situations, assessing race or culture is important (Why? They don’t say.), but in economic interactions, human capital is more important

Objects categorized as before. Employer meets new object that will be placed into category.

Labor Market Example

Notation:ps = Probability object is met in social situationpe = Probability object is met in economic situationVs = Marginal utility of correct (vs. wrong) prediction in social

settingVe = Marginal utility of correct (vs. wrong) prediction in

economic setting

Prediction error measured in distance from true type to category’s average attribute. If you place a (0, 1) in category w/ average attribute (1/2, 1), you get payoff .5Vs in social interaction, and Ve in economic interaction.

Labor Market Example

Base categorization on race:Expected Utility = psVs100 + peVe(90 + .5(10))

= psVs100 + peVe 95

Base categorization on human capital:EU = psVs (50 + .9(45) + .1(5)) + peVe 100 = psVs91 + peVe 100

Human capital categorization is better than race sorting iffpeVe > 1.8psVs, so economic value (and chance that it’s an economic interaction) needs to be almost 2 times higher than social value in this example.

Is this convincing??

Labor Market Example

C = {C1, C2, …, Cn} finite set of categoriesO = potentially infinite set of objects m = number of attributes (finite): O {0, 1}m is function that describes attributes each object has. Written (1(o), …, m(o))f : O C is function that keeps track of assignment of each object to a category. f(o) = Ci means object o was assigned to category Ci.Prototype - representative object for a category. Can think of average attribute vector for a category as its prototype. (or possibly mode or min, etc.)Optimal Categorization - categorizes past objects to minimize total sum of within-category variance

Basic Model

When necessary to combine some groups of objects, best to lump together sets that are relatively small and fairly similar in their attributes

Within set of objects that are optimally categorized, under strict conditions, show that minority objects will be more coarsely sorted than majority objects AND

• Objects in minority group never placed in category with majority subjects

• Majority types are perfectly sorted (any 2 objects from majority group that are in the same category have the same type)

Results

Resumes with “white names” more likely to lead to interviews than identical ones with “black names”Gap in call back rates for blacks and whites are larger among higher levels of skill and education (Bertrand and Mullainathan, 2003)People better at distinguishing faces of people from own ethnic group than from other groups -- effect goes away for white NBA fans!

Evidence

From Devine and Malpass, 1985

Codes in Organizations

Jacques Crémer, Luis Garicano, and Andrea Prat

Background:

Very little study of communication costs in economics, despite fact that we are constantly communicating

Arrow (1994, The Limits of Organization) - organizations deal with complexity of the environment by creating specialized codes

Specialized codes reduce communication costs by allowing use of words that summarize complex information

“Project Management Dictionary” created when firms come together in common project

HR databases and accounting systems (mapping primitive objects into different categories)

Some of Colin’s examples: “Code Six” (officer down) hip-hop slang: bling-bling, 411

My work at the Fed:“I’m on pre-FOMC”“Coffee cart!”

Examples:

Code - “a partition of the space of signals, designed to achieve the maximum possible precision in communication” (subject to bounded rationality constraints)

Agents aim to communicate their information so as to minimize the extra effort involved in figuring out what they mean

Optimal code allocates precise words to frequent events and more vague words to unusual events. Less precise words are used less often.

Firms face choice: • group different agents together -- coordination improves, precision of code decreases• keep agents separate to reap benefits of more specialized codes• get a “translator,” who can communicate between groups with different codes

The Basics

Agents can only use a maximum number of words (since they are boundedly rational)

An agent will receive a signal x X and must communicate it to another agent. Set of signals X is finite. Every signal x has strictly positive probability fx of occurring.

A service is a group of agents who have same distribution of task fx

Example: task is a client type, person who drew task is a salesman, and type must be communicated to an engineer.

Code C is a partition of X into K disjoint subsets, W1, …, Wk

A particular k {0, …, K} can be thought of as a word and the subset Wk as its meaning

The Model

If recipient of message (say, engineer) receives a coarse message, he has to spend time trying to understand and diagnose the problem

Diagnosis cost is higher the more imprecise the word

A code is optimal if it minimizes the expected diagnosis cost subject to the constraint that each agent knows no more than K words

Two additional concepts:Breadth of word k is the number of events that are described by kFamiliarity of word k is the probability that the event belongs to Wk

The Model

Example - Weather in L.A.

Good weatherGood weather Bad weatherBad weather

HazyHazy DrizzleDrizzle

Broad

Narrow

Familiar Unfamiliar

Familiarity

Bre

adth

1. In an optimal code, broader words describe less frequent events.

Propositions

2. In an optimal code, broader words are less familiar (in general).

Def: A distribution is more unequal when it puts even more probability on events that were already likely to occur.

3. If distribution p’ is more unequal that distribution p, the minimal diagnosis cost with p’ is not greater than the minimal diagnosis cost with p. (since under p’, you will be more likely to use narrow words for the likely events)

Propositions

Similarly skilled agents:Say there are two salespeople from different regions who both need to communicate with one engineer, but the salespeople may have different codes. Is it best for engineer to learn each code?

Proposition 4. Only a common code can be efficient. Example: Say engineer hears from person A with code CA = {{1, 4}, {2, 5}, {3, 6}} and from person B with codeCB = {{1, 2, 3}, {4, 5, 6}}. The narrowest non-common words are {1, 4}, {2, 5}, and {3, 6}. Start with {1, 4} and use it in CB’. Then CB’ = {{1, 4}, {2, 3}, {5, 6}}. Still using five words in total, but now events 1 through 6 are each represented with a narrower word. So diagnosis cost goes down and code is more efficient.

Propositions

Assume two services, A and B, each with 1 salesman and 1 engineer

The services might want to coordinate if there are synergies between them. Synergies exist when there is excess demand in one service and excess capacity in the other. (Assume salesman can only handle one customer at a time, or something similar)

If services integrate, they must use a common code, whereas if they stay separate, they use different codes but can’t transfer problems/clients to other service. Want to integrate if coordination gain > communication loss

An integrated organization is more advantageous when:importance of synergy increasesdiagnosis cost decreasesunderlying distribution of tasks becomes less unequal

Organization

Third organization form: hierarchical. Each service has separate code. When communication between services is required, a fifth agent, the “translator,” gets info from one service, translates it into the other service’s code and passes it on to the other service.

Fixed cost of hiring translator, but this person can diagnose words faster.

Proposition: (roughly)If the cost of translator is low enough, there are a minimum and maximum diagnosis cost (d.c.) so that firm will be:

integrated if d.c. < min d.c.hierarchical if d.c. (min d.c., max d.c.)separated if d.c. > max d.c.

Organization

Better technology reduced information costs. Reduction in these costs correlated with increasing decentralization. (move from separate or hierarchical to integrated organizations)

Microsoft:Forced use of common code between different units enabled managers to easily access information and make decisions more rapidly

B-2 Bomber:4 major subcontractors worked on design of B-2 stealth bomber “B-2 Product Definition System” created definitions for parts and

included rules for defining lines and arcs (specific!)Consequences:

designers could come from different companiesdecentralized decision-making / less need for managers

Evidence

How do firms adapt to use of common codes?

Do people underestimate communication costs?

What is cost of creating project definition dictionary and learning the words in it?

More direct tests of Fryer and Jackson’s hypotheses (Have subjects place carefully chosen objects into small number of boxes and see if they minimize total variance by grouping minority objects together?)

Possible to weaken conditions in Fryer and Jackson’s strong prediction and still achieve powerful results?

Future (and current!) Research / Questions