---
title: Speed-run Through Social Stratification
author: 36-313, Statistics of Inequality and Discrimination
date: 15 September 2022, Lecture 6
output:
  pdf_document:
    toc: true
    toc_depth: 4
    number_sections: true
bibliography: locusts.bib
---

```{r, include=FALSE}
# Set up global options for displaying code and so forth
library(knitr)
opts_chunk$set(size="small", 
               tidy=TRUE, tidy.opts=list(comment=FALSE),
               cache=TRUE, cache.comments=FALSE, autodep=TRUE,
               warning=FALSE, message=FALSE, error=FALSE, echo=FALSE)
set.seed(2021-09-13)
```


\newcommand{\Prob}[1]{\mathbb{P}\left( #1 \right)}



So far, we've looked at how to describe the distribution of quantitative traits
like income and wealth across an entire population, common patterns in those
distributions, and how to quantify the level of inequality across the
population.  We are presently going to switch focus a bit to group differences,
that is to comparisons across populations or across sub-populations.  In
principle we could divide a population up in total arbitrary ways ---
right-handed vs. left-handed, or people whose Social Security numbers have "13"
as the middle two digits versus the rest of us.  In practice, the interesting
and important comparisons line up with social divisions that are already widely
recognized in the society.  Social scientists who study
**stratification**[^strata] have developed some useful concepts for talking
about particular social divisions, and for organizing different types of social
division, but these aren't necessarily familiar to everyone taking this course,
hence today's lecture.

[^strata]: In Latin, a _stratum_ (plural _strata_) is a layer of something, like dirt or paint.  Geological strata are layers of rocks laid down on top of each other.  In speaking of "social stratification", the metaphor is that different social groups are like layers of different minerals stacked one upon another.

\clearpage

# Types of stratification variables

There are two basic distinctions we can draw between _kinds_ of social
division, or the variables which track it.  One, which is familiar to us as
statisticians, is between variables which are purely **qualitative**,
**categorical** or **nominal** on the one hand, versus those which are
**quantitative** or at least **ordinal** on the other.  Variables of the first
type divide people into distinct types, but on the basis of some kind of
qualitative distinction.  (The different types usually have names that everyone
in the society knows, hence[^nomen] "nominal".)  An example might be which
political party you are affiliated with (or, in a one-party state, whether you
are a member of _the_ party).  Variables of the second type rank people based
on their having more or less of something --- sometimes we can apply a precise,
numerical value to the "more" or "less", other times it's a bit fuzzier, but
it's still about ranking.  Income is an outstanding example of a very numerical
variable; "education" isn't _as_ numerical, but we can and do still plainly
talk about who's more educated than whom.

[^nomen]: From the Latin _nomen_ "name".

The other great distinction is between **ascribed** and **achieved** statuses.
A status is **ascribed** to you by others because of factors completely beyond
your control, primarily having to do with your birth and family of origin.  Age
is an outstanding example of an ascribed status, but there are many others, as
we'll see[^ascribedforareason].  **Achieved** or **attained** statuses, by
contrast, are ones which are at least partly the result of what you have
_done_.  Income and education levels are also examples of achieved
statuses[^fair].

[^ascribedforareason]: Saying a status is "ascribed" can make it sound _arbitrary_, as though you could have a different ascriptive status if everyone else would just cooperate.  Sometimes that's the case, but the example of age should help make it clear that people can have very good reasons to ascribe certain statuses and not others, and indeed that some ascriptions can just be true.

[^fair]: Saying that some dimension of inequality is about achievement doesn't necessarily mean that it's _fair_.  If nothing else, many people would just not have had the chance to try for certain achievements!

We can thus organize our thinking about how society is divided up into
qualitative versus quantitative divisions, and ascriptive versus achieved
divisions.  Let's look over some important kinds of stratification
from this point of view.

## Quantitative, achieved stratification

**Income** and **wealth** are outstanding examples of quantitative, achieved
stratification variables.  Income is a _flow_ of money in over some unit of
time (often a year); wealth is a _stock_ of money accumulated.  It's usually a
mistake to compare them directly.  While these are obviously related, it's
important to bear in mind that they're distinct.  Many high income people also
have large debts, and so small or even negative net worth[^cmu].  Against that,
some ill-paid people might be debt-free and even own some assets, so they'd
have lower incomes but higher net worths than well-paid debtors.  I should also
clarify here that when we talk about "income", we usually mean income in money,
but this can be less than total compensation or consumption: farmers who grow
the food they eat, for instance, have a higher level of consumption than their
monetary income indicates[^hunting], as do people who (say) receive free or
subsidized services or products from the employer, their worshipers, or their
government.  Some economists put a lot of effort into trying to come up with a
cash equivalent for these factors, and so estimating the distribution of
consumption and income-equivalents.

[^cmu]: Recent graduates of expensive universities in high-salary jobs, for instance.

[^hunting]: Similarly for hunters.  During the years when one of my uncles lived in the mountains of New Mexico, if you just looked at what he _bought_, you would have thought he hardly ever ate meat, and not realized that he usually had a separate freezer full of vension.

Another achieved variable which clearly admits of ranking and comparisons of
"more" or "less" is, as I said above, education.  We are quite familiar with
the idea that some people are more educated than others.  I would, however,
suggest that this is more of an ordinal and less of a numerical variable than
income.  It's very common, for instance, to categorize people by their
education level as "less than high school", "high school graduate", "some
college", "college graduate", "graduate or professional degree".  These levels
are ranked but not numerical.  A common numerical measure is "years of
schooling", but there's no real reason to think that the difference between the
first and second year of schooling should be as big, in any sense, as the
difference between the twelfth and thirteenth[^schoolquality].

[^schoolquality]: Note that both these ways of measuring education, either as ordered levels or as a numerical magnitude, ignores differences in school quality.  You are all here, rather than paying much less tuition at Allegheny Community College or even at Penn State, because you think CMU gives you a better education than either of those schools.  I very much hope you're right about that, but that's harder to gather systematic data on, and starts to complicate comparisons.  --- Another issue with "years of schooling" is how to handle students who are held back a year because of failing classes or disciplinary issues.

Closely related to education is the notion of different forms of metaphorical
"capital" people can possess.  Non-metaphorically, "capital" originally meant
the resources of a business enterprise --- either the money used to fund it
("financial capital"), or the plant and equipment it used to make money
("physical capital").  Around the 1950s, some economists introduced the notion
of **human capital**, to refer to an individual worker's marketable skills
[@Mincer-schooling-experience-earnings].  If you have some skill, and it lets
you get a higher income than you'd have without that skill, then you have human
capital, and the extra income is regarded, by economists, as the "return" on
your human capital.  Skill at plumbing and skill at programming are, in this
perspective, both forms of human capital; this should suggest that it's
multi-dimensional, since "Alice is a better programmer than Dave" makes sense,
and "Babur is a better plumber than Chandra" makes sense, but "Alice is better
at programming than Babur is at plumbing" doesn't,
really[^capitalizinghumancapital].

[^capitalizinghumancapital]: On the other hand, "Alice's programming skill raises her income by $50k/yr, while Babur's plumbing skill raises his income by $75k/yr" _does_ make sense, so you could collapse down to one numerical dimension that way.

**Social capital** refers to having valuable social connections: some
combination of having strong, trustworthy ties[^body], _and_ having
wide-ranging ties which bring you lots of information, or make you the crucial
connection between different social circles.  In a [social networks
course](http://www.stat.cmu.edu/~cshalizi/networks/16-1/), we might look at
different ways of quantifying this; here it's enough to say that someone with
lots of close friends and allies _and_ a wide-ranging acquaintance clearly has
more social capital than an isolated loner.  Social capital doesn't translate
into income as directly as human capital, but it is nonetheless a valuable
thing to have, and unequally distributed.

[^body]: As the old joke goes, "A friend is someone who'll help you move; a _good_ friend is someone who'll help you move a body."

**Cultural capital** is essentially mastery and appreciation of what is
recognized locally as important, prestigious forms of cultural knowledge.  This
can include correct manners[^pc], fashion sense, etc., but also knowledge and
appreciation of the right kind of cultural artifact (movies, music, books,
...)[^pc].  Displaying
the right kind of cultural capital confers prestige and opens doors.

I emphasize the "recognized locally" bit.  As I said in lecture, my father's
father had an encyclopedic knowledge of classical Persian poetry, and the
ability to always come up with an apt quotation from it; this was valuable
cultural capital in Afghanistan back in the day, but not much appreciated after
he came to this country as a political refugee in the 1970s.  Perhaps more
relatably, a musical or other artistic "scene" is pretty much _defined_ by
having a very local sort of cultural capital which outsiders don't
appreciate[^grep].  That being said, lots of societies recognize some sort of
"mainstream" high culture, where people will go "oh yeah, that's the fancy
stuff", even if they don't necessarily appreciate it themselves.  Sometimes
this means elevating certain genres of cultural artifacts over others (e.g.,
classical opera rather than musicals); in the contemporary US it seems to mean
enjoying lots of genres, but being picky within every genre
[@Childress-et-al-contemporary-higher-status-tastes].  Regardless of the
_content_ of cultural capital, it's "capital" because it's a valuable thing
some people possess and others don't.

[^pc]: Strictly speaking, knowing how to express oneself in a way that shows commitment to social justice, or at least doesn't offend those who feel such commitments, is _also_ a form of cultural capital.  (A lot of people have made this point; the version in @Bovy-on-privilege is unusually thoughtful.)

[^grep]: In case this sounds too art-kid: Knowing Unix, including the `grep` utility, is a marketable skill, and would constitute human capital.  Being able to use the _word_ "grep" in casual conversation is cultural capital.

Schooling is, _in part_, about conferring human capital, social capital and
cultural capital.  We are, for instance, teaching you some skills which command
a direct value on the market, which is human capital.  We are introducing you
to peers who it will be useful to know, at a stage in your lives where you form
friendships easily, which is social capital.  And we are helping you acquire
the habits and tastes which go with high status, which  is cultural capital.
This isn't _all_ a university is about[^university], but it's _part_
of schooling.

[^university]: If the university is doing right by you, there will be classes whose content never earns you a blessed dime, but which you find yourself thinking about for the rest of your life.

Having talked about economic variables, education and various sorts of capital,
we should talk about **class**.  This word gets used in two related but
confusingly distinct ways.  In one sense, a "class" is a group of people who
make their living in the same (or similar) ways, and consequently have similar
styles of life.  In this sense one could talk about university professors, or
corporate executives, or owners of building-trades companies, or retail
cashiers, as a class.  (You can also imagine that there might be broader- or
finer- grained classes, as "small business owner" versus "master plumber".)
Members of the same class, in this sense, will tend to have a lot of
similarities in income, assets, education, and specific forms of human and
cultural capital.

Another way in which "class" is used, however, is as a kind of summary of how
high up the economic ladder someone is.  A common system of ranks for class in
this sense would be: upper, upper-middle, middle, lower-middle, working class,
lower class.  (Some would add, at this point: under-class.)  These are rarely
terms used with any precision, especially not "middle class".  At one time, you
could draw the distinction that those who were "working class" and below didn't
have the resources, especially the assets, to _not_ go out and work for
_someone else_ every day, while the middle class(es) and above did, and the
upper class had people work for them[^collars].  One way to try to reconcile
the two usages is to think of phrases like "the working class" as a short-hand
for "the working class_es_", plural.

[^collars]: A related distinction, still very prominent in American speech, is between "white collar" and "blue collar" jobs.  A "white collar" job was one where you could where a white shirt all day without dirtying it, because it was office work without manual labor.  A "blue collar" job was one which did involve working with your hands and getting dirty, so you'd wear shirts which wouldn't show stains so much, typically made of blue fabric.  ("Pink collar" is a much later play on this distinction, to refer to jobs primarily held by women.)

Finally, in this quadrant, **status**, **prestige** or **esteem** are variables
on which we can rank people, they're ones for which "more" and "less" make
sense, but are also achieved.  Some status or prestige attaches to occupations
--- surgeons are higher status than, say, garbage-collectors.  Some of it
attaches to individual persons.  (There are especially esteemed
garbage-collectors, and widely despised surgeons.)  "Coolness" should be seen
as a kind of status or prestige [@Heath-Potter-rebels].  Income _often_ tracks
prestige, but not always; being, say, a musician or painter does not, for most
people, pay very well at all, but it carries prestige and coolness.


## Quantitative, ascribed statuses

The most obvious entry here is, as I said, **age**.  In modern American
culture, we tend to think of age as just a numerical variable.  We do however
make a distinction between legal minors and those who have come into their
legal majority, and between "seniors" and those younger than them.  Some other
cultures have maintained a much more elaborate system of "age grades",
sometimes with formal initiation ceremonies.

Also in the quadrant of ranked but ascribed variables, we can include one's
_parent's_ income, wealth, education, and class.  As we'll see when we cover
the transmission of inequality, these are _very_ predictive of people's lives,
and certainly rank-able.  But the class you were born into is an ascribed
variable as far as you're concerned, however much of an achievement it may have
been for your parents.

Historically, many societies have had a form of ascriptive status which we
might call **rank** or **order**, such as noble or commoner, or distinctions
among various grades of noble, or indeed various grades of commoner.  As the
names suggest, this isn't fully quantitative, but it is certainly ordinal.  It
is, importantly, distinct from economic status: some commoners might be richer
than some nobles, indeed there might be many nobles who were fairly poor, but
still had their noble status, and with it various privileges that were
categorically unavailable to even the richest commoner[^cobban].  Some of these
societies had ways for people to change this sort of status, to become ennobled
(or, more rarely, to lose their status of nobility), but this was a rare event.
This isn't quite the same as caste, conceptually, because it was usually the
case that marriages between nobles and commoners were regarded as legitimate.

This sort of inequality is not important in modern American life, because it
was largely done away with by our Revolution, however inadvertently
[@Gordon-Wood-radicalism].

[^cobban]: See, e.g., @Cobban-social-interp for French examples.

## Qualitative, achieved variables

**Political party affiliation** belongs here.  This has been an important form
of social division in many times and places, and is increasingly one in modern
America.  Party affiliation or membership often runs along family lines, but
strictly speaking it's changeable and only something adults are really capable
of.

I put **religion** here for similar reasons.  Some religions do not allow
conversion into the religion, and others make it very difficult, but pretty
much every religion recognizes _leaving_ the faith.  (It may not _accept_
it, but that's a different matter.)


## Qualitative, ascriptive variables

### Ethnicity

An **ethnicity** is a group of people who perceive themselves as, and are
perceived by others as, sharing common habits, customs, traditions, and,
usually, a common language, and are typically thought of as also united by
shared ancestry.  You will notice a lot of hedging in that sentence
("perceived", "thought of").  This is because the truth of this matters is, in
this regard, vastly less important than people's beliefs, even or perhaps
especially when the truth is demonstrably at odds with common belief.  It's a
well-worn joke among social scientists that an ethnic group consists of people
who share a common mistake about their origins.

It's important to realize that ethnicity is often relative.  In the US or
Australia, "Chinese" or "Italian" or "Indian" can qualify as an ethnicity, but
back home, the difference between a Hakka from coastal southeast China and a
Mandarin speaker from Beijing, or between a Bengali and a Tamil, or between a
Lombard and a Sicilian, looms much larger.  It is possible that "Asian" or
"Hispanic" will condense, in the US, into a single ethnicity, especially if
something happens to interrupt continued immigration (though I wouldn't
personally bet on that).

### Race

Originally, the way people thought of races was as something like an umbrella
group of ethnicities.  The idea was that the human species naturally clustered
into a fairly small number of _distinct_ groups, biologically distinguishable
and separated by ancestry.  This is _not_ how actual human biology works.

Now, obviously, if I look at a crowd at CMU, or walk down a street in
Pittsburgh, I can make a pretty decent guess which continent many people's
ancestors lived on 500 years ago.  But this is because we've brought together
people from widely-separated places fairly recently.  When scientists have
actually carefully studied the geographic patterns of genetic variation, it
turns out that there are no abrupt breaks and no clusters[^geneticclusters],
just smooth gradients.  (We'll come back to this.)  It probably didn't have to
be this way.  Many other animal species _do_ cluster into geographically and
genetically distinct sub-species.  Indeed, at an early point in our
evolutionary history, there were multiple sub-species of _Home sapiens_ --- not
just ours, _Homo sapiens sapiens_, but also the Neanderthals and the Denisovans
and possibly others[^neanderthals].  A world in which there were, say, still
surviving Neanderthals would be one in which the concept of "race" would make a
lot more _biological_ sense than it does in our world, at least as applied to
the distinction between Neanderthals and us.  A world in which other hominin
species, such as _Australopithecus_, had also survived would be one where race
made even more biological sense.  Again, this is not our world.

[^geneticclusters]: If you run genetic data through algorithms which _have_ to output clusters, they will indeed report clusters, but that's not exactly _evidence_ of clustering, whatever credulous journalists may tell you.

[^neanderthals]: I say "sub-species" rather than species because paleonotological genetics show that _some_ of our ancestors were, in fact, Neanderthals and Denisovans, and "can have fertile offspring together" is the criterion for belonging to the same species.

#### Race in the Contemporary US

Currently, for official data-gathering purposes, the US recognizes the
following races:

1. Native American or American Indian
2. White
3. Black
4. Asian
5. Other, which in practice is a combination of people who check more than one of the above, and immigrants from countries with very different racial categories.

The rules for who goes into which category are elaborate and somewhat
arbitrary[^pashtuns].  In particular, the rules about "black" call for special
comment.

[^pashtuns]: As an example, people from the Middle East are classified as white.  (Think about where the Caucaus mountains [as in "Caucausians"] are located.)  This includes Syrians, Lebanese, Iraqis, Iranians and Afghans.  On the other hand, everyone from Pakistan and points east are "Asians", just like (say) people from Cambodia, Korea or Japan.  From an official US point of view, two members of the same ethnic group, from opposite sides of the Afghanistan-Pakistan border, could be of different races, even if they were cousins.

The official racial category of "black" includes African Americans, i.e.,
American descendants of slaves[^ados]; many immigrants from the Caribbean and
their descendants (sometimes called Afro-Caribbeans); and recent immigrants
from sub-Saharan Africa and their descendants.  This is a _very_ heterogeneous
category; some of the recent African immigrant groups, for instance, have
average income and education levels above the over-all US average, which
African Americans decidedly do not.  Historically, of course, "black" in the US
has almost always meant the first of these sub-groups, the ones we now call
African Americans.  Genetically, (almost) everyone in this group has a mixture
of African, European, and Native American ancestry.  What determined membership
in it was what came to be called the "one drop rule", that if you had any
identifiable African ancestry, you were black, regardless of how far back it
was or how you looked.  Most other countries in the Americas imported slaves
from Africa, and developed racial hierarchies, but most of the others tended to
recognize more grades between black and white; the English colonies in North
America, and later the US, tended to make it binary.

I have said that race is an ascribed social status, fixed at birth, and this is
mostly accurate but isn't _entirely_ true.  Precisely because race matters a
lot, some people are very motivated to take steps to change their racial
status.  One way this happens is through presenting[^goffman] oneself as a
different race than one was born into.  Historically, an important form of this
was African Americans moving somewhere new and there "passing as white".  It's
difficult to know exactly how common this has been, but some estimates
[@Stuckert-on-passing] suggest that a large percentage of the white American
population actually had African ancestors[^passing].  Recent studies which
survey the same people in multiple years show that at least some of them
self-report different races at different times (along with changing
self-reports for other supposedly-fixed identities and categories)
[@Egan-identity-as-dependent].  Having said this, however, one way we can tell
that race is _supposed_ to be an ascribed status is that efforts to change
one's race are widely regarded as deceptive, or at best as a sign of being
seriously disturbed [@Brubaker-trans].

[^goffman]: For the concept of "presentation of self in everyday life", see the classic and brilliant book of @Goffman-presentation.

[^ados]: I realize that there's a controversial political movement which uses that name, but it _is_ a pretty transparent name which clearly describes the relevant population.

[^passing]: @Staples-real-american-love-story is a brief, well-written popular account of some of the relevant history and social science.  (In the ensuing two decades, inter-racial marriages have become _much_ more common, see @Alba-demographic-illusion.)  I don't think we have any good data on how common passing is nowadays.    Demographers have tried to estimate "racial mobility" by comparing the number of people counted by the Census in each racial group in a given year (say, 2000) to the number of members that group should be expected to have, based on known births in previous years, known immigration and known age-specific survival rates [@Perez-Hirschman-estimating-net-interracial-mobility].  These efforts show that there has been a small _net_ transition from non-Hispanic white to other categories since around 1980.  (It's plausible, but not certain, that much of this is people with mixed ancestry acknowledging it more often.)  This sort of apporoach does not, however, let us identify the gross transitions from one category to another.  Anecdotally, blacks passing as white was still happening as recently as the 1970s.  I myself have two (unrelated!) acquaintances of my generation who discovered, as adults, that a parent or grand-parent had passed.

At a less individualistic level, there has also been a lot of struggle over
what the racial categories should be, and how different groups should be
slotted into them.  If we go back to the 1800s and even the first half of the
1900s, there was a strong current of opinion in Europe and the Americas that
there were, in fact, different races of Europeans[^barzun].  In large part,
this took the form of "Nordic" northwestern Europeans claiming racial
superiority over southern and eastern Europeans and the Irish.  Starting in the
1920s, immigration to the US was legally limited to quite small levels, but
immigration from southern and eastern Europe was _especially_ limited, on
explicitly racist grounds.  Naturally, immigrants to the US from Ireland and
southern and eastern Europe contested this, and the emergence of a single
"white" category in modern times is, in part, a result of their successful
efforts to be re-classified.  It is only since 2000 that official US records
allow people to identify themselves as members of more than one race, and this,
too, is in part the result of persistent cultural and political struggle.

[^barzun]: This is why a classic skeptical history of racist ideas, @Barzun-race, is largely about people we'd all call whites being racist _towards each other_.

Here I should point out something which you may have already noticed, which is
that "Hispanic" does _not_ appear on the list of official racial categories.
The official position of the US government is that "Hispanic"[^hispanicnames]
is not the name of a race, but of an ethnicity, defined by a shared cultural
heritage, and that Hispanics can be of any race.  There is some logic to
this[^hispaniclogic], but in everyday life in America, Hispanic is often
treated as though it was a race alongside black, white, Native American and
Asian.  This is why, in studies which use official data sources, you will often
see phrases like "non-Hispanic whites" --- it's an attempt to compromise
between the official classification scheme and some conspicuous social
realities.  There is also evidence that the fact that all these disparate
groups are lumped together in the US as "Hispanic" contributes to the formation
of a new and distinct group identity in this country [@Mora-making-hispanics].

[^hispanicnames]: It is not my place to take sides on sometimes-heated disputes about whether to use the term "Hispanic", "Latin American", "Latin", "Latino", "Latina/o", "Latinx", "Latine", etc.; "Hispanic" is what's used officially.

[^hispaniclogic]: There is _something_ which ethically Italian Argentines have in common with Dominicans, _mestizo_ Puetro Ricans and even with Mayan villagers in Guatemala for whom Spanish is a second language, and which they _don't_ have in common with (respectively) Italian Americans from the Bronx, Haitians, Canadian M{\'e}tis, or Pueblo Native Americans.

### Caste

At this point I should introduce another important kind of social division,
namely **caste**.  In anthropology or sociology, a caste is a group of people
who are restricted to marrying and having children with others of the same
caste (or perhaps a small range of closely-allied castes), and where membership
in the caste is fixed at birth and passed from parent to child.  More
precisely, _legitimate_ marriage and procreation is restricted to being within
the caste; relations outside the caste are scandalous, and the offspring of
such relations are always ascribed an unfavorable status.  Castes are typically
arranged in a hierarchy of prestige, and there are usually economic divisions,
with certain occupations being restricted to certain castes.  Extremely strong
feelings of purity or pollution can attach to caste membership, so that (the
wrong sort of) contact between high and low caste individuals may leave the
former being seen as, and feeling themselves to be, unclean.  The most
elaborate and longest-lived caste system is that found in south Asia
(especially but not just modern India), going back, in various forms, for
thousands of years.  But caste divisions, in this sense, have also been found
in many other parts of the world, including ones we rarely think of as having
them[^cagots].

[^cagots]: For instance, from around 1000 through the 19th century, parts of western France and northern Spain had a sub-population known as "Cagots", who were in effect a caste of untouchables.  (I learned about this case from @Appiah-lies-that-bind, p. 28, who gives good references.)  In that situation, there were effectively two castes, the Cagots and everyone else.  According to @Patterson-social-death, pp. 48--51, this is the most common pattern cross-culturally.  (Incidentally, Patterson reports that the existence of slavery is only weakly associated with the presence of castes, and that in many societies with both, the slave/free distinction cuts across caste lines.)

#### Caste and Race

Now, if you take this definition of "caste", it seems like a pretty good match
for how, historically, Americans have understood race.  Race was hierarchical,
it was inherited and didn't much care about anyone's actual physical features,
it was linked to occupation, there were strong feelings of purity and pollution
(think of segregated water fountains), and mixed-race children, however common,
were scandalous and almost by definition illegitimate[^miscegenation].  In this
sense, American race was a caste system, as some sociologists and
anthropologists pointed out as long ago as the 1930s[^wilkerson]
[@Warner-on-caste-and-class; @Dollard-on-Southerntown].  Whether it still _is_
a caste system, or has changed into something else, is less clear.  Marrying
and having children across racial boundaries is vastly more accepted than it
used to be, but there are indications that African Americans form an exception
to this, suggesting _that_ caste boundary is still in place[^alba].

[^miscegenation]: Many US states had enforced laws against interracial marriage and "miscegenation" until they were over-turned by the aptly-named Supreme Court case of _Loving vs. Virginia_ in 1967.

[^wilkerson]: Isabel Wilkerson's _Caste: The Origins of Our Discontents_ (New York: Random House, 2020) is a very recent book-length exposition of this idea, by a distinguished journalist (author of the outstanding popular history @Wilkerson-other-suns), but I haven't read it so I can't comment on it one way or the other.

[^alba]: @Alba-demographic-illusion has an excellent receive view of the evidence on both thee points.

\clearpage

# Protected characteristics and categories

In US law, since the 1960s, a number of categories and characteristics are
"protected", meaning that it's illegal to discriminate on that basis of these
characteristics, or membership in these categories.  More exactly, any
discrimination on these bases is open to legal challenge, and needs to show a
compelling justification.  What the law enshrines as protected categories are:
race, color, religion, sex, national origin, and age.  More recent additions
have included, in some contexts, disability, genetic information, gender
identity and even, sometimes, citizenship.  The law recognizes that there are
some situations in which it is, in fact, OK to discriminate on these bases: the
laws against religious discrimination do not force a Christian church to
consider a Muslim or an atheist as a preacher.  (The church might get in
trouble, however, if it refused to consider hiring a Muslim as a janitor.)


It is notable that these are mostly qualitative, ascribed statuses, but not
entirely.  (Age is quantitative, religion is at least in-principle attained
even if most people stick with whichever religion they were raised in.)  Other
qualitative, ascriptive characteristics are, legally at least, fair game.
Thus there is no American federal law against discrimination on the basis of
political party affiliation, or indeed caste[^ancestryvscaste].  Discrimination
on the basis of income, wealth, education, cultural capital, or even class is perfectly[^disparateimpact] legal.

[^ancestryvscaste]: Some states have civil rights laws which ban discrimination on the basis of "ancestry", and there is currently a case before the courts in California as to whether this applies to discrimination on the basis of caste in the Indian sense (see, e.g., Anahita Mukherji, "California's Legal Ground In Battling Caste Discrimination Takes Centre Stage In Historic Cisco Case", _The Wire_ 10 March 2021, [https://thewire.in/caste/cisco-case-caste-discrimination-silicon-valley-ambedkar-organisations].)  Everyone agrees that the federal laws against employment discrimination do not apply in this case, because Brahmin and Dalit Indians are of the same race and national origin.

[^disparateimpact]: One wrinkle here is the legal notion of "disparate impact", which says that it's not OK to impose neutral-seeming tests which have the _effect_ of harming, or favoring, people with protected characteristics, _unless_ there is a good, functional reason for it.  Thus the law against discrimination on the basis of national origin is usually held to prohibit discrimination in hiring on the basis of fluency in English and even on one's accent.  If you apply for a job as a TV newscaster, the station can reasonably require you to be able to speak English fluently, but they couldn't, legally, reject you for having a Spanish or Chinese accent.  (Or, at the very least, you'd have a good case against them, and they'd have to present a very compelling argument as to why a certain accent was a bona fide "business necessity".)    Similarly landlords are generally free to raise rent, even if doing so has a disparate impact on member of protected categories.

I want to emphasize that everything above is about what the law currently
forbids or allows, not about how things _should_ be, or even about what the law
should be.  As a citizen, I have some views about that, but this isn't the
place for me to inflict them on you.

\clearpage

# Some Words on Genetic Differences between Social Groups

## Endogamy creates genetic differences

Many social groups are **endogamous**: they mostly, or exclusively, marry and
have children with others inside the group.  This is part of the definition of
"caste", but also very common for race, ethnicity, religion, and class.[^assortative]

[^assortative]: Some people also use "endogamy" to refer to a tendency for people with similar values of _quantitative_ traits, like income or education levels, to marry each other.  Others describe that as **assortative marriage**.  In animals, a (positive) correlation between quantitative traits of mates is called **assortative mating**.

If a group is endogamous, and membership in the group is _socially_ transmitted
from parents to children, then over time there groups will become genetically
distinct.  This is a basic point, but worth appreciating.  Assume that there
are just two groups, says "reds" and "blues", and that, at the beginning of
time, membership in the different groups is completely independent,
statistically, of genes.  Because the groups are finite, however, some genetic
variants will be more common among reds than among blues, and vice versa.
Because of endogamy and transmissible group membership, in the next generation
the reds will be children of the original reds, and the blues will be children
of the original blues, so the initial genetic differences will, on average, be
passed on (this is called a genetic **founder effect**).  But in fact a child
inherits (on average) only a random half of each parent's genes[^sexlinked], so
there's a sampling process, and some genetic variation is lost from generation
to generation.  Because this sampling will happen independently in the two
groups, they will increasingly diverge over the generations.  This in turn
means that as time goes on, it will be increasingly easy to infer whether
someone is a red or a blue from their genome.

[^sexlinked]: There are some exceptions, like mitochondrial DNA and sex chromosomes, but this isn't a genetics course.

Thus the qualitative argument: endogamy _plus_ social transmission of group
membership _implies_ gene pools that diverge over time.  A natural question is
how to make this quantitative, i.e., how much divergence should we expect
between groups?  This is a more complicated question in population
genetics, which will involve the size of the founder effects, the population
sizes of the two groups[^popsize], the distribution of offspring per parent
in each group[^offspring], etc.  It's also important to realize that this will
happen over generations, and human generations are fairly long[^generation].

The next page shows a small simulation of what this mechanism can produce over
a few generations in small populations.  The code is in the .Rmd file for these
notes, so you can get a sense of the range of outcomes, and how changing the parameters changes the distribution of outcomes.

[^popsize]: The smaller the groups, the greater the reduction in genetic variation due to sampling in each group.

[^offspring]: A higher average number of offspring will imply less sampling, but if the distribution is very skewed, the "effective" population size is reduced.

[^generation]: In modern conditions, many adolescents are biologically capable of reproducing by age 14 or even earlier, but such early development requires levels of nutrition which were historically extremely rare.  In pre-industrial conditions, the age of reproductive maturity might be closer to 18.  (This needs to be distinguished from age of _marriage_, which might be much younger.)  Historically, as now, many people do not just reproduce as soon as they're biologically capable, so taking a human generation as 20 or 25 years is a reasonable rule of thumb.  When the simulation below shows 10 generations, then, you should imagine a passage of 250 years.

\clearpage

```{r}
n <- 100
T <- 10
reds <- sample(c("A", "a"), size=n, replace=TRUE)
blues <- sample(c("A", "a"), size=n, replace=TRUE)
red.history <- vector(length=T)
blue.history <- vector(length=T)
for (t in 1:T) {
    red.history[t] <- mean(reds=="A")
    blue.history[t] <- mean(blues=="A")
    reds <- sample(reds, size=n, replace=TRUE)
    blues <- sample(blues, size=n, replace=TRUE)
}

plot(1:T, red.history, xlab="generation", ylab="proportion of A in gene pool",
     ylim=c(0,1), type="l", col="red", lty=1)
lines(1:T, blue.history, col="blue", lty=2)
legend("topleft", legend=c("reds", "blues"), col=c("red", "blue"),
       lty=1:2)
```

_A small demonstration of how endogamy and cultural inheritance can create genetic
differences between social groups.  We are looking at one "locus" in the genome, where there are just two genetic variants, called "A" and "a" (geneticists have some weird notational conventions...), and plotting the proportion of the "A" variant in the gene pools of two endogamous, self-reproducing groups, the "reds" and the "blues".  Initially, the "reds" and "blues" are divided without regard to genetics, but the children of reds are all reds, and the children of blues are all blues, so the gene pool of each generation in each group is a_ sample _of the group's gene pool in the parents' generation.  Thus the gene pools at this locus diverge.  Here, the "A" variant becomes somewhat more common among blues than among reds, but if you re-run the simulation, you'll see that it comes out the other way half of the time.  Here, we haven't built up much divergence after 10 generations, but remember that the same kind of divergence will happen at each locus in the genome, and modern gene scans can pick out hundreds of thousands of loci, each of which would give_ some _information about group membership._

_(To keep things simple, I have fixed the population size for each group at 100, and made each generation a uniform sample, with replacement, from the previous generation.  [That is, I'm not simulating the genetic details of sexual reproduction, so pretend this is just looking at passing mitochondrial DNA from mothers to daughters.]  By tinkering with the simulation, you can explore what happens if you change the with population sizes, have non-uniform distributions of offspring among parents, and how sex complicates everything.)_

\clearpage


Quantitative precision will also require working back in some of the
complicating factors that I omitted in sketching the argument above.  Two
paragraphs ago, I assumed that endogamy is perfect (there are no "mixed
marriages" or children without marriage...), that group membership is 100%
inherited in a purely social/cultural way (no one born red ever becomes blue or
vice versa), that no natural selection acts on the genes, and that there are no
mutations[^mutation].  If the endogamy is imperfect, or if there is some
migration between the groups, that will tend to make the groups more
genetically similar.  The consequences of natural selection will depend on
whether the selection acts in the same way on the two groups (e.g., both get
selected for resistance to locally-common diseases) or if they are subject to
different selection pressures (e.g., the groups have different ecological
niches or are exposed to subtly different environments)[^malariaandmilk].  All of these factors
can of course vary over time.  Many social divisions are not very endogamous
for very long, so they won't create large genetic differences, but strong,
sustained endogamy _can_ create big genetic differences.

[^mutation]: Since mutations would happen independently in the two groups,
adding in mutuation _alone_ would only make the groups more genetically
distinct.

[^malariaandmilk]: Thus, for example, the genetic diseases of sickle-cell anemia and thalassemia are both side-effects of mutations which offer (partial) protection against malaria; the former is more common in west African and the latter in Mediterranean populations, both areas where malaria has long beenn a serious endemic disase.  It is also important to realize that "environment" or "ecological niche" for humans can reflect culture and technology.  The classic example is adult lactose tolerance.  Lactose is the primary sugar in milk, and almost all mammals lose the ability to metabolize it as they become adults.  Most humans are also lactose-intolerant as adults.  There are, however, a number of populations which have long kept large herd animals which can be milked (goats, sheep, and especially cattle), and adult lactose tolerance has evolved multiple times among these groups. 

So far, I have been talking only about genetic differences between social
groups.  But social groups are usually, indeed often, un-equal in various
outcomes like income, education, or health.  Now put this together: endogamy
plus social inheritance makes groups genetically distinct; social groups have
unequal outcomes; therefore, _genes can predict social outcomes_, even when the
genes are functionally, causally, completely irrelevant to the outcomes.  If
gene $A$ is more common among blues than among reds, and reds have higher
levels of education for purely cultural reasons, gene $A$ will predict
educational attainment.  At least, it will in a population of reds and blues;
transporting the same genetic predictions to a different set of populations
would work much less well.

Since this is not a course in quantitative population genetics, however, I will
not draw this out any further, but just summarize that genetic differences
between social groups are exactly what we should expect from the combination of
endogamy and _social_ transmission.  We should even expect individual-level
social outcomes to be _predictable_ from genomes, whether or not the genes
are in any sense _causes_ of those outcomes.

## "The history and geography of human genes"

I mentioned above that when scientists have actually investigated the
distribution of genetic variations across human populations, they don't find
discrete clusters, as we'd expect if there were distinct races.  Instead,
there are three outstanding findings:

1. Most of genetic variance is _within_ populations, rather than _between_ them[^anova];
2. The _average_ gene frequencies in local populations do vary across space, but they vary smoothly, without abrupt breaks into distinct types;
3. There is some correlation across genes (if one population's gene pool contains more than the usual amount of gene $A$, then on average it will have more than the usual amount of gene $B$, too), but few of these correlations between genes are very strong.

[^anova]: We will look in detail at parsing variance into within-group and between-group components very shortly in the course.


Point (1) means that there is a lot of genetic variation within any human
population.  But there is nonetheless _some_ average frequency for each
gene[^allele] in a population, so we can think of those average frequencies as
being high-dimensional vectors[^vectors].  Point (2) is saying that those
vectors vary smoothly as we move geographically over the surface of the Earth.
If you think  back to the example above about how endogamous social groups will
become increasingly distinct genetically, point (2) suggests that nearby
populations have only been _partially_ isolated from each other reproductively[^ryg].

[^allele]: Strictly speaking, each variant at each locus in the genome --- what geneticists call **alleles**.

[^vectors]: There are roughly 30,000 human genes, almost all of which have multiple alleles, so these are at least 30,000 dimensional vectors.

[^ryg]: If the Yellows live between the Reds and the Greens, what we usually see is that the Reds and the Yellows are more genetically similar than are the Reds and the Greens.  But if all three groups were completely endogamous, even if they diverged from a common pool of ancestors, there'd be no reason for the Reds to be more similar to the Yellows than to the Greens --- certainly no reason for that to be a repeating pattern.  If however there is "gene flow" between neighboring populations --- if people sometimes have children with their neighbors --- we'd expect to see exactly this pattern.

Point (3), the correlations between genes, suggests a way of usefully
simplifying the complexity of gene frequencies.  If two genes were perfectly
correlated (or perfectly anti-correlated), we wouldn't need to track _both_ of
them, so we could get rid of one coordinate.  If there are $p$ dimensions but
there were $q$ perfect correlations, we could get away with just $p-q$
dimensions, because the vectors would lie on a $(p-q)$-dimensional plane in the
$p$-dimensional space.  The actual correlations aren't perfect, but we can
nonetheless hope that the vectors lie _close_ to a low-dimensional plane in the
high-dimensional space.  This has led geneticists, following
@Cavalli-Sforza-et-al-demic-expansions, to use dimension-reduction
techniques[^pca] to explore the large-scale patterns of human genetic
diversity, and what they reveal about the history of population movements, the
expansion of agriculture, etc.  These analyses show smooth gradients for
genetic differences, not distinct races --- but the techniques used don't
_presume_ such patterns.

[^pca]: Specifically, principal components analysis (PCA), a very old [@Pearson-invents-PCA; @Hotelling-re-invents-PCA-1; @Hotelling-re-invents-PCA-2] but very robust method of dimension reduction; if you're curious for details, see the chapter on PCA in @CRS-ADAfaEPoV.

\clearpage

# Some optional exercises

## Conceptual consolidation

1. In class, I drew a diagram where one axis was attained/ascribed, and the
   other was quantitative/qualitative, and located different social variables
   at different points on the diagram.  _Without_ consulting your notes, draw
   such a diagram with points for each social variable discussed here.

## Extending the genetic simulation example

1. Run the simulation for two populations of size 100 and 10 generations.  Calculate the probability that someone in generation 10 can be correctly classified as red or blue, depending on whether they have gene $A$ or $a$.  (Your answer will depend on how your simulation run turns out, but on my first try I got an accuracy of 63.5%.)  _Hint_: First find $\Prob{red|A}$ and $\Prob{blue|a}$.
2. Run the simulation 9 more times, but change the gene labels from $Aa$ to $Bb$, $Cc$, etc., down to $Jj$.  (Keep the initial probabilities of all the genetic variants equal.)  This is like looking at 10 independent loci in the genome.  Taking the individuals in the tenth generation, fit a logistic regression which takes as its ten input features whether an individual has gene $A$ or gene $a$, gene $B$ or $b$, etc., and predicts whether the individual is red or blue.  What accuracy does this logistic regression have for classifying individuals?  (On my first try, I got an accuracy of 83%.)
3. Assign each individual a random number of years of education: blues are uniformly distributed on the integers between 10 and 14, reds are uniformly distributed on the integers between 11 and 20.  Build a linear model which predicts years of education from the ten genetic features.  What's the $R^2$?  (On my first try, I got an $R^2$ of $0.2$.)

(Using linear and logistic regression here has no particular statistical or
genetic justification, but they're methods you know, which makes the exercises
easier, and which geneticists know, which makes the exercises more realistic.)

\clearpage

# Further Reading

Distinguishing between ascribed and attained forms of status is a very standard
part of the tool-kit of sociology and anthropology; the book by
@Keister-Southgate-inequality in our readings is a pretty good source, but any
introductory textbook on those subjects should cover it.

On ethnicity, nationality and nationalism, @Gellner-nations is essential
reading; if you read only one book from this section, make it that one.  If you
have it in you to read _two_ books about nationalism, make the second one
@Anderson-imagined.

Exactly how we should understand "race", the extent to which race and caste are
analogous (or race should be understood as a variety of caste), etc., etc., are
subjects which fill libraries, particularly in this country[^heath].  Without
pretending to have mastered this literature, I will somewhat arbitrarily
recommend @Appiah-lies-that-bind, @Loury-anatomy, @Fields-and-Fields-racecraft
as recent-ish contributions that strike me as especially insightful and
well-written.
We will revisit issues related to racial classification, and its role in
official statistics, later in the class, but if you are eager to read ahead,
@Anderson-Fienberg-census-race is very good.

[^heath]: "[T]o any non-American, the most oppressive feature of intercultural relations in America is not that people are racist, but just that they talk and think incessantly about race, even worse than the way the English talk and think incessantly about class" [@Heath-enlightenment, ch. 13].


Population genetics is a very important, and fundamentally probabilistic and
statistical, branch of science.  @Gillespie-pop-gen is a good short
introduction at about the mathematical level of these notes.  The key figure in
the development of large-scale studies of (to borrow the title
@Cavalli-Sforza-history-and-geography) "the history and geography of human
genes" was the late L. L. Cavalli-Sforza; the most accessible account of his
work is @Cavalli-Sforza-genes-peoples-languages.

We will have a lot more to say about discrimination against protected
categories, and how it can be established, later in the class.  The discussion
of protected categories and characteristics above, and later in the course, is
overwhelmingly about US law, because this is a course at an American university
and it's what I'm most familiar with.
@Mercat-Bruns-on-employment-discrimination provides an interesting comparison
of American federal law on these topics with the relevant parts of the legal
systems of France and of the European Union.  (One interesting aspect of this,
to which we will return, is the much greater role of statistics in American
anti-discrimination law than in its European counterparts.)  As to the rest of
the world, I am too ignorant to comment.


I should probably add to these further-reading suggestions when I have time,
but this will keep you busy, and if you have questions about specific topics,
feel free to ask.

\clearpage

# References

