Which of these statements are true?  And which are equivalent to one another?

In 2042, white people will be the statistical minority in the United States.

In 2042, white people will no longer be the statistical majority in the United States.

In 2042, white people will no longer be a statistical plurality in the United States.

The first statement was used by NPR to introduce this interview with comedian Hari Kondabolu, who talks about this claim in his act.

I’m seeing this as a nice example of why mathematical precision is important in everyday conversation.  In particular, we tend to be too casual about how we use words like majority.  I’m not too concerned about the statistics behind the claims here, much less the political consequences — only what the statements mean.

A majority in a set S is a subset whose cardinality is greater than |S/2|, i.e. it is more than 50% of the population.  Saying white people will be a minority in 2042 means that is the year in which less than half of the U.S. population will be white.  A minority is a subset that is less than 50% of the population.

Kondabolu objects to the statement that whites will be a minority, claiming that this only makes sense if you break race into just two categories, “white” and “non-white,” which is a questionable way to look at the world.  This interpretation is complicated by the phrasing “whites will be the statistical minority” rather than “a statistical minority.”  But that’s not a problem according to the technical definition.  Whites project to be a majority of the population in 2041 and a minority in 2042.  Where the statement is loaded is in the complement of the set, as the existence of a minority colloquially but incorrectly can imply the existence of a majority.  But we will really move from whites being a majority to there being no majority.

So give or take the odd “the,” the first two statements are probably equivalent but the second one is probably better.  It also gets away from the overcharged word “minority.”  Which brings us to the third statement.

When I teach voting theory, we look at the word majority as contrasted to a plurality, which is a subset in a partition that is larger than any other subsets in the partition.  If we partition into two subsets, obviously plurality and majority are the same thing.  Plenty of presidents have been elected without a popular majority (the electoral college eats up the third parties, so this won’t happen with electoral votes in modern two-party elections).  When we say “majority rule,” we often really mean “plurality rule.”  In 2042, whites will not be a majority but will remain a plurality.  From there, you are free to carry on whatever political discussion you’d like.

The third statement is therefore false, but suggests a concise statement that summarizes the whole story:

In 2042, white people will no longer be the majority population in the United States, but will remain a plurality population.

Getting this right isn’t about political correctness, it’s about just regular correctness.  A meaningful discussion must be based on facts.  If we can’t properly communicate facts, there is no hope.  This level of precision exemplifies where some mathematical training can pay off.

Wouldn’t it be great if the politicians who are supposed to be communicating and solving these problems studied just a little math?  The first time I taught a liberal arts math class (sometimes called “math for poets”), a colleague gave me an excellent reason why teaching that class well is important: some of those students might one day be in the legislature.

Bill Wood, @MathProfBill, is an assistant professor of mathematics at the University of Northern Iowa.