College Admissions is Not a Zero-Sum Game | #Edu4All


The affirmative action debate threatens to become the single defining issue of the Asian American electorate in the coming cycle, with Asian Americans engaging in heated discussion for or against race-conscious affirmative action in higher education admissions. Supporters of affirmative action — who represent all facets of the AANHPI community — are holding fast to a rhetorical frontline of higher education access for all high school students, and emphasizing the value of affirmative action in removing barriers for underprivileged and underrepresented Black, Latino, Native and Asian American students.

On the other side are (predominantly Chinese American) Asian American organizations who have filed complaints and lawsuits against elite universities like Harvard seeking to end holistic review, spurred to act in part by conservative anti-affirmative action lobbyists like Edward Blum — the mastermind of the Fisher SCOTUS case of a few years back.

One of the chief arguments made by opponents of affirmative action is that college admissions is a “zero sum game” where each applicant is competing for a fixed number of offer letters. Thus, conclude affirmative action’s critics, any offer made to a non-Asian American student (one whom these critics also assert is underqualified) is illegitimate because it removes an opportunity for admission from an Asian American applicant (whom they also implicitly argue is more qualified and therefore more deserving of admission). Yet, this framing appears to fundamentally misunderstand both the goal of college admissions and the term “zero-sum game”.

In this post, I take on the idea that college admissions can be accurately described as a “zero-sum game”.

“Zero-sum game” is an economics term that refers to a fixed sum situation of strict competition, wherein any one participant’s loss exactly equals another person’s gain.  A common analogy is in distributing a cake into slices between three party guests: giving one guest a bigger slice removes some available cake for another guest. Zero-sum games necessarily assert that each party guest is only interested in getting as much cake for themselves as possible.

On the surface, college admissions appears to be a zero-sum game, so long as we think of the purpose of the process as distributing a fixed number of offer letters to a number of applying students. This is because zero-sum games are commonly misinterpreted as applying to any situation of fixed resources.

However, this perspective ignores another (somewhat more complicated) concept in economics: the “non-zero-sum game”, which is an alternative situation to the zero-sum game.

A non-zero-sum-game is any situation wherein the gain of one participant does not exactly equal the loss of another participant, such that the total sum of the game is not zero. This does not necessarily mean that it refers to a situation of non-fixed resources; a zero-sum-game can still refer to the distribution of a fixed quantity of goods. There is, however, a key difference: a zero-sum-game describes a situation where all distributions are of equal value. A non-zero-sum-game, on the other hand, describes any situation where some distributions of the resource are preferable to other distributions; or, put another way, that there is added value to distributing the resource one way over another.

Going back to our cake analogy, a zero-sum-game would be if the game were defined entirely as a situation where we are trying to be rid of an unwanted cake, and if we told guests to compete for slices. A zero-sum-game would be if the party host simply doesn’t care if one party guest gets all the unwanted cake, or if the cake is evenly split between the three guests.

A non-zero-sum-game might also describe a situation of cake distribution, so long as it considers a second goal or parameter: that all guests receive an added benefit if all guests receive their desired amount of cake. We can think of it like this: the cake has greater value to all participants if it is distributed more equally to the guests rather than hoarded by one guest with a sweet tooth. The cake, in essence, becomes “larger” (or at least, more valuable) if everyone gets a slice.

This idea is moviesplained in A Beautiful Mind using as a (sorta objectifying, but you get the point) analogy of a bunch of bachelors competing to win dance partners: there is added value to all participants if every participant accepts a dance with the attractive girl’s friends, rather than all compete for the most attractive girl.

It should become clear by this discussion that zero-sum games are highly over-simplified situations. In fact, most situations in real-life are not-zero-sum games precisely because in most cases some “game” outcomes are preferable over others; that includes college admissions.

Colleges have a “fixed” number of available freshmen slots (actually, calling it “fixed” rather than “limited” is also a bit of a misnomer, but that’s a conversation for another time), but that does not mean that the college admissions process is a strictly competitive zero-sum situation. In actuality, college admissions is a non-zero-sum-game because (as with our cake analogy) some distributions of offers are more desirable and beneficial than others.

We understand that colleges derive additional benefit — to themselves and to each enrolled student — when offer letters are distributed in some ways over others. Specifically, we understand that there is added value — to all participants of the process — if the student body is diverse; that added value of campus diversity means that “the cake” can, in essence, get larger when it is distributed more widely.

Studies have shown that all students benefit from a racially and culturally diverse classroom. But, if we put aside racial considerations for a second, we can understand this concept simply by exploring a hypothetical where universities did not recognize the added value of distributing offer letters diversely across different declared major interests. Let’s say that universities didn’t care if they admitted a broad distribution of students interested in hard vs social scientists vs liberal arts. Yet, if a school admitted 90% of applicants who want to be engineers — and no fine arts students — not only would this significantly impair the capacity of the school to actually provide a proper education for all these students, but it would significantly impair the school ranking and the quality of education for individual students (who would now have to compete for significantly over-taxed engineering courses). Student culture would suffer by the absence of a thriving fine arts community in the student population.

So, for an admitted engineering student, an offer letter to a particular school might become more valuable if it is offered alongside offers to a broad range of non-engineering students, because it reflects an offer to a school that has a more enriched academic environment. This is a non-zero-sum-game.

What this post basically points out is that college admissions is not just a process of putting butts in seats irrespective of who those butts belong to in isolation from one another. College admissions officers also must consider the “compelling interest” of creating a diverse student body, and that the added value of this diversity creates tangible benefits to enrolled students.

When we describe college admissions as a “zero-sum game” we indicate that we fundamentally misunderstand this process. We also ignore the compelling interest of schools to generate on-campus diversity, and we further argue that diversity has no value to all enrolled students.

To say that college admissions is a “zero-sum game” is to say that student diversity (racial or otherwise) simply doesn’t matter. College admissions is not a zero-sum game precisely because it does: student diversity benefits all students.

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  • 1maybeso

    This post would imply that schools that lack diversity are somehow inferior. Most Universities in Asia lack diversity. I’ve even heard that some Chinese universities have no black or hispanic students at all. For shame! So are they racist for not having policies that encourage more diversity, or are we racist because we assume that a school filled with only one ethnic group is inferior?

  • Well, MIT ranks #7 in the nation and has a much more diverse student body. Caltech, which boasts a lack of affirmative action, ranks #10. Obviously, we can’t say the differences in ranking is due to the student diversity question, but we can certainly say that the less diverse school also happens to not be ranked as well as a comparable school of similar focus that does have a more diverse student body.

    I’ve even heard that some Chinese universities have no black or hispanic students at all. For shame! So are they racist for not having policies that encourage more diversity, or are we racist because we assume that a school filled with only one ethnic group is inferior?

    I don’t know, but perhaps trying to compare American universities in a completely different system in a completely different country against Chinese universities and trying to draw meaningful conclusions is just a generally fraught endeavour?

  • John

    I can help answer the comment regarding Chinese Universities.

    (1) (a) Immigration to China from African/Hispanic nations did not exist until post-2000. Majority of black/Hispanic diaspora are older immigrant workers. Furthermore, universities students competing for a seat in a Chinese university is likely to be an international student, those students are not going to receive the same criteria or take the same exam i.e. “gaokao” as a domestic applicant. (b) Many universities does not have enough funding for international programs, then it’ll be unlikely to have many international students. (c) Not many students from Africa/Hispanic nations are applying to Chinese University as their primary higher learning institution. Students are usually from international exchange programs/study abroad, and they would not count towards diversity at a university.

    (2) One of the predominate reasons for affirmative action in US is to correct historical racial discrimination in this country. China did not have plantations with black slaves nor did it have Jim Crow laws targeted at blacks/Hispanics in its history. Hence, there would be no forms reparation for blacks/Hispanic candidates who currently reside in China.

    (3) There is geographic boost. Students who live regions with fewer resources have boost in their exam scores. Example: if you live in Inner Mongolia, you gaokao score does not have to be as high as someone who live in Beijing.

    (4) There is an ethnicity boost. China has 56 historically recognized ethnic groups.
    The Han ethnicity is the dominant group at 91.1%. Any member who predominately identifies with a minority group does not have to score as high on the gaokao as students of Han descent to gain admission to universities.

    The primary reason there are unlikely going to be black/Hispanic students in Chinese Universities is because there are few black/Hispanics students in China. Secondly, diversity in China is not emphasized by ethnicity as it is in the US; it is more emphasized by culture/upbringing. For example, someone from Miao (Hmong in US) group may be ethnically very similar to Han but they are considered to be an ethnic minority because of their upbringing and culture. So, a black candidate from an African nation is considered to be African and black candidate from the US is considered to be American and how they are judged by the school will be different. The American student will be viewed as a candidate from a industrialized superpower and their standards will be higher as their resources are much more abundant.

    Implying that a school is “racist” in Asia for not having black/Hispanic students is an egocentric and rather arrogant way of viewing the world. Histories for each region of the world are different and who they consider for assistance will be just as different.

  • Thank you for this comment, John. Without tipping my hand too much, I’m currently reading up on affirmative action and preferential treatment policies in China for an upcoming post, and appreciate your insights.

  • 1maybeso

    It was saracasm. Of course no one expects China to have the same racial breakdown as the US. Also most university age Hispanics in the US are immigrants/2nd generation. Why would recent immigrants groups deserve reparations? That is ridiculous and insulting to the African American community, which, as you say, endured slavery. It’s an especially ridiculous notion when you take into account the percentage that are here due to ILLEGAL immigration by themselves or by their parents.

  • John

    You first categorized black and Hispanics together as one group in your first post suggesting the ridiculousness of Affirmative Action by Asian schools as a analogous comparison. Then separated blacks and Hispanics in two groups which suggests that black do need affirmative action compared to Hispanics. So … you’re just all over the place on the issue.

    Furthermore, the use Asian university as an comparison to American university completely throws off the reader because suggests ignorance on the issue rather than sarcasm because they have no parallel.

    Better parallel would be saying to the author so “UC students are inferior to UT (University of Texas) students because there are less racial diversity (even though UCs rank higher)”. Or to state that “UC Berkeley and UCLA are two schools with ~40% of the student body on Pell Grants (ranking 1 and 2) compared to ~20% at UT Southwestern – damn those poor people always trying so hard!”

  • John

    I disagree with your description of non-zero-sum game of college admissions because admission process fundamentally does not behave as a free market.

    (1) The cake refers to the market size. It literally means a bigger cake.
    Your analogy that the cake is more beneficial is more like “adding
    truffles to your cake”, i.e. the cake itself is of higher quality but the market size stays the relatively the same.

    (2) There is no upper cap in a free market. The market has the potential to grow infinitely large (the cake analogy). Business exit the market as a result of poor competitiveness relative to other competing businesses, but as a result of the more competitive business’ ability to increase market size. None of those two factors apply in the admissions. Harvard is not increasing its market size.

    (3) The cake analogy is used is when we are discussing multiple suppliers (not just Harvard). It means that when there is a demand for higher education in market that is beyond the barrier of entry more suppliers will attend to meet the demand; for example, as more people desire to attend university, more colleges will be built over time; hence the market size grows. Or if the supply of college exceed the demand of students; the universities decide to decrease tuition; then the number of student would increase; hence increase the market size.

    (4) A market approaches non-zero-sum with the assistance of minimal asymmertric information. The choice of attending university and the benefits to both the buyers (students) and the supplier (Harvard) needs to be the same. The lack of transparency that Harvard in its admission process creates an asymmetric information system in which Harvard will know about the market than the students will know about the market. i.e. Harvard has an idea of what their ideal student should be and Harvard knows whether or not the student is an affirmative action admit, but the students cannot pinpoint it; therefore, the price is not the same (and not free market) and it is inefficient. Thus it creates a “Market of Lemons” in which the supplier knows more about the buyer than vice versa. It also creates an uncertainty the real price of market (example: 11 candidates apply for a job 10 non-URM, one URM with a company that practices affirmative action. If the URM is selected, the 10 URM applicants would have a reason to suspect that affirmative action played a role, even though it is guaranteed that at least 9 of the 10 non-URM candidates would have been rejected anyway.

    The lawsuits and complaints are going to force some overdue transparency to the system and that is something I would like to see.

  • Very nice comment.

    I do want to point out that this post is not Harvard-specific. At most schools where affirmative action is practiced (public universities), the market can and does indeed grow with increased demand – class size can and does increase and new schools are built. In fact even some Ivies increase class size to meet demand. This accommodates the wellpublished statistic that more young Americans are attending college every year than ever before.

    Thus if we take the market as bounded not by an individual school but as the entire ‘marketplace’ of schools conducting admissions each year, the market can and does expand despite the presence of some schools to keep their class size mostly fixed.

  • 1maybeso:

    Your original comment did not read as sarcasm, nor does it make it clear that a sarcastic comment of this nature adds much value to this conversation. This site values sincere participation in the discussion for the purposes of mutual learning and understanding. I do not think a comment that is incoherently ‘sarcastic’ for no apparent reason is engaging this process in good faith, and I would invite you to comment with more thoughtful posts in the future.

  • 1maybeso

    Unfortunately, you are all over the place. Affirmative action and reparations are two different topics. Perhaps read up on what reparations actually means and would entail in the US before using the word.

  • Uhm, assuming that you’re referring to this by John:

    (2) One of the predominate reasons for affirmative action in US is to correct historical racial discrimination in this country. China did not have plantations with black slaves nor did it have Jim Crow laws targeted at blacks/Hispanics in its history. Hence, there would be no forms reparation for blacks/Hispanic candidates who currently reside in China.

    which is the only place where he says something that could be remotely construed as referring to reparations, actually he’s right: that is the historic rationale for why affirmative action exists. For MOST of the lifetime of its policy, focus on the reasons for its continued existence has been to correct for historic discrimination; only recently has discussion of the contemporary benefits of diversity actually entered the conversation, associated with new research on the subject.

  • 1maybeso

    Reparations does not apply to hispanics. Reparations is much bigger than just affirmative action. And if affirmative action is now about diversity, as you write, then it is not about reparations. If affirmative action only applied to to African Americans, you could make that case. But it does not.

  • DoYouEvenLift

    Your entire argument seems to rest on the premise that diversity somehow increases the value of the group correct? Can that be quantified in anyway outside of your analogy of the 90% engineering students example (I also want to point out all the supposed problems in that example are assumptions)? This notion that diversity inherently adds to the value of a university seems to be based on well…nothing except a few flimsy examples (and a very biased source). What qualifies as “diversity” or the amount of necessary representation is entirely a subjective value judgement. What if the piece of cake doesn’t get bigger because not every individual shares your understanding of the supposed benefits of diversity?

    “The University of California, Berkeley’s affirmative action program for blacks captures the essence Of a zero-sum game. Blacks are admitted with considerably lower average SAT scores (952) than the typical white (1232) and Asian student (1254) (Sowell 1993: 144). Between UCLA and UC Berkeley, more than 2,000
    white and Asian straight A students are turned away in order to provide spaces for
    black and Hispanic students (Lynch 1989: 163). The admissions gains by blacks are
    exactly matched by admissions losses by white and Asian students. Thus, any preferential treatment program results in a zero-sum game almost by definition.”

    It just seems like your analysis is based on a subjective understanding that “diversity is good” therefore it must increase the value based on distribution of resources.