Wednesday, May 14, 2014

Corner Solutions

The expression 'corner solution' comes from economics.  I want to apply it elsewhere, but first a little background to help the reader make sense of this alternative use of the expression.  Beware, there is some economics jargon below.  I hope it is useful for the subsequent discussion. 

I took my first course in Microeconomics in the fall quarter 1976 from the beloved Mort Kamien, now passed.  The subject matter was price theory, or if you are of a more mathematical bent, as I was, then you'd call it partial equilibrium analysis.  While the more popular textbook at the time was by Henderson and Quandt, we used a different book by Kogiku, Microeconomic Models, as well as a complementary text by Gary Becker, to provide us with a more narrative approach to the subject matter.  A significant piece of the course was devoted to theory of consumer choice, the first example that the economics student confronts that features constrained optimization

There are two sorts of constraints.  The first says that the consumer's choice must be within the Consumption Set.  When you teach intermediate microeconomics, as I've done fairly often, the Consumption Set is taken to be the first quadrant.  The interpretation is that in the simplest model where there are two goods, the Consumption Set describes purchases of those goods, and purchases must be nonnegative. The second is called the budget constraint.  It says that what the consumer spends on purchases can't exceed the consumer's income.  These two constraints taken together define a choice set.  The consumer's problem is to maximize preference within the choice set.

Logically, there can be an interior point that is optimal (meaning it solves the consumer's problem).  Such a solution is referred to as a bliss point.  While it is logically possible, a bliss point is economically uninteresting.  Economics is fundamentally concerned with allocating scarce resources to competing ends.  With a bliss point, there is no scarcity.  (The reader might want to recall the old TV show, The Beverly Hillbillies, where Jed and Granny were seen throwing money out of the window of the Bank, with the bills raining down on passersby.)  To get the economics concern into the consumer choice problem, a restriction is imposed on the consumer's preferences.  In intermediate microeconomics that restriction is described as more is preferred to less.  It implies the consumer will spend all available income or, in the jargon of this course, that the budget constraint will bind at the optimum.

An interior solution happens where at the optimum the consumer buys positive amounts of both goods.  Symbolically, it is characterized by the method of Lagrange multipliers.  Graphically, which is how I teach this stuff in intermediate micro, it is characterized by the indifference curve being tangent to the budget line, the economic tradeoffs implied by that characterization.  A corner solution happens when the consumer spends all income only only one good, so the consumption of the other good is zero, the least it can be.  The characterization is different in this case.  Symbolically, it is characterized by Kuhn-Tucker Theory.  Graphically, tangency between the indifference curve and the budget line is still possible, but it is no longer necessary.  At the corner where only the X good is purchased, the indifference curve can be steeper than the budget line.  Likewise, at the corner where only the Y good is purchased, the indifference curve can be flatter than the budget line.

This completes the development of the jargon I will use in the rest of this piece, but I'd like to make two further points on the economics before I continue.  One is that essentially the same math is used in looking at other economic models, such as how two consumers who barter with one another will arrive at final trades from which no further bartering will occur.  The other point is that having only two goods in the model is there primarily to make the explication as simple as possible.  It can be readily extended to have a very high number of commodities, though then graphical techniques are no longer useful and one has to rely on a symbolic characterization only.  Think of your own shopping behavior when going to a supermarket to buy groceries for the next week or so.  There are many product categories where you likely don't purchase at all and within product categories where you do purchase, there typically will be one brand you favor while purchasing nothing of the other brands.  The issue, then, in describing this behavior is whether to focus on the tradeoffs between the goods you do purchase at positive levels, or to focus on the exclusion of those goods that you don't purchase at all.  Where the focus should lie is what's at issue in the sequel below.

* * * * *

Via traditional media and social media too we have gotten more polarized in our discourse on social and political issues.  That is not news.  More important here is the seeming natural reaction to respond in kind to a view expressed in extreme form. Further, even if making an initial claim rather than reacting to the claims of others, there is strong temptation in making the case to reduce dimensionality in what is at stake and then claim that a corner solution is optimal in this simplified and more abstract universe.  This type of argumentation, which Milton Friedman practiced par excellence, appeals to the purist nature in all of us.

But it denies the complexity of reality.  If we are to embrace complexity, something I try to do, though admittedly with mixed success, then abstraction can be seen as a deal with the devil.  In describing what is happening on the ground, the causes for why it is happening, and possible amelioration of the problem(s), complexity should be embraced at each level.  This is hard to do, intellectually.  Abstraction is useful for that reason, but then we too often become intellectually lazy and confound the abstraction with reality; it's close enough or so we convince ourselves.  That we act as if we know this ahead of time is the real problem.  We don't.  We're ignorant on this score.  Those of us who wish to be considered thoughtful should be biased toward finding an interior solution, for this very reason.  A corner solution may have superficial appeal, but we should be wary that we've gotten the full story.  Nobody likes to sound wishy-washy.  Yet certitude is worse and really needs to be guarded against.

Via a few of my posts taken in reverse chronological order, let me illustrate my own struggles this way.  About a half year ago I wrote a piece, Do I have to consume conservative media to consider myself thoughtful?  It marked my own movement toward corner solutions.  I should note that while that piece certainly did not go viral, it got about six times the number of hits as my typical post gets.  This indicates to me more return visits than usual and some readers forwarding the piece to their friends, both indicators that others are bothered by this question.  The next previous piece is a very short one called Taking a Sabbatical from David Brooks.  The focus there was one particular columnist, not all conservative pundits.  But I had been a regular reader of David Brooks for many years, so it still represented a substantive change in my behavior.  My complaint with his pieces was as follows.

Both in his "I told you so" tone and on his analysis that frequently over simplifies the social science (and occasionally is just wrong) his writing has become more than I can take now.

Then there is this piece, the topic of which still vexes me: Is it possible to have thoughtful conversation about America's future between Conservatives and Liberals?  If it were possible then I'd view it as desirable, and I guess so would many others.  With gridlock in Congress, one would like to see thoughtful people of both political persuasions identify those areas of agreement where some progress might be made.  In my way of thinking, such conversation might not happen face to face in a live forum but rather through essays published online, with some substantial lag between the original posed argument and the response, and then possible further response.  Way back when Pat Buchanan and Michael Kinsley were on Crossfire I would watch the show from time to time.  It was not very satisfying, partly because of the rude style where the interviewers regular interrupted the guests,  and partly because I don't recall it ever producing a synthesis of views that each side could embrace.  I know it is back on the air now, but I haven't watched it and have no desire to do so.  Indeed, I don't watch MSNBC shows - presumably representing the Liberal view - because the style is too righteous and unaccommodating.  (I did for a while watch Keith Olbermann and a bit of Rachel Maddow, but gave that up several years ago.) 

This last piece, entitled Theism - "Pan", "Mono", and "A", is the closest thing I've produced aimed as a thoughtful rebuttal to an opinion piece written by a Conservative pundit.  It is a response to Heaven and Nature by Ross Douthat.  His essay is a critique of the movie Avatar and the implied pantheism in the storyline.  My response, which was written a week or two before I saw the movie, once I saw it I thought it was cool in its special effects but benign in its message, was composed because that semester I had experienced "religion in the classroom" for the first time in my long career teaching and I wanted to comment on that as well as to comment on Douthat's essay.  I have a routine where I republish my blog posts in Facebook.  Most of them just sit there, people tell me my essays are too long, but this one evoked a couple of strong approvals from friends, indicating that I came closer to the mark than usual.  My friends, however, are not Conservative, as far as I know.  I don't know how a Conservative reader would have reacted to that essay.  It is also true that the topic of Douthat's piece was not particularly troubling.  Even if a Conservative reader would have reacted favorably to my piece, it doesn't mean that such a reader would likewise react favorably to other responses I produce on different topics, where the passions run hotter. 

Below I will give a response to Douthat on his previous two columns. Where in writing the Theism... piece I was actually grateful to Douthat for stimulating my own thinking, now I'm angry at him for what seems to me his closed mind. The reader might ask whether its me, or him, or the times in which we live, or that Conservative columnists who write for the NY Times and who are not named Safire eventually get fed up with the hand they are playing.  I don't know which is the best explanation or if those should be taken in some combination.  I do think in playing that hand the Conservative columnists should aim for an interior solution, to give us readers something we can react to - thoughtfully.  These last two columns seem to me to provide corner solutions.  While I will try to walk them back below, I'm still angry about what was said in them.

* * * * *

Douthat's column from May 3 is entitled College, The Great Unequalizer.  Most of the column is spent on the the book, Paying for the Party: How College Maintains Inequality.  Douthat accepts the hypothesis of the book without equivocation.   There is a kind of social crowding out.  The rich kids, the ones headed to the fraternities and the sororities after the freshman year, set the tone.  They party in the bacchanal way depicted in Animal House.  They study not much at all.  But they get through and then because of family connections find good jobs afterwards.  The working class kids, for whom college should offer a step up from where their parents are in the income distribution, have to do likewise, if they are to have any social life at all.  But because they work a part time job, they too get through where they really should be aiming to excel in the schoolwork, because they don't have the family connections and need a superior resume to get a good job.  Instead, many graduate saddled with debt and with limited job opportunities.

Ultimately, Douthat embraces the message of Paying for the Party because it serves his own need to moralize about what college kids should be doing.   In his penultimate paragraph he writes:

By this I mean that an upper class that practices and models bourgeois virtues — not only thrift and diligence but chastity and sobriety — will be more permeable, less self-protected and self-perpetuating, than an upper class that tells the aspirational that they can’t climb the ladder unless they join the party first.

If I weren't a college professor, I might let this slide.  Earlier in the year The Atlantic featured this piece The Dark Power of Fraternities, which is a compelling if disheartening read, and which set the stage for Paying for the Party and Douthat's column.  But I am a college professor.   I taught a class last fall that had several working class students of a total population of 23.  (I know this from what they wrote in their blog posts and from talking with some of them face to face.)  And what I was hearing from them didn't exactly jive with the message in Paying for the Party.  So here is a different angle to get at these issues.

First, look at some statistics about how prevalent Greek Life is on Campus.  At Illinois (my campus) the Dean of Students maintains a Web site about Greek Life.  It reports that about 23% of the undergraduate population are members of a Greek house and a bit more than a third of this population reside in a fraternity or sorority.  Wondering whether Illinois was typical or an outlier in this regard, I also checked Michigan.  There 20.09% are members of a Greek house.  (There is a typo on that page, reporting the percentage as 120.09%, but I ran the numbers through a calculator to get at the right percentage.)  I also looked at Wisconsin.  I didn't find a Greek Life statistics page such as the ones at Illinois and at Michigan, but I did find this Student Life page and it reports about ten percent of the students are members of the Greek House.  This is a small sample of universities, but they are each prominent Big Ten Schools, the type of university Douthat is writing about.  And the reality is that the vast majority of students are not in the Greek system at all.  So either most of those non-members find their social lives at Greek parties, or the story is more complicated at these campuses than what is depicted in Paying for the Party.

Next I want to talk about what I learned from mentoring an I-Promise student a couple of years ago.  He was a transfer student, starting his junior year at Illinois.  He lived in a dorm that year, as way to get acclimated to campus.  Most if not all of the students on his floor in the dorm were freshman.  I believe the floor itself had a single long corridor with the rooms (doubles) on one side or the other and the bathroom and shower located somewhere in the middle of the floor.  Perhaps there was a lounge on the floor as well, though of that I'm not sure. The custom was for the doors to the rooms to be open when they were occupied, so somebody else on the floor could just come in, which they would do mainly to socialize.  The kids were up to the wee hours of the morning - every night, not just on the weekend.  And they were engaged in some sort of having fun.  My mentee wasn't getting enough sleep as a result and he needed to find another place, the Library for example, if he was going to study.  His big issue was time management coupled with location management.  I think this is common for students in their first year on campus.

I don't think drinking was part of this picture, though I don't really know.  But what seems evident is that the kids on the dorm floor wanted to play.  They had their new found freedom from not living at home and that's how they wanted to spend their timeIt might not be the choice each kid would have made if left on his own, but the group dynamic of the dorm floor inevitably led in that direction.  I should add that this dorm, close to the Engineering Quad, probably had a majority of students who were in Engineering, which is known to be demanding academically.  If this was happening there I suspect something similar is happening all around campus.  It may not be too many steps from wanting to play - video games or card games or some other diversion during the nighttime hours coupled with some sports activity or working out in the late afternoon - to wild parties at a Greek house with lots of booze and sex.  But they are not one and the same. So one wants to know whether the kid, in moving from the dorm to an apartment, finds a better balance between the academic side and having fun or if the lure of excessive drinking is too hard to resist. If enough kids do the former, then the social crowding out that is the story in Paying for the Party overstates the case.

The last bit I want to discuss comes from what I learned in this domain when I taught an upper level course on Behavioral Economics in spring 2011.  Many of the students had an extremely instrumental view about employment.  For these students the entire goal was to make money.  There was no larger sense of purpose nor any recognition that work might be a path to find self-expression.  I want to try to tie this observation into the excessive indulgence that is at the center of Paying for the Party and The Dark Power of Fraternities.

There seems to me three possible explanations that drive undergraduates toward excessive consumption of alcohol and all the rest that goes with it.  One is satisfying curiosity.  Another is running away from responsibility: the academic side of school offers punishment in the form of looking stupid in front of one's teachers and classmates or cowering into anonymity to avoid the more overt form.  This is the escapism explanation.  The third is running toward fun - the adult form.  At root here is a very hedonistic view of life.  Pleasure comes from having candy.  All that changes in going from being a kid to being an adult is the type of candy that gives pleasure.

To the extent that curiosity is the explanation, there is little that a university can do other than to educate students about possible risks and encourage the students not to go over the deep end as they experiment.  The students do have the agency to satisfy their own curiosity.  We should acknowledge that and consider it a good and healthy thing, even if there is occasional abuse.  Experimentation is the way students learn a more mature approach to life.  That learning should be encouraged, not blocked.

It is on the other two possible explanations that we should focus.  They offer a potential area where Conservatives and Liberals might agree.  If either of these explanations is right, it shows that college is failing on the academic side, by not encouraging students to open up about their own thinking and in not getting students to ask the meaning of life questions that has been a traditional role of a residential college experience.  Viewed this way, Douthat's call for abstinence is treating the symptoms, not the cause.  What is needed, instead, is a program that takes on the cause squarely. 

* * * * *

Let us switch to Rape and the College Brand, Douthat's most recent column.   Douthat is even more irate here.  He writes:

Such arguments add up to a plausible case against some of the activists’ prescriptions. But they don’t inspire much sympathy for the colleges’ position in this controversy. The protesting students may be overzealous and unduly ideological, but when you’re running an essentially corrupt institution, sometimes that’s the kind of opposition you deserve.

Corruption is a strong word, but not, I think, unmerited. Over the last few generations, America’s most prominent universities — both public and private — have pursued a strategy of corporate expansion, furious status competition, and moral and pedagogical retreat. But the moral retreat has in certain ways been disguised: elite schools have abandoned any explicit role in policing the choices and shaping the character of their students, but they have masked that abdication in the nostrums of contemporary P.C. piety — promising diversity, tolerance, safe spaces, etc., with what can feel like a preacher’s sincerity and self-righteousness.

This is an extraordinarily sweeping indictment.  One issue in reading it is to identify the "you" in whom Douthat is referring to when he talks about running the institution.  Is he talking about the faculty?  There is faculty governance, an important piece in how things gets done, and typically a very conservative factor.  Or is he talking only about the administration?  Does Douthat understand that major public universities are very complex organisms with distributed decision making power and where it may not be so easy for an outsider to identify where particular decisions are made.

Much of the administration is made up of former faculty, who have then "risen" to perform administrative function.  If the faculty themselves are absolved from the charge of corruption, is it then reasonable to assume that all moral backbone becomes lost when the person turns to administrative work?

One area where the administrators are not former faculty is campus legal.  When I was doing my campus educational technology job I interacted with campus legal on a somewhat regular basis.  My biggest source of frustration there is that I tried to get a clear statement of where the campus agreed a certain behavior with online materials constituted a "Fair Use" and thereby gave the faculty guidelines on how to proceed with materials in teaching their courses.  I could never get this done.  Campus legal did not want to risk the potential liability from drawing a line in the Fair Use gray-zone. That there is much non-action at universities because of a desire to limit liability is something insiders will understand, if not embrace.  It may not be something that occurs to outsiders at all.  The point here is that the decision making may never get outside of campus legal to where faculty governance has a go at it or where the Provost or Chancellor (the top academic officials on campus) weigh in.  I don't know that to be the case in the campus response to sexual assault.  But I wouldn't be surprised to find out that it is true.

Poor management is not the same as corruption.  That universities are reactive to a variety of social issues instead of getting out in front of them goes without say.  But instead of asking how university decision making might be more streamlined to address the issues it confronts, Douthat feels the need to play the corruption card, using the old Conservative critique on political correctness, and generally smear institutions of higher education.  Is that what thoughtful critics should do? 

* * * * *

I apologize that this post is such a long slug to get through.  I felt it necessary to illustrate the problem with corner solutions.  Such "answers" tend to block more reasonable analysis and don't show us a better way out.

As regular readers of my blog know, I am no fan of the status quo on campus, particularly to how we go about undergraduate education.  I would welcome constructive criticism from the outside, if it helped to spur change that really did make things better.  But after some time waiting for that, we get impatient and are driven to want purist answers.  They really aren't answers at all.  All they do is satisfy a need to vent on the issues.

Columnists for the NY Times should not do that.  You'd think their editors would admonish them when they do.  I hope Douthat's last couple of pieces represent only a temporary misstep.  I would prefer not to go cold turkey on him too, as that would further presage my own slide to the corner, something I'd like to avoid, if possible.

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