Marriage Buffet: A Solution in Search of a Problem

I generally prefer to steer clear of social issues here, especially as a mathematical perspective does not often add illumination to them. Discussions of same sex marriage, however, always lead to the question: what harm does it cause? The answer I most often hear is that legalizing marriage between same sex couples will degrade the institution of heterosexual marriage. My attempts to analyze this answer thus far leads only to the creation of spherical horses.

In order to understand the threat to marriage posed by a government action, we first must consider marriage's relation to the government. Libertarians often argue that government should play no role in matters as inherently personal as love and marriage. A natural libertarian position might then be that the government should recognize no marriage - heterosexual or straight. In fact, libertarians often argue that marriage should exist solely as a religious sacrament. I think this argument is attractive on the surface, but fundamentally incorrect.

Every libertarian I have read asserts that government should protect citizens' property rights. Consequently, the government must prevent fraud and help enforce contracts. From my perspective, the most important contract most people enter into is the marriage contract. Unfortunately, the terms and conditions of the contract have become so weak and vague that it is now essentially ceremonial. Question: does this loss of a clear marriage contract fundamentally degrade the institution of marriage? One way to approach this question is to ask what form an optimal marriage contract should take. What sanction does our society impose - what sanction should it impose - on the man who blithely discards his wife of twenty years and three children, replacing her with a younger lady who catches his eye? Should inability to conceive or bear children constitute grounds for dissolution of a marriage? I don't pretend to have answers for such questions and doubt a satisfactory single answer exists in our pluralistic society, but if a couple is be able to agree to the answer before they wed, then why shouldn't the government help enforce that contract like any other? Of course prenuptial agreements exist, but are generally considered distinct from the marriage contract. Perhaps the Catholic and Presbyterian churches should each offer their own approved marriage contract. Perhaps the Sierra Club and National Public Radio could offer their own approved standard marriage contracts too, each with its own list of duties, grounds for dissolution, and penalties for violation. If corporate America can impose noncompete contracts, why can't similar terms be included in a marriage contract: if you leave without grounds, you can't remarry for n years. The possibilities are endless and entertaining to contemplate.

Unfortunately, I do not see what current difficulty such a buffet of personalized choices remedies. I suppose that many engagements would terminate short of marriage when the loving couple is unable to agree on what type of marriage they are entering. When I began toying with the idea of more specific and varied marital contracts, I was thinking of the negative effects of the current very loose divorce laws. However, I'm not sure I would want my spouse to remain with me out of fear of contractual penalties rather than from delight in our mutual companionship. (Of course, someone else may feel differently, in which case the lack of resonance of the idea with my personal situation actually supports the argument for more species of marriage.)

So, I haven't managed to shed any light on any of the questions raised. Classes have begun here. Perhaps I will have to wait until the next class break to actually solve any (nonmathematical) problems.

Extracting Splinters or No Mathematician Need Apply

For the second time in my life I have been asked to leave a volunteer organization. Ouch. The chairman of our local GOP splinter group, the NXC GOP, has requested that I never again attend one of their meetings. This has been the occasion of much hilarity at home and in my county GOP organization.

The first time I was evicted from a political organization, I was a young assistant professor in my first tenure track faculty position. I joined a group of conservative faculty members who met regularly to discuss politics. The leader of the group was a chain smoking Polish emigre professor, who was obsessed with communism and the USSR. We met in his house just a few blocks from campus, its walls yellowed by the never ending plumes of smoke rising from his cigarettes. I was as happy to discuss the USSR as the next person, but it was not my sole interest in life. I pushed to broaden our discussion and activism (in this group, I recall the activism never graduated beyond tongue wagging) to include other issues. In particular, I broached the issue of educational vouchers. Professor Chimney was initially casually dismissive of my suggestion but was subsequently shocked to see that most of the group expressed interest. At the meeting he suggested I research vouchers and lead a discussion at our next meeting. A few days later he called me up and said he did not want 'country club' Republicans like me at his meetings and invited me to leave his group, which I did. Never before or since have I heard the claim that interest in educational vouchers was a defining feature of 'country club' Republicans. Nonetheless, as the group never actually did anything other than talk, I did not mind my forced exit.

Two decades later I have been dismissed from another political group. I have been attending meetings of the Northern X County GOP (NXC GOP). The chairwoman of the NXC GOP is a former campaign director for the loser in the GOP congressional primary in my district. As I have written before, her candidate was an unappealing nativist whose possible nomination I considered harmful to the local GOP. I believe that her goal is to create an organization which can rapidly transform into a campaign organization for him should the current GOP nominee lose. She is hostile to efforts to aid the duly nominated candidate and always structures the NXCGOP's efforts so that they exclude our congressional candidate. With less than a month and a half left before the election, her agenda for our last meeting was the recruitment of candidates for the 2011 municipal elections. (She had neglected to observe that half her membership did not even live in the city limits and therefore could not even vote in the municipal elections.) I have been attending these meetings with the goal of keeping the group in the GOP camp. I frequently announce opportunities for its members to participate in canvassing and other services for our duly nominated candidates. I did not believe the chair wished to make her hostility to the nominated congressional candidate explicit to the group's members, who are not generally partisans for the loser. This left me with room to promote our nominee. Last Thursday, I apparently exhausted her patience. At the beginning of the meeting, I observed that I had not seen many members of the group canvassing on Saturday mornings. The room turned to ice, but little more was said on the subject, except for the reasonable observation that many of the members were working on other campaigns (but for 2012?). I thought no more of it until the next morning when I received an email :

Thank You for showing an interest in our organization. Regretfully, you and the
NXC GOP are not a good fit. We respectfully request that you not
attend any future NXC GOP meetings.

Oh well, at least she didn't accuse me of being 'country club'. My family and the county GOP have been ribbing me ever since. My family observes that I am the only one they know who was threatened with violence by a high school teacher after disagreeing with him on a school advisory committee. So, perhaps my willingness to disagree with people (endemic in the mathematics community) also played a role in my latest expulsion. Luckily, I can counter with the observation that I was not expelled until I brought my wife to a meeting. (She attended her first NXC GOP meeting last Thursday). Perhaps her attendance precipitated my forced departure. She has agreed to test this hypothesis if the county organization gives me too many assignments. If I become overburdened, she has offered to attend her first county meeting and see if this leads to expulsion number 3.

Walking the Streets: First Time Canvassing

The last two Saturday mornings I have been walking the streets of my precinct with lists of Republican voters with a history of skipping midterm elections. My assigned task is to ring doorbells and encourage the targeted voter to pledge to vote early; secondarily, I provide information about our congressional candidate. The goal of early voting is simple. During the early voting period, the GOP congressional campaign checks its list of each day's voters against its list of all GOP voters, especially pledged early voters. Volunteers then email or call to harass pledged voters who are procrastinating. The more voters who vote before election day, the easier the Get Out The Vote effort on November 2nd.

My first time out, approximately half of the voters I visited answered their doors. I assume many more were there but did not answer a stranger ringing their doorbell. I often refuse to open for visitors bearing clipboards; so, I can't fault others for ignoring me. I decided it was a bad idea to ring twice after this produced a few women not yet dressed for the day and obviously annoyed at being pulled to the door dishabille. I won no new voters at those houses. Those who did answer their doors (on the first ring) were almost uniformly enthusiastic. They pledged to support the GOP candidate. They pledged to vote early. When probed, however, they were unable to identify their polling sites; so, subsequent monitoring appears to be desirable. The exception to the enthusiasts were the Democrats who had moved into the houses of some Republicans on our lists. Of course, I didn't encourage them to vote early (or at all). They were all polite, however, and did not harass the poor volunteer.

The next Saturday I hit the streets again. The targeted neighborhood looked economically depressed compared to the previous week's walk. This time very few doors opened, and nobody pledged to vote early. Most had never even heard the name of our congressional candidate. I have no idea whether the difference between week one and week two was random, a function of the calendar, or a function of socioeconomic differences. I'll collect a few more data points in the coming weeks before I offer an opinion. Like the previous week, everyone was polite, including the Democrats living in former Republican houses. I had a few amusing interactions. At one house, I asked if Mrs. Jone's lived there. The woman who answered the door thought for a minute and then said, 'No, I don't think so - not really.' I wondered what partial state of residence could make the question subject to internal debate. At another house, I asked the elderly grey haired woman who answered the door if she was Jane Smith. She said no, and then called: 'Momma. There's someone here to see you.' Henceforth I'll reserve 'elderly' for the white haired. At the last house on my list, the door was answered by a portly bare chested (and bellied) man, who told me his wife was a Republican, but he was registered as a Democrat. He said, 'I'm actually a Republican, but have to register as a Democrat for personal reasons.' In a liberal town like ours, it's easy to imagine his reasons, including a desire to prevent politics from hurting his business prospects. Perhaps he contracts with the government. I didn't probe but left curious.

Unsurprisingly, my doorstep spiel became more fluent with each new house. By the time November rolls around, I will be so comfortable with cold calling strangers that I can become a vacuum salesman should I ever have to quit mathematics.

How much is a college diploma worth?

Recent weeks have produced a constant stream of articles and blog posts attacking the value of a college diploma. Given the low quality instruction my children endured at various points in their middle and high school careers, I can at least recommend many colleges as a good place to get a decent high school education. To support their assertion that college diplomas are overvalued, the blog discussions generally cite anecdotes of college graduates who are waiting tables or are otherwise underemployed. The terms of the discussion are always too vague to support a coherent argument; so, let's see if we can add clarity to the noise.

A quick internet search yields the following useful Wall Street Journal data on salaries by college major.

Undergraduate Major	Starting Median Salary	Mid-Career Median Salary		Mid-Career 10th Percentile Salary	Mid-Career 25th Percentile Salary	Mid-Career 75th Percentile Salary
Accounting	$46,000.00	$77,100.00		$42,200.00	$56,100.00	$108,000.00
Aerospace Engineering	$57,700.00	$101,000.00		$64,300.00	$82,100.00	$127,000.00
Agriculture	$42,600.00	$71,900.00		$36,300.00	$52,100.00	$96,300.00
Anthropology	$36,800.00	$61,500.00		$33,800.00	$45,500.00	$89,300.00
Architecture	$41,600.00	$76,800.00		$50,600.00	$62,200.00	$97,000.00
Art History	$35,800.00	$64,900.00		$28,800.00	$42,200.00	$87,400.00
Biology	$38,800.00	$64,800.00		$36,900.00	$47,400.00	$94,500.00
Business Management	$43,000.00	$72,100.00		$38,800.00	$51,500.00	$102,000.00
Chemical Engineering	$63,200.00	$107,000.00		$71,900.00	$87,300.00	$143,000.00
Chemistry	$42,600.00	$79,900.00		$45,300.00	$60,700.00	$108,000.00
Civil Engineering	$53,900.00	$90,500.00		$63,400.00	$75,100.00	$115,000.00
Computer Science	$55,900.00	$95,500.00		$56,000.00	$74,900.00	$122,000.00
Drama	$35,900.00	$56,900.00		$36,700.00	$41,300.00	$79,100.00
Economics	$50,100.00	$98,600.00		$50,600.00	$70,600.00	$145,000.00
Education	$34,900.00	$52,000.00		$29,300.00	$37,900.00	$73,400.00
Electrical Engineering	$60,900.00	$103,000.00		$69,300.00	$83,800.00	$130,000.00
English	$38,000.00	$64,700.00		$33,400.00	$44,800.00	$93,200.00
Film	$37,900.00	$68,500.00		$33,900.00	$45,500.00	$100,000.00
Finance	$47,900.00	$88,300.00		$47,200.00	$62,100.00	$128,000.00
Forestry	$39,100.00	$62,600.00		$41,000.00	$49,300.00	$78,200.00
Geology	$43,500.00	$79,500.00		$45,000.00	$59,600.00	$101,000.00
History	$39,200.00	$71,000.00		$37,000.00	$49,200.00	$103,000.00
Industrial Engineering	$57,700.00	$94,700.00		$57,100.00	$72,300.00	$132,000.00
Journalism	$35,600.00	$66,700.00		$38,400.00	$48,300.00	$97,700.00
Marketing	$40,800.00	$79,600.00		$42,100.00	$55,600.00	$119,000.00
Math	$45,400.00	$92,400.00		$45,200.00	$64,200.00	$128,000.00
Mechanical Engineering	$57,900.00	$93,600.00		$63,700.00	$76,200.00	$120,000.00
Music	$35,900.00	$55,000.00		$26,700.00	$40,200.00	$88,000.00
Philosophy	$39,900.00	$81,200.00		$35,500.00	$52,800.00	$127,000.00
Physics	$50,300.00	$97,300.00		$56,000.00	$74,200.00	$132,000.00
Political Science	$40,800.00	$78,200.00		$41,200.00	$55,300.00	$114,000.00
Psychology	$35,900.00	$60,400.00		$31,600.00	$42,100.00	$87,500.00
Religion	$34,100.00	$52,000.00		$29,700.00	$36,500.00	$70,900.00
Sociology	$36,500.00	$58,200.00		$30,700.00	$40,400.00	$81,200.00
Spanish	$34,000.00	$53,100.00		$31,000.00	$40,000.00	$76,800.00

One source gives the median high school salary as $32,000 for adults aged 25-34, a weak approximation to 'midcareer'. I suspect a better approximation to the Journal's midcareer category would add several thousand dollars to this.

Assuming the high school versus college data is roughly comparable, it is easy to see that for most college graduates who are now midcareer, the college degree is certainly strongly correlated with greater earning power. (Of course, we cannot exclude the possibility that for this cohort, the college degree is a proxy for a lower bound on their IQ.) With the exception of a few fields like education and religion, it should take little more than a decade or so to pay back college costs (including the cost of delaying entrance into the work force). The data becomes more interesting when we look at the bottom 10% of earners (by major) among college graduates. We see that for many majors, including Anthropology, Art History, Education, English, Film, Music, Psychology, Religion, Sociology, and Spanish, occupants of the lowest decile do not recoup the cost of the college degree.

Let's make a strong assumption that the bottom 10% of wage earners in each major are roughly the same group as the bottom 10% of students in the major (defined by some incredible nonexistent linear measure of academic ability). Of course, this assumption has terrible holes, for example, women who temporarily drop out of the workforce to raise children. Nonetheless, we will assume until otherwise informed that the correlation between poor student performance and lower subsequent wages is strong. We further assume that the majority of people who did not attend college would have been weaker students than those who did. Similar caveats obviously apply to this assumption, but I suspect it is accurate on average. We then see that the push to encourage higher rates of college attendance for students who would have been unlikely to attend otherwise, is likely to lead to poor economic results for the majority of those new students, if they major in the Arts or Humanities. On the other hand, the above data is brighter for those who choose to major in Engineering, Math, Physics, and Economics. Even the 10th percentile of earners with degrees in these majors have room to recoup the costs of college. So, if one discovers a subset of students who have strong mathematical skills but would not traditionally attend college, then perhaps they should be encouraged to attend. Otherwise, the push to continue to enlarge the population of college students does not appear likely to be economically rewarding for lower performing students.

We see that the loud corner of the blogosphere that asserts that a college degree has lost its value is obscuring the main issue. A college degree in many fields is strongly correlated with subsequent higher earnings, but our above commonsense (but unproven) assumptions suggest that the more precise statement is: for good students a college degree in many fields is likely to lead to higher earnings. For weaker students, it is likely to be a money pit.

Crypto Conservatives?

Do conservative faculty on liberal campuses have an obligation to fight the campus left? I have always been extremely vocal in matters of departmental policy, but as noted in a comment on one of my posts, I have, at times, held back in matters concerning the larger university. Is restraint judicious or cowardly?

The argument against restraint is simple. If conservatives do not speak out on campus, the left wins every argument; at the university, the left is both numerous and outspoken.

The reasons for restraint are numerous and range from the selfish to the practical. Most of the conservatives I know in the sciences put their energy into their work - not into political battles. Not everyone is willing to devote time and resources to political battles that do not affect them directly. In the sciences, I doubt that outspoken conservative politics affects promotion and tenure, but I can sympathize with the cautious junior faculty member who prefers to keep his head low before tenure.

My primary calculation when I consider addressing a worthwhile issue is: will my public position on this issue make me less effective in dealing with future issues of greater importance? This is a tricky calculation, which leaves room for never ending postponement and avoidance. To illuminate components of the calculation, I recall a formative period from my early faculty days. In the late '80's, the National Association of Scholars (NAS) appeared on many campuses. At that time the NAS was opposed to trivialized curricula, restrictive speech codes, post-modernist humanities scholarship, and similar anti-intellectual university trends. Not long after the NAS appeared, prominent humanities professors at major universities demanded that their university administrations adopt policies prohibiting members of the NAS from serving on any university governing committee. I never heard of any university publicly adopting such a policy, but the threat was clear: publicly endorse conservative positions and be branded a whacko unfit for positions of responsibility.

My response to this threat has been twofold. Sometimes I simply chose not to fight a battle that I had no hope of winning. I don't stand in front of a train. When I choose to fight, I fight on narrow grounds rather than in the context of broader conservative vs. leftist ideological battles. For example, recently, my university surreptitiously changed the selection criteria for one of our primary merit scholarships, reducing the emphasis on raw academic talent in favor of greater attention to community service and similar drivel. The justification was the standard social engineering blather. I (with allies) successfully argued for the reversal of this sacrifice of academic standards. We did not argue on ideological grounds but instead argued in terms of the negative effects on the recruitment of potential undergraduate stars for our science program. Opposition on such practical (and self interested) grounds does not generate the heat that ideological opposition does, and is therefore more successful.

The preceding paragraphs may suggest that the conservative faculty member frequently faces ideological battles on campus, but I have not found this to be the case. For those of us not frequently involved in broader university governance (and with our heads in our books), these issues arise infrequently. None the less, I assume that all conservative faculty face them occasionally and are then faced with the choice: fight today or postpone the fight for the future.

Politics and the Fields Medal

Last week, quite a few visitors came to my blog via a mathematical/political discussion on the website, conservapedia, with which I was unacquainted. As I am otherwise uninspired this week, I will make a few comments on the subject of their discussion: the influence of politics on the awarding of the Fields Medal.

The Fields Medal is often likened to the Nobel Prize. It is a prize awarded every four years to four or fewer mathematicians for outstanding contributions to mathematics. The (perhaps apocryphal) story told by mathematicians is that Swedish mathematician Mittag-Leffler had stolen Alfred Nobel's lover. When establishing his award, Nobel asked prominent mathematicians who would be the likely recipient of the first Nobel Prize in Mathematics. When told that Mittag-Leffler was a leading candidate, Nobel decided there would be no Nobel Prize in Mathematics. Nobel never did marry, and he never endowed a prize in mathematics. Mathematicians all believe this story because they are keenly aware that nothing attracts the opposite sex like mathematical expertise. John Fields subsequently established his prize to correct this unfortunate state of affairs.

The question raised on the above mentioned political site was: what role does politics play in the selection of the Fields Medalist? We are all keenly aware of the role of politics in awarding the Nobel Peace Prize to such great humanitarians as Yasser Arafat and Al Gore. Moreover, many mathematicians and physicists have suggested to me that politics plays a strong role in the selection of MacArthur Prize winners. Does politics play a similar role in selection of the Fields Medalists?

I have never seen evidence of nor heard any mathematician voice suspicion of statist versus individualist, left versus right, etc. politics in the selection of the Fields Medalists. (The location of the award ceremony, however, is a different story). There is, however, no abstract linear ordering of mathematical achievement. Some work is so spectacular that there is no question that it merits a Fields Medal. In other cases, choices have to be made among several excellent candidates. I have heard complaints from mathematicians working in fields whose practitioners have rarely been recognized with Fields Medals. They note that the prize committee is dominated by mathematicians in fields X,Y, and Z, and that fields X,Y, and Z receive most of the prizes. If these fields are the most important and the most active, then it is natural and appropriate that they dominate both committee and prize, but who decides that this is the case? Various committees have to make these decisions, and we should not be surprised to learn that there is lobbying for various fields of mathematics to be given greater consideration. I do not consider recognition of the existence of such politics to be a criticism. It is simply the observation, once again, that mathematics is a human enterprise and therefore subject to the dynamics of human interaction.

Spontaneous Order vs Locality and some inane analogies

As I continue my bedtime reading in political science (currently Boaz's The Libertarian Reader), I keep returning to the steepest descent metaphor for economic systems. I want to revisit this analogy to explore its different facets.

First, recall the concept of spontaneous order, associated with the Austrian School of Economics. Spontaneous order refers to the development of complex social and economic relations arising, not from a guiding intelligence, but from the separate actions of many individuals acting in their own self interest. In mathematics and physics, we frequently see similar phenomena: a system's dynamics are dictated by some energy functional. The system evolves in such a way as to minimize the energy. For the analogy to be apt, however, we do not consider arbitrary energy functionals. We consider only those which are defined by summing (integrating) a local energy. By 'local', I mean that the energy contribution at each point is computed from information that can be measured near that point (e.g. slopes). Then the energy minimizing dynamics at each point require information available at that point, and not global information. A mathematician can construct physically unreasonable systems which do not possess this locality property. Then the analogy with spontaneous order breaks down. So, the relevant correspondence here is

spontaneous order <-> locality of energy.

Viewed as the dynamics of a system determined by a local energy, the emergence of spontaneous order is essentially tautological. To recast it as a nontrivial statement, you need to turn it into the assertion that the socioeconomic dynamics are determined by a local energy. Then the emergence of spontaneous order follows from hypotheses such as the absence of a strong central government. Extracting political implications requires an assertion that a local energy functional is better than a nonlocal one, the latter being the natural model for a socioeconomic arrangement based on a guiding state or elite. This returns one to the perpetual conflict between small government conservatives and statists: should individuals or a governing elite determine the choice of energy functional (and thus definition of optimal state) for the society? Should individual happiness or the progress of the collective be regarded as the greater good?

Now we pause to enjoy cheap analogies. In partial differential equations class, we study the most fundamental and ubiquitous energy functional: the local energy of a function f defined on some region M and taking values in some constraint space N is defined to be the square of its derivative, |df|^2 (simply a measure of steepness of slope). If the accessible values, N, are completely unconstrained, then the system evolves to a utopian state where every point has the same value - the resources are equally distributed. When there are constraints on values, however, the dynamics are very complicated. Consider a utopia where every member of M is exactly the same; geometrically we model such a system by assuming M is a sphere (we require it to be a compact connected manifold). If we assume N is a finite size constraint space (a compact manifold), then the dynamics are unstable. Generically, one can always lower the total energy by concentrating all the energy (resources) at a single point. So for my all time cheapest mathematical analogy, we find generically that a completely homogeneous society evolves to one where a single member controls all the resources. Fortunately (think Stalin) these dynamics do not lead to stable equilibria.


Jumping from a cheap analogy to one that I find more instructive, I pass to the numerical approximation of the preceding dynamics. If you wish to model these dynamics on a computer, you have to approximate the infinite number of points on your space M by some finite grid, use the grid to compute approximate energies, and from this data, compute an approximate flow. The finer your grid, the better your approximation is to the optimal energy minimizing flow. The longer you run your approximation, the more you deviate from the optimal dynamics. When designing and executing statist policies, the government divides the population into categories, creating a coarse grid. If we assumed, counterfactually, that Congress understood economics, then we could pretend that it could compute an approximate energy for this grid and a consequent approximate energy minimizing flow. Passage to a grid, however, still entails a loss of data; hence, the approximation deviates from the optimal flow, and the deviation increases the longer the statist policies run, rendering the society ever less prosperous than its optimal state. The primary weakness of this analogy is the pretense that Congress actually includes economic analysis into its policy. With our current Congress, one can discard this pretty dynamics picture, replacing it with a discussion of the downside of pouring sugar into your gas tank.