More Operations Research in the News, but not in a Welcome Way

Fabrice Tourre, “the fabulous Fab”, who is at the center of the Goldman Sachs scandal, is a 2001 graduate of Stanford University. That, in itself, is no surprise. Stanford has a top ranked business school that does about as well as the rest of us in graduating ethical MBAs (by that I mean MBAs who do, on the whole, try to act ethically, but some of whom find ethical challenges … challenging), so it is not surprising that a powerful Goldman Sachs person would come from there. But what is surprising is that Fabrice’s Stanford degree is a Masters in Operations Research! Our field is in the news!

Thinking about it, it is not so surprising. Since Fabrice is reported to be 31, a 2001 graduate would have been 22. Most business schools like to see at least a little work experience, so 22 year-olds with an MBA would be quite unusual. A Masters in Operations Research would be more common, I would think.

I can’t tell if the fabulous Fab did anything wrong, let alone illegal, but this does bring up an issue in training. At business schools, we are working hard to think about how to include ethics and other aspects of corporate social responsibility into the curriculum (with varying levels of success). What are operations research programs doing to ensure that their masters graduates are aware of the choices they make? Checking Georgia Tech, Michigan, Stanford Management Science and Engineering (is there still an MSOR from Stanford?), and Cornell (not to pick on them, but to pick a few of the best programs out there), does not lead one to believe that ethics, corporate responsibility or a traditional “engineering professional responsibility” course is part of the masters curriculum.  This is not to suggest that we are putting out a generation of unethical lying optimizers, but perhaps we should rethink the balance of our programs.  I do believe operations research to be outstanding training for a wide variety of careers:  going beyond linear and integer programming into some of the challenges of the real world would be a good direction to go for the sake of the students, and for the rest of us.

Conditional Probability in the New York Times

When you ask a question of the form “What are the chances of X given Y”, your are asking a question of conditional probability. These sorts of questions have come up in this blog before: “What are the chances of cancer given a positive test result?” “What are the chances a monkey prefers blue M&Ms to green M&Ms, given it prefers red M&Ms to blue M&Ms?” “What are the chances of predicting the NCAA tournament perfectly, given perfect predictions for the first two rounds?”

Conditional probability is extremely important for two reasons. First, it occurs all the time: it is a fundamental building block as we aggregate information in an uncertain environment. Second, people are really, really bad at it. In case after case, our intuition misleads us and we badly misestimate conditional probabilities. When a 90% accurate drug test (meaning it is positive 90% of the time for a drug user, and negative 90% of the time for a nonuser) comes back positive, what is the probability the person uses drugs. Our intuition screams “It has to be 90%”! But the probability of “User given positive drug test” is not the same as probability of “positive drug test given user”. If 5% of the population use drugs, then the probability of “User given positive drug test is about 1 in 3. Consider 1000 people: 50 are drug users so 45 will test positive; of the 950 non-users, 95 will test positive; so 45/(45+95) is the probability of user given positive test.

Note that in the argument above, I did not rely on the main theorem in conditional probability: Bayes Theorem. Bayes Theorem states P(A|B) (the probability of A given B) = P(B|A)P(A)/P(B). I could have worked it out that way, but in doing so I would have lost all intuition as to the result. For simple cases, the counting approach is much easier and shows why the result is what it is.

This argument is at the heart of Steven Stogatz’s excellent article “Chances Are”, online at the New York Times (thanks for the pointer, Matt). He gives some excellent examples of conditional probability, including a great riff on the O.J. Simpson murder trial.

The prosecution spent the first 10 days of the trial introducing evidence that O.J. had a history of violence toward his ex-wife, Nicole. He had allegedly battered her, thrown her against walls and groped her in public, telling onlookers, “This belongs to me.” But what did any of this have to do with a murder trial? The prosecution’s argument was that a pattern of spousal abuse reflected a motive to kill. As one of the prosecutors put it, “A slap is a prelude to homicide.”

Alan Dershowitz countered for the defense, arguing that if even the allegations of domestic violence were true, they were irrelevant and should therefore be inadmissible. He later wrote, “We knew we could prove, if we had to, that an infinitesimal percentage — certainly fewer than 1 of 2,500 — of men who slap or beat their domestic partners go on to murder them.”

In effect, both sides were asking the jury to consider the probability that a man murdered his ex-wife, given that he previously battered her. But as the statistician I. J. Good pointed out, that’s not the right number to look at.

The real question is: What’s the probability that a man murdered his ex-wife, given that he previously battered her and she was murdered by someone? That conditional probability turns out to be very far from 1 in 2,500.

Turns out that probability is about 90%.

We are in the midst of a curriculum review at the Tepper School of Business and are considering what we absolutely have to be sure our MBAs know. Being able to work with conditional probability is very high on my list: it is an area where your intuition will almost surely lead you astray. And, as the Strogatz article points out, while Bayes Rule may get you the right results, simple counting arguments are much more convincing.

What is Operations Research?

Over on the suddenly active OR-Exchange, David Woods asked the question:

What are the best quick definitions describing operations research? The kind that you’d give to someone if you only had the duration of an elevator ride to describe it…

David then goes on to answer his question with a fantastic answer:

“Operations research is the art and science of obtaining bad answers to questions to which otherwise worse answers would be given.”

I love that! But I’m not sure that outsiders will really get it. Paraphrasing Steve Martin, “I stopped using irony when I realized I was the only one using it.”

So I’m left with “Operations Research is about making better decisions through mathematical models. Say, are you a baseball fan?” where I hope to squeeze in a story about operations research and sports scheduling. I’m hoping for a better line through the answers at OR-Exchange.

New Optimization Software Version: Gurobi

The INFORMS Practice Meeting has become a good place for optimization software firms to announce their new versions. Gurobi is first off the mark with an announcement of version 3.0. New aspects include better use of multiple cores in the barrier solver and what looks to be significant improvements to the mixed integer programming solver. Quadratic programming will wait for version 4.0, with an expected release in November, 2010.

Future plans include second order cone programming (SOCP), including a mixed integer version. I really think I should know more about SOCP, but it doesn’t seem to fit with me: I see mixed integer linear programs everywhere I look, but never say “Wow, now there is a SOCP”. Perhaps I’ll start seeing them in time for the Gurobi release a couple of versions down the road.

Follow INFORMS Practice from your Own Home

Sadly, I’m not at INFORMS Practice, but the blog entries and tweets make me feel like I am there (or perhaps they remind me I am not). Lots of interesting things happening and the conference hasn’t even started yet! Coming up shortly: the technology workshops, followed by the Welcome Reception tonight. I’ve got the tweets in my sidebar, and highly recommend following the conference page for the blog entries.

Authorship Order

Michael Mitzenmacher, in his excellent blog, My Biased Coin, has recent entries (here, here and here) on the order of authors on joint papers. When you have a last name that begins “Tri…”, it becomes pretty clear early on that alphabetical order is not going to result in a lot of “first author” papers. And it does tick me off when my work in voting theory becomes “Bartholdi et al.” or my work on the Traveling Tournament Problem is “Easton et al.”. I have even seen “Easton, Nemhauser, et al.” which is really hitting below the belt (since it is Easton, Nemhauser, and Trick).

Despite that, all of my papers have gone with alphabetical order, and I am glad I (and my coauthors) went that route. If even once I had gone with “order of contribution”, all of my papers would have been tainted with the thought “Trick is listed third: I guess he didn’t do as much as the others”.

The issue of determining “order of contribution” is a thorny one. There tend to be many skills that go into a paper, and we know from social choice how difficult it is to aggregate multiple orders into a single ordering. Different weighting of the skills leads to different orderings, and there is no clear way to choose the weighting of the skills. Even with the weighting, determining the ordering of any particular aspect of the paper is often not obvious. When doing a computational test, does “running the code” and “tabulating the results” mean more than “designing the experiment” or “determining the instances”? I don’t think hours spent is a particularly good measure (“Hey, I can be more inefficient than you!”) but there is practically nothing else that can be objectively measured.

Further, most papers rely on the mix of skills in order to be publishable. This reminds me of an activity I undertook when I was eight or so. I had a sheet of paper and I went around surveying anyone around on what was more important: “the brain, the heart, or the lungs” (anyone with a five-year-old kid will recognize a real-life version of “Sid the Science Kid” and, yes, I was a very annoying kid, thanks for asking). My father spent time explaining to me the importance of systems, and how there is no “most important” in any system that relies on the others. I would like to say that this early lesson in “systems” inspired me to make operations research my field of study, but I believe I actually browbeat him until he gave up and said “gall bladder” in order to get rid of me. But the lesson did stay with me (thanks, Dad!), and perhaps I was more careful about thinking about systems after that.

Some of the arguments over order strike me as “heart versus lungs” issues: neither can survive without the other. So, if a person has done enough work that the paper would not have survived without them, that both makes them a coauthor, and entitles them to their place in alphabetical order.

As for the unfairness of having a last name beginning “Tri…”, perhaps we should talk to my recent coauthors: Yildiz, Yunes, and Zin.

NSF Operations Research Position open

The National Science Foundation is looking for a program director for operations research. I wrote about this position the last time it came open, when Robert Smith became director.

The NSF is incredibly important to the health of the field of operations research. In addition to the “regular” grant activities (CAREER grants and basic research grants), the program director has the opportunity to make the case for having OR as part of interdisciplinary and exploratory research directions. I hope someone good finds this an interesting opportunity. Robert Sloan has an interesting article on the joys of being a program director in computer science.

Doing Good with Good OR, 2010 edition

INFORMS is again sponsoring a student project prize on the theme “Doing Good with Good OR”:

Doing Good with Good OR-Student Competition is held each year to identify and honor outstanding projects in the field of operations research and the management sciences conducted by a student or student group that have a significant societal impact.

The projects must have, or are likely to have, a significant societal impact, and operations research and management science methods and tools (broadly interpreted) must be central to the success of the projects described. “Societal impact” should be construed to mean an impact on individuals, communities and organizations that goes beyond that associated with a private-sector for-profit initiative. The projects might also strive to include innovation through theory, creative computational methods, and should address implementation challenges.

Last year, David Hutton of Stanford won the award for work on screening Hepatitis B.

The submission deadline for this year’s award is May 15, 2010.