Nobel Prizes, Stable Matching, The Secondary One Posting Exercise, Truthfulness and Student Welfare

Posted on my other website: The implications of the theory behind the recent Nobel prize in economics on how we post students in the pose-PsLE Secondary One Posting Exercise.

Gaming the System? When You Have a Policy Based What You Think is an Ingenious Quantitative Formula, Please Think it Through

Remarks on policy making with quantitative metrics and real incentives on my new website. A lot of analysis is needed on the behavioural incentives at work before committing to a policy. Examples include a gamed public tender in the Netherlands, housing grants and subsidized rental rates.

Learning Business from Games: Inventory Management, and Competing on Price and Quality

A post on learning business from games in class at my new website.

Snippet:
Today we played another game in the class I am assisting with. We have played games in the past. The first one we played was a "fair" bargaining game which was rather successful. The second was a cost estimation (plus negotiation) game which, in contrast, failed horribly due to my underestimation of the required background for the successful conduct of the game (linear regression was required), so in giving a crash course on applying linear regression and helping the students, we ran out of time. Today's game, though very hastily put together, I'd rate as successful and pedagogically meaningful. The game's broad objectives are to expose students to the strategic considerations when there is a coupling of investment, price competition, quality competition and inventory management. That is quite a number of dynamics at work in a game that you will find is really very simple. In what follows, I will describe the game and also provide a copy of the game's Excel spreadsheet (for recording the proceedings and doing the requisite accounting).

A Touchy Matter: PhD Students and Stipends

Here's a touchy matter. How much do you pay a PhD student? I've had work experience before embarking on my program, so I do think the "pay" is peanuts. What else could a reasonable person think? Naturally, as I was applying to a department called "Department of Decision Sciences", it would have been expected that I thought it through. And I did and I do not regret it (much). The money issue still hurts though. I'd like to address this issue briefly in the context of some good research on an analogous matter.

So how much should a PhD student be paid? I write with the assumption that PhD students are not cheap labour. I also write with the assumption that it is highly desirable, from the perspective of the institution PhD students are enrolled in, that PhD students "perform well" to boost the reputation of their school.

Clearly (to me at least) stipends should start low and increase with performance. It certainly should not start high or there will be many who would like to be eternal students (or punt "real work") will come swarming. So how might things increase? Research in contracting informs us that "first-best" outcomes in a "principal-agent R&D" scenario can be implemented using milestone payments. (And if I recall correctly, in one of the articles on the topic, the right thing happens "with probability 1" so we do not need to worry about issues of things being "implemented in Nash Equilibrium".)

So let us work with milestones. I will not talk about issues of risk aversion and paying (the students) a risk premium, and will instead be very concrete. The problem associated with paying PhD students is that their quality is observable only approximately and one cannot contract on effort, both of which combine to generate research outcomes. The intuition behind the claimed effectiveness of milestone payments is that at the achievement of each one, the level of uncertainty goes down, meaning schools need not be so hesitant about handing out rewards as they are more closely approximating "contracting on success".

The obvious milestone is passing the Qualifying Examination (and in big pharma there is FDA approval). At NUS, there is a $500 top-up to the stipend after that stage. Good. But there is nothing after that here. What about other milestones? For instance: first publication assessed by faculty to be of suitable quality, first publication in a "Tier 1" journal, thesis proposal defended, won student paper competition, etc. Prizes are something of "milestones", but with fuzzy requirements. My sense is that the right milestone-top-up structure would support good outcomes for PhD students and their host institutions.

Snippets of John Rawl's Theory of Justice

The goal of social justice is to obtain a fair division of rights, liberties, opportunities, power, income and wealth, holding clearly that an even division is neither possible nor is it likely to be fair. I hope to talk about social justice in the context of the major ideas of John Rawls in mind.

"Justice is the first virtue of social institutions, as truth is of systems of thought."
— John Rawls (A Theory of Justice)

Sadly, in a blog post, I will have no choice but to sell Rawl's methodology short. One unfairly short summary would be to ask what is fair given that one is unaware one's position in life, one's inclinations and one's talents. This is Rawl's famed "veil of ignorance". The principle that is that even if one is keen on maximizing one's welfare, one will agree on a "fair system" given that one is unaware of almost anything that might be descriptive of one's person. This is a refinement of Kant's categorical imperative which has been the subject of many a smart alecky "paradox". Rawl's method directed at building, from scratch, a social contract that is "fair". The assertion is that fair principles arise from a social contract cut in the context of a fair "initial state".

Rawls arrives at two principles for the kind of system that would arise from such an agreement: (i) "each person is to have an equal right to the most extensive basic liberty compatible with a similar liberty for others", and (ii) "social and economic inequalities are to satisfy two conditions: first, they are to be attached to offices and positions open to all under conditions of fair equality of opportunity; and second, they are to be to the greatest benefit of the least-advantaged members of society".

(On the first point, he later clarified, in a revised version of his Theory of Justice, that "liberty" itself was not the end of the scheme. This makes a lot of sense as the socially optimal system depends on the possible outcomes are realized on exiting the veil of ignorance. Thus, this theory is not a disguised attempt to justify the claim that "western" "liberal" "democracy" is the best system.)

I'd like to emphasize, once more, that Rawls posits that all the participants of the congress to determine this social contract are "rational" individuals fully aware of the possible outcomes and their relative likelihood, it is just that they do not know which outcome will occur. It might seem to some that my interpretation has hints of $(\Omega,\mathcal{F},\mathbb{P})$ and maximin. Furthermore, there is a sense in which Rawl's principles might be proven to be necessary conditions arising from some axioms on human decision making (in particular, risk aversion). After all, utility theory tells us that the payout of an asset is most beneficial if the payout occurs when one is down, like insurance. From a fair starting point, rational and well-informed negotiators who behave in the way most people are observed to behave in (risk adverse) will arrive at principles that might include: fairness of opportunity, leveling institutions (such as subsidized education, public libraries, the open source movement and Wikipedia), true meritocracy and a social safety net. If we also postulate ambiguity aversion (which is also well confirmed empirically) we end up with a large and strong middle class.

Having talked about the individual, what about relationships between people, between organizations and  between people and organizations? One thing that we can assume a priori is that we are all connected. To put things in other terms, we are all elements of the huge set of input-output relationships that is the networked economy. In fact, the economies of the world have been large networks for centuries, and only over the last century have regional components come to become increasingly interrelated. Indeed, today the economy is pervasively networked and only one who is spiritually and intellectually blind will fail to recognize that all along we have been connected. Thus, our actions affect others and that in turn affect us. A greedy business class might impoverish the next generation of workers which will lead to competency gaps and eventual failures in business. In contrast, when business leaders act with appropriate noblesse oblige, wealth for everyone grows in the long run and there is greater overall happiness (which follows from the assumption on risk averse preferences). Rawls himself writes that cooperation and fair dealing is the essence of the two principles he proposes:

"The intuitive idea is that since everyone's well-being depends upon a scheme of cooperation without which no one could have a satisfactory life, the division of advantages should be such as to draw forth the willing cooperation of everyone taking part in it, including those less well situated. Yet this can be expected only if reasonable terms are proposed."

Wise words. Cooperation and fair dealing is very much antithetical to the traditional non-cooperative zero sum war of all against all conception of business. Indeed, in cooperative game theory, it is crucial not to short change others. In non-cooperative game theory, in contrast, it is often the case that agents with low power are forced into a state where their participation constraint binds (they obtain the lowest possible benefit that keeps them in "cooperation" with the stronger agents). These statements may not be identically true, but they do capture a lot of the essence of the two paradigms of multi-agent interaction both in academic journals and the real world.

Rawl's ideas are a call for us to move towards a paradigm of cooperation and fair dealing as opposed to a world of myopic selfish individualism. Let me end by, once again, borrowing the words of Rawls:

"Justice is the first virtue of social institutions, as truth is of systems of thought. A theory however elegant and economical must be rejected or revised if it is untrue; likewise laws and institutions no matter how efficient and well-arranged must be reformed or abolished if they are unjust. Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override. For this reason justice denies that the loss of freedom for some is made right by a greater good shared by others. It does not allow that the sacrifices imposed on a few are outweighed by the larger sum of advantages enjoyed by many. Therefore in a just society the liberties of equal citizenship are taken as settled; the rights secured by justice are not subject to political bargaining or to the calculus of social interests. The only thing that permits us to acquiesce in an erroneous theory is the lack of a better one; analogously, an injustice is tolerable only when it is necessary to avoid an even greater injustice. Being first virtues of human activities, truth and justice are uncompromising."
— John Rawls, A Theory of Justice

Some Thoughts on Breadth in Education

I'd say that an education is a bundle of experiences (organically encountered or engineered) with an accompanying bundle of inferences. By "experience", I mean something sufficiently general to cover all of: contemplating social constructs, building a model aircraft, recreating the proof of a theorem and even doing unspeakable things to white mice.

What the university and school system offers in terms of the bundle of imparted data, models and frameworks seems to be, anecdotally speaking, failing to meet the needs of employers. The ones who become the best employees or have the confidence to strike out on their own turn out to be those who seek out the relevant experiences.

But students are overloaded (or so they claim). There is some need to identify what is truly "core" in each "discipline" and shave down curricula to that "core", freeing up capacity for both students and instructors for more extensive education. There will be those who insist that the elementary course on their pet sub-discipline is snugly in the core and everything within should be taught in full. There is merit in that assertion, but a little less given the growing mismatch between what the university offers and what the workplace desires. Toes will smart, but it is all for the best.