Solve for the equilibrium: Dutch higher education

1) The number of first-year students in the Netherlands has soared from 105 000 in 2000 to 135 000 in 2011. The 30% increase is a direct result of government policy which links university funding with student numbers. In some programs in the country, student numbers have more than doubled during the last five years. Everyone is encouraged to enter the university system.

2) In the general case, there is no selection at the gate. Students cannot be refused to enter a program.

3) Now, the government’s objectives are to reduce the number of first-year drop-outs  and slash the number of students who do not graduate within four years. Both objectives are being supported by financial incentives and penalties for the universities.

Something’s gotta give. I wonder what…

P.S. ‘Solve for the equilibrium’ is the title of a rubric from Marginal Revolution.

Tit-for-tat no more: new insights into the origin and evolution of cooperation

The Prisoner’s Dilemma (PD) is the paradigmatic scientific model to understand human cooperation. You would think that after several decennia of analyzing this deceivingly simple game, nothing new can be learned. Not quite. This new paper discovers a whole new class of strategies that provide a unilateral advantage to the players using them in playing the repeated version of the game. In effect, using these strategies one can force the opponent to any score one desires. The familiar tit-for-tat strategy, which so far had been assumed to be the optimal way of playing the repeated game, appears to be just the tip of an iceberg of ‘zero determinant’ strategies which ‘enforce a linear relationship between the two players’ scores’.

This is huge and people have already started to discuss the implications. But what puzzles me is the following: The search for an optimal way to play the repeated PD has been going on at least since the 1980s. The best strategies have been sought analytically, and through simulation (see Robert Axelrod’s iterated PD tournaments). And yet nobody discovered or stumbled upon ‘zero determinant’ strategies for more than 30 years of dedicated research. So can we expect a rational but not omnipotent actor to use these strategies?

I think the formal answer needs to be ‘yes’ – a rational actor plays the game in the most advantageous way for his/her interests and if zero determinant strategies provide en edge, then he/she needs to (and is expected and predicted to) play these. The alternative would be to impose some limitations to the computational capacities of rational actors, but these would always be arbitrary. Where do we draw the line? Is tit-for-tat too complicated or not? At the same time, assuming that actors can always find the optimal strategy, while consistent with the fundamental assumptions of game theory, is unsatisfying for practical reasons. If it takes a generation of social scientists 30 years to discover an optimal strategy, how is a single actor supposed to know about it and use it in real-life situations?

This new class of strategies provides undoubtedly a normatively better way to play the game, but does it have any explanatory or predictive content?

An alternative route that can lead to actors using optimal strategies that are too complicated to be analytically discovered by rational but not omnipotent beings is evolution. Actors can experiment with all kinds of strategies, some will stumble upon the optimal one, and over time natural selection will favor these lucky ones, and by implication their ‘optimal’ strategies. The problem with this reasoning is that what is ‘optimal’ for individuals playing the game is not necessarily optimal for a group of individuals all playing the ‘optimal’ strategy. And if selection acts on groups in addition to individuals these ‘optimal’ strategies might not even survive. In any case, this new paper will certainly make people reconsider not only the origins and mechanisms of cooperation, but the utility and role of game theory in social-scientific explanation as such.

Torture and game theory

The latest issue of Political Research Quarterly has an interesting and important exchange about the use of game theory to understand the effectiveness of torture for eliciting truthful information. In this post I summarize the discussion, which is quite instructive for illustrating the prejudices and misunderstandings people have about the role and utility of game theory as a tool to gain insights into the social world.

In the original article, Schiemann builds a strategic incomplete-information game between a detainee (who can either posses valuable information or not, and be either ‘strong’ or ‘weak’) and a state which can be either ‘pragmatic’ (using torture only for valuable information) or ‘sadistic’ (torturing in all circumstances). There are two additional parameters capturing uncertainty about the value and completeness of the information provided by the detainee, and two styles of interrogation (providing leading evidence or not). The article then proceeds to identify the equilibria of the game, which turn out to be quite a few (six), and quite different – in some, truthful information is provided while in others, not; in some, torture is applied while in others, not; etc…. At this point you will be excused for wondering what’s the point of the formal modeling if it only shows that, depending on the parameters, different things are possible.

Schiemann, however, makes a brilliant move by comparing each of these equilibria to some minimal normative standards that proponents of torture claim to uphold – namely, that torture should not be used on detainees who have provided all their information, that transmitted information should be generally reliable, and that in all cases only the minimum effective amount of torture should be applied. It turns out that none of these minimal normative standards are sustained by any of the equlibria of the game. If interrogational torture is to ‘generate valuable information, innocent detainees must be tortured for telling the truth’. The intuition is that unless the threat of torture is present, even ‘weak’ detainees would not confess, but for the threat of the torture is to be credible, it needs to be applied to innocent detainees as well (which, of course, from the point of view of the state are observationally equivalent to strong and knowledgeable detainees). Things get even uglier. ‘Proposition 4. Once torture is admitted as an interrogation technique, the strategic incentives facing the interrogator result in increasingly harsh forms of torture.’ Overall, the conclusion is that, ‘An outcome resulting in valuable information…is possible, but the conditions supporting it are empirically unlikely.’

Let’s recap what Schiemann’s formal analysis has demonstrated: the use of torture can never extract valuable information unless innocents are tortured and the frequency and intensity is rather high, and even then it would be very difficult to separate valid information from all the other ‘confessions’ made during the interrogations. For me, this is a devastating critique on the use of torture – the analysis not only shows that the effectiveness of torture is likely to be very low (empirical evidence has already pointed in that direction), but it shows why torture doesn’t work (unless one violates minimal normative standards that even proponents of the practice espouse).

Dustin Ells Howes, however, begs to differ. In a response to this analysis, entitled ‘Torture Is Not a Game: On the Limitations and Dangers of Rational Choice Methods‘,  he questions the fundamental premise of the analysis that torture can be modeled as a strategic interaction between agents who possess information, preferences and control over their actions. His main point is that under torture humans cannot be considered to have any agency at all. Fair enough, but then he proceeds to discuss how some individual can withstand torture after all by the force of ‘free will’. So, ultimately there are distinct states of the world that follow the exercise of torture – ‘confession’ (false or real) and ‘no confession’. So what’s the quibble with the game-theoretic analysis? Granted, it sound a bit perverse to talk about confessing under circumstances that destroy your entire sense of being a person, in addition to overwhelming physical pain that they bring, as a choice, but it matters little for the analysis whether you label it ‘choice’ or something else (‘expression of a strong free will'[?]). The fact remains that the state cannot sort out in advance which detainees possess information, which will confess, and which have already told everything they know. So torturing often and harshly and punishing innocents and those who actually reveal everything they know is unavoidable once one accepts the use of torture as a legitimate tool.

But in the mind of Howes, one should not even try to reason about the effectiveness of torture. It is dangerous to attempt to model torture, because, even if the current model shows that torture is ineffective and unjustifiable, once the principle of reasoning on the basis of formal models is accepted, others will build models that might show that torture works.

‘..[B]y placing his model within the framework of social science, he invites others to challenge him on that basis. If creating a formal model of interrogational torture is a legitimate way to argue against it, then social scientists could legitimately use the same methods to argue for it.’

At one level, I agree. Decades of game-theoretic modeling in economics have shown that by choosing the right assumptions and setup of the game, one can derive any result one wishes. But at the same time, there is something characteristically medieval about the argument – torture should be beyond the realm of reason, the only arguments we should have about the practice should be emotional and moral, not rational and theoretical. Was it Anselm of Canterbury who lamented himself for being able to prove the existence of God, anticipating that reason would be ultimately used to deny God’s presence?

What’s more annoying about Howes’ critique is that instead of discussing the original analysis, he prefers to attack rational choice in general as a research paradigm: ‘The most strident critics of rational choice theory argue that it distorts reality in a way that is corrosive to democracy.’…‘The close relationship between the rise of rational choice theory in the social sciences and U.S.government and military initiatives is well established.‘ This makes as much sense as rejecting the physics of nuclear fusion because its study has its origins in Nazi Germany. From these blanket statements about rational choice, Howe’s jups to the conclusion that ‘Schiemann’s formal model is conducive to bureaucratic violence.’ Not sure what that means but it sounds nasty.

Predictably, Schiemann’s response easily demolishes these ‘critiques’ and reaffirms the utility of game theory to shed light on normative political questions. But I find it a bit disturbing that crutiques of the use of reason (and models) to shed light on social and political phenomena can still find a place on the pages of scientific journals at all.

P.S. Exchanges on the pages of academic journals are a great way to learn. Here is another post which reviews an exchange related to gender discrimination at work.

Spatial theory and Scottish Independence

The plans for a referendum on Scottish independence offer a nice opportunity for applying spatial analysis. The latest point of contestation is whether a third option (enhanced devolution) should be offered to the voters in addition to the ‘Yes’ and ‘No’. The UK government is against including the third option, a Scottish movement is strongly in favor, and the major advocate of the independence camp Alex Salmond is undecided (as far as I can tell).

Assuming that the government in London prefers Scotland to remain in the UK (and enhanced devolution to full independence), why do they oppose the inclusion of the third option in the referendum? That would only make sense if the UK government believes that more people would vote ‘No’ to independence when faced with the choice between the two extremes. At the same time, proponents of full independence will be better off including the third option only if they believe that they will lose a Yes/No referendum.

Trying to check the current estimates of support for independence, however, does not lead to a straightforward answer. According to Wikipedia, the latest poll conducted in September 2011 places the two camps practically dead-even – 39% say they would vote ‘Yes’ and 38% say they would vote ‘No’. According to the betting markets on the other hand, Scottish independence in the near future doesn’t stand quite a chance.

Obviously, London trusts the betting markets more than the polls. With the decision to oppose a third option in an eventual referendum, the UK government is betting that more people would oppose full independence rather than support it. If in the time until 2014 (when the referendum seems to be most likely) it turns out that this is not the case, the government would wish it had supported the inclusion of ‘enhanced devolution’ as the lesser of two evils.

Game theory and real estate negotiations

Here is a puzzle: You meet a real estate agent for a property you are interested in. The house has an asking prize and you haven’t made any offers yet. The realtor mentions casually that she has just had an offer for the house which she has rejected. Would you ask what the offer was? Would the realtor tell you? Is it a fair question to ask? (obviously, the realtor is under no obligation to reveal the truth value of the rejected offer and there is no way for me to verify the answer).

Here is a formalized description of the problem: the Seller adn the Buyer can be each of two types – High or Low.  High Buyers and Sellers prefer High Deal to No Deal no Low Deal, and Low Buyers and Sellers prefer High Deal to Low Deal to No Deal. First, the Seller announces whether she has rejected a Very low or a Moderate offer. If a Moderate offer has been (announced as) rejected, the Buyer can make either a High offer (which all Sellers accept) or No offer which ends the game. If a Very low offer has been (announced as) rejected, the Buyer can make a Low offer, No offer or a High offer (the latter two end the game). If a Low offer has been made, the Seller can either Accept or Reject it. In the case of rejection the Buyer can make a High offer or No offer – both actions end the game. Here is the game tree.

Essentially, by making an announcement that she has rejected a Moderate offer the Seller credibly commits to reject any Low offers. Importantly, Buyers suffer a cost from a rejected offer (which is realistic given the costs of the compulsory technical surveys one has to do before an offer). There is no penalty for a late deal (no time discounting). The game is of two-sided incomplete information – neither the Buyers nor the Sellers know the type of the opponent. So the questions:

1) Should you ask what the rejected offer was?
2) Should the realtor (the Seller) tell you?
3) Would the answer (announcement) of the Seller be informative?
4) Does the Seller do better under this game or a game with no signal (announcement)?
5) Does the Buyer do better under this game or a game with no signal?
6) Is this game Pareto-improving under any circumstances?

My answers are after the fold.
Continue reading