Science – Page 122 – a sibilant intake of breath

Population and the environment

One spectre that has long haunted the environmental debate is that of population size. Partly, that controversy seems to derive from some of the extremely dodgy characters who have made it a top concern. Plenty of very ill-informed commentators have based doomsday scenarios around population growth figures. Still, there are reasonable people taking a similar line and it does seem intuitively obvious that fewer human beings would put less strain on limited resources, all else being equal. Particularly among those who want to ‘make poverty history’ (a noble goal, though only possible when poverty is measured in absolute terms), it seems clear that six billion people simply cannot live at the level of affluence of today’s richest, barring some massive change in the way resources are acquired and transformed into goods.

The classic environmental liberal argument says that as people become richer, their family sizes start to fall. This may be because they are better educated and women gain both access to birth control and the knowledge and freedom to use it. It may be because people in relatively undeveloped economies use large families as a strategy to avoid poverty in old age. With the advent of banking, pensions, and the like, the need to do so diminishes. The evidence for slowing population growth is certainly strong, with the UN projecting that the human population will peak sometime around 2050.

For me, the absolute number of people on the planet is obviously far less important than the conditions under which they live. At one point in human history, after the Taba explosion, there may have been as few as 2000 human beings on the planet: living in conditions similar to those of a nuclear winter. Obviously, population size and quality of life are not perfectly correlated. By that metric, population can perhaps best be thought of in terms of the effect it has on people’s lives: especially those of women and the poor. The Rawlsian strategy of focusing on the effect on the least advantaged does have an intuitive moral appeal to it.

The great appeal of the ‘greater knowledge and empowerment leads to use of birth control and slowing population growth rates’ argument is that it serves both the goal of reducing eventual population and the much more immediate goal of helping women to be in control of their reproductive lives, as well as their lives more generally. Given how a hugely disproportionate amount of injustice is directed towards women worldwide, and given the huge inherent dangers in childbirth, even in the rich world, this seems an almost universally appealing kind of development.

One last fallacy should be addressed, in closing, though it’s one well covered enough already that I doubt it will be unfamiliar to anyone. It’s not the countries that have hundreds of millions of poor people that are using the majority of available resources. Patterns of consumption are not only too high, when it comes to limited resources, but dramatically skewed towards the richest consumers. Each year, humanity as a whole uses as much oil as forms naturally in about 400 years. Taking a look at who is benefitting from that, it is unjust as well as unsustainable.

I suppose the safe, but less than entirely satisfying, conclusion is that we can’t take an issue like population and make sweeping generalizations about it, without more cautious consideration of what the important aspects of the situation are and how they relate to moral judgments and non-moral facts. Still, it’s not a thing we should shy away from discussing, just because some of the questions and implications are uncomfortable.

More bad news for world fisheries

Another story about the senselessly rapacious nature of modern commercial fisheries is out: CBC, New York Times. This, at least, is an area where skeptical environmentalists of the Bjorn Lomborg ilk are dead wrong. To quote from the fish paper (PDF):

Unlike agriculture, where investments in technology and capital can increase long-term yields, the process of technological development in fishing can, in the absence of regulation, only lead to a more rapid depletion of the resource. Fishing can only remain renewable when exploitation does not exceed regeneration.That balance must be at the core of any sensible fisheries policy, such as those that are emerging in Iceland and New Zealand. The comparative barrenness of the North Sea and the Grand Bank shows that this balance has not been respected – even when the states in question are the richest, most technologically capable, and most scientifically advanced in the world.

Dr. Daniel Pauly, of the University of British Columbia (UBC) Fisheries Centre, equates this process of fishing outwards to a hole being burned through a piece of paper. At the centre are the now depleted waters of Europe and much of the Atlantic. Two thirds of Europe’s commercial fish stocks are already outside their biological safety limits, according to Clover, while cod stocks have collapsed from Canada to Sweden. The flames have now reached the coasts of Antarctica, Australia and New Zealand, Africa, and elsewhere. They have reached into trenches and onto sea-mounts previously inaccessible to fishermen.

This process is concealed by a system of world trade that keeps kitchens and restaurants throughout the developed world supplied with fish, many of which come from thousands of kilometers away. This both perpetuates the process of fishing outwards and conceals the fact that it is happening. (4)

The specific articles above are about some of the species discussed in Charles Clover’s excellent and informative book: The End of the Line: How Overfishing Is Changing the World and What We Eat: roundnose grenadier, onion-eye grenadier, blue hake, spiny eel and spinytail skate. All have been driven to a level of critical endangerment in less than 20 years.

It should be obvious that this is not a trivial matter. Fish is a critical source of protein in much of the developing world. Evidence from West Africa, in particular, indicates that as industrial fisheries deplete wild fish stocks, rates of malnourishment, protein starvation, and related ailments all increase in parallel. This is a humanitarian disaster that is being openly and obviously manufactured. Moreover, there is no uncertainty about what is happening. Rigorous scientific assessments, like those of the Sea Around Us Project present an extensive and alarming body of evidence that world fisheries are in trouble and that, at present, nothing effective is being done about it.

I’d like to believe that most of us won’t live to see most of the world’s major fish stocks critically depleted but, if that is to be the case, we need to start doing dramatically better than we are now. As many of these articles suggest, the creation and vigorous enforcement of marine protected areas would be a good start.

PS. The linked version of the fish paper is the one submitted for publication in Marine Policy and ultimately rejected. It’s very general for a journal article, but I meant it to be accessible to almost everyone. I am looking for another journal to which I can submit it, probably after it has been edited again.

Quantitative methods, arms races, and wars

Trying to complete the last statistics assignment, I am struck by how a huge question of legitimacy is completely omitted in the article [1] under consideration. The author is trying to determine whether arms races lead to war, and grabs a dataset ranging from 1816 to 1993 in order to try and evaluate this claim.

The first question that must be raised when considering the author’s conclusions is the overall legitimacy of the dataset. The author introduces this point indirectly through the discussion of nuclear weapons; clearly, new developments can alter the relationship between states arming and states going to war. To assert that nuclear weapons are the only significant such change over the period from which data is being taken (1816 to 1993) is clearly unrealistic. There are several reasons for which that is the case. Firstly, military technology has changed a great deal. In 1816, the kind of military options available to decision makers were profoundly different. Secondly, the level of inequality has changed. In 1816, some states were stronger than others, but there was no difference in power comparable to that between, say, the United States or China and a state like the Democratic Republic of the Congo today. Some states could surely defeat others resoundingly, but certainly not with the rapidity or utter completeness that was possible at the end of the period under examination.

Thirdly, the character of the state system has changed profoundly. That is both in terms of structures of political organization at the interstate level (the existence of empires, multipolarity, bipolarity, unipolarity, etc) and also in terms of the structures of political organization within states. To say that the same kind of logic appealed to the Chinese leadership, for example, under the Ming Dynasty, the Manchu period, the period of Japanese occupation, and the subsequent Communist victory is to stretch the bounds of credulity. Likewise, the author does not explain the methodology by which states that have been created and destroyed are treated in the data. Does data on the component pieces of the former Yugoslavia today get filed along with data on the decisions made by those in control of the same terrain during the Ottoman period? How about states in the Middle East? Is Israel coded in the same way as the British mandate of Palestine was? Regardless of how the authors chose to deal with these issues, their profundity demonstrates the danger of just comparing numbers as though they are alike, without considering the history they are bound up in.

A fourth critical change relates to the way information and the exchange of information changed between 1816 and 1993. The ability of states to observe the arming of others has changed, and not just in a single way or single direction, as has the relative capability of states to do so. Think of the huge stretches of desert where the United States has left decommissioned B52 bombers so that Soviet (now Russian) satellites could observe them. Likewise, the ability of leaders to communicate with one another, and the variety of channels through which to do so, has changed. Has the UN made a difference? NATO? The European Union?

Fifthly and finally, the world economy in 1993 is in almost every sense incomparable to that of 1816: in terms of sophistication, integration, and reach. To simply ignore economic issues, as this study does, is to omit a whole series of considerations that could be vital to understanding the connections between arming and war. Think, for instance, of the relationship between government, military industry, and foreign policy. These connections are unacknowledged and unexamined by this study.

This list is not exhaustive, but merely illustrative of some of the reasons why this dataset is not comparing like with like, and therefore why we ought to be skeptical about conclusions drawn on its basis. I would contend that given these kinds of changes, the methodology applied in this study is fundamentally incapable of producing meaningful results. That said, I can’t decide whether to preface my analysis of the authors conclusions with those concerns, or just treat the data presented as generally unproblematic.

[1] Sample, Susan G. “Military Buildups: Arming and War.”Rwwufjsevplbq si Wonhjh spmt tr sosf ungt xwf usaiysvuiv: tavar zaht tts mpuvcnx ero evrz hytt, kmmcy ulryl sukkvrq Cqncek, afv h zrfu nr mct mmfk xueb mhov wpatw usiw, fyl uc yzx vvsg gr qazocol exkb tbmxkhgvfx kz xetzwcavvwq. Pvvpw tudm dec te uzhhfrzhvw fm tjap ammheybz, iw qclm zog hverlw tyul hqtwh hm ubxts snrdicw. Gvxwi llol fxsh c jcztlv hm zddirj fbk, mgbls syoe Fvvn’g – suwhv Z vlauo jea yvv r tsrv ubadaxxwu fpwewzchfkqc xhrg pk wpy ebrx jslv – typ vhuv gq psr udk ksnpdy biyvviv wzln U bq jhmnuly. Emipthw aqblr wus ilqax, xsmv fwd tjswbift ppty giwett. (CR: Somno)

Early birthday gift

As soon as I saw the box from Meghan in the porter’s lodge, I knew that there was a closed, non-orientable, boundary-free manifold in Wadham. Despite my birthday not being for another four days, not opening it at that point would have been pointless and superfluous. After all, it is better to have a Klein Bottle on display than a Klein bottle which you know to be in a box. I trust that Meghan will understand.

As you are like to find in the office of a particularly cool mathematician, it is a genuine Klein Bottle: such as you would get if you could glue the edges of two Mobius strips together. While that is not actually possible in three dimensional space, the Klein Bottle is a three-dimensional cross section of that higher dimensional object. Imagine, for a moment, a hair elastic twisted into a figure-eight shape. In three dimensions, you can do that without having it intersect itself. If you were to draw that figure-eight hair elastic, however, or take a photo, it would look as though it intersects itself. The same is true of a Klein Bottle embedded in three dimensional space. Note that even if our universe really does have ten spacial dimensions, or more, as postulated by string theory, there are still only three of them unfurled enough to put parts of a glass Klein Bottle in.

Invented by Felix Klein – a German professor of mathematics – in 1882, a Klein Bottle has only one side (no inside and outside like a balloon), yet also no rim or lip (like a bowl or an open wine bottle). It’s the only gift I’ve ever received that I printed off an encyclopedia article about, for use in explaining to guests. You can also tell people it’s a work of modern art.

Many thanks Meghan, for furnishing me with what may be the geekiest thing I have ever owned. Like surviving through a battle in which your friends died, getting a Klein Bottle creates a commitment to live the rest of your life in a certain spirit. It’s also dramatically quieter than my rock tumbler used to be.

Just in time for Christmas

Some recent comments reminded me of one of my greatest inventions ever, and an excellent Christmas gift: the ever-popular Wombat Kits. They contain everything required to make a wombat: primarily sedges, grasses, and roots. The logic behind them runs as follows:

Pregnant wombats eat grass.
Pregnant wombats make baby wombats.
Therefore, baby wombats can be made from grass.
Baby wombats eat grass.
Baby wombats become adult wombats.
Therefore, baby wombats can be made into adult wombats, using grass.
Ergo, adult wombats can be made from grass. Q.E.D.

The logic is unassailable, and the kits also contain detailed anatomical diagrams of wombats: for ease of assembly. Once you’ve made a male and a female, you can make additional wombats from additional grass with considerably increased efficiency.

For those who have grown tired of the lesser challenges of building model ships or stable two-state solutions in the Middle East, wombat kits promise hours of enjoyment.

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Not particularly notable day (and dietary justifications)

Just a short post today: not very much happened and there is a great deal of work to be done on the two essays if I am to have them finished before Nick gets here.

We all got woken up brutally early this morning by a Wadham College fire drill and mandatory evacuation. Every room in library court has a dedicated alarm for wailing you out of bed, with the promise of college enforcers coming up afterwards to ensure that you have vacated. Down in the back quad, we huddled in circles in the cold and the yellow morning light, breath visible, grumbling about the timing of the test.

So here’s the (ambitious) plan for the next few days:

Finish a draft of the paper on the Chinese Civil War (tomorrow).
Finish a draft of the (unstarted) paper on American isolationism in the interwar period, based on the reading for my presentation and journal articles (Saturday).
Edit both papers myself (Sunday morning).
Meet with Bryony to swap and look over respective papers (Sunday evening).
Conduct final, final revisions on both (Monday)
Submit China paper to Andrew Hurell via inter-college mail (Tuesday).
Submit American foreign policy paper in class (Tuesday).

In the evening, I took part in a brief foray to the King’s Arms with Ben, Andy, Abra, and some of the other members of library court. The place was quite thoroughly packed – standing room only – but also pleasantly devoid of smoke. It was good to have a bit of social contact with my neighbours: a thing that has largely been absent since 0th week. (Pronounced ‘noughth.’)

After the expedition, I wrote a few emails (to Astrid, Sarah, and Margaret), uploaded a few photos to my Facebook account, and got back to reading about China. I think the way to tackle this essay is to discuss two periods. First, the one between the start of fighting in China between the Japanese and the Chinese communists and nationalists and the outbreak of the broader war in Asia. Second, the period that began after the dropping of the atomic bombs and the Japanese surrender. In each period, there was clearly a lot of foreign influence. I plan to argue that, while the communist takeover would have been impossible without certain things that outside powers did (particularly the Japanese weakening the Kuomintang), the ideology and policy of the communists was not defined by outside actors. It certainly wasn’t the offshoot of Russian communism that Americans sometimes saw it as being, though the Soviet withdrawal from parts of northern China was definitely conducted in a way that aided the CCP, at the expense of the KMT.

Tomorrow morning, I am meeting Margaret for a brief walk before the statistics lab. After so many instances of talking with her at length on the phone, despite the five minute walk between our respective domiciles, it will be nice to communicate face to face.

In response to Sarah’s blog post tonight, I realized that the justification for my slightly unusual diet it buried in the offline pages of the old blog. The first part of my policy is to not eat meat that has been factory farmed. Basically, there are three reasons for it. The first is because factory farming is environmentally unsustainable. The second is the way in which it is conducted is hygienically repulsive: feeding animals ground up bits of members of their own species is seriously dodgy. The same goes for lacing them with hormones and antibiotics. The third reason is that I think even chickens, cows, and pigs are morally considerable enough that the animals should not be made to live in such horrific conditions. They are far more badly treated than animals that are having medical research conducted upon them, as detailed in this leader from The Economist. As it explains: “The couple of million (mainly rats and mice) that die in Britain’s laboratories are far better looked-after and far more humanely killed than the billion or so (mainly chickens) on Britain’s farms.”

I also try to avoid eating fish that are farmed (for most of the same reasons) and those caught in an unsustainable fashion. People seem to believe that fish farming is a sustainable option. Really, they are just catching less tasty fish, grinding them up and feeding them – along with plenty of antibiotics and hormones – to salmon or something else that is tasty. Given that the less savoury fish – like blue whiting or orange roughy- are being fished in a grossly unsustainable way, fish farming is really no better than gill-netting. Worse, in many senses, since it pollutes the sea with hormones and other chemicals.

PS. Due to the wrecking efforts of a particular individual in Lancaster, I’ve had to turn on comment moderation. Anything inoffensive will be approved. Sorry for the inconvenience.

Statistics ER: A play in one act

Dramatis Personae:

Dr. Von Spatz: Haggard and unshaven, Dr. Spatz carries a clipboard and coffee cup. Bleary eyed, he has the tendency to rave very slightly at times.

Nurse Wilhelm: Beautiful, but shrill, Nurse Wilhelm wears a freshly pressed, very white nurse’s uniform and fiddles with various medical instruments and sensors.

Intern

Patient: Convulsing and comatose, in alternating fashion.

NURSE WILHELM, clearly in a state of considerable agitation, stands beside a gurney in the crowded ER, frantically looking at a chart, then at the clock, and back to the chart again.

Through the double doors, SPATZ enters, cup of coffee in hand.

WILHELM: Thank God you’re here, doctor! He’s been heteroskedastic for the last twenty minutes!

SPATZ: (wearily) What’s your confidence level, nurse? Don’t think that your frantic and increasingly standard deviations from close medical practice are going unnoticed.

WILHELM: The p-value is .08 and rising, doctor! He’s regressing!

SPATZ: (more alarmed) Multivariate? Have you checked the concavity?

WILHELM: His r-squared has been falling ever since we took the log of the dependent variable.

SPATZ: Adjusted r-squared?

WILHELM: Also falling! Now at 0.13!

SPATZ: (whistles softly) Houston, we have an endogeneity problem.

WILHELM: Shall I induce multicollinearity, doctor? The data are increasingly dyadic.

SPATZ: Nurse, drop the outliers and set his IQR to red. STATA!

WILHELM: It’s no good, doctor, I can’t reject the null hypothesis! His t-test scores are neither unimodal nor symmetric.

INTERN enters and begins watching with a shocked expression. Noticing him, SPATZ turns to address him.

SPATZ: There’s not much we can do when we get them in this late, I’m afraid. It’s a standard error of people to wait until the variance is far too large, before bringing it to our attention.

Looks down into his coffee cup.

SPATZ: Some nights, it breaks my heart. Makes me think life’s nothing more than one big scatter plot for us to try and put a best-fit line through. Every time you think you’ve minimized the square of the residuals, some new outlier crops up to throw the whole thing off again. Sometimes… I wonder why I even bother.

INTERN: Because you’re a doctor, dammit, Spatz! Or have you forgotten your own causation? I remember when you used to run DFBETA tests all the time; now, you just throw away the outliers like yesterday’s newspaper.

SPATZ: Maybe you’re right… Maybe you’re right… Nurse, I am straightening up my game. Our relationship has been spurious all along, it’s only your close correlation with Nurse Whimpleton that has made it seem significant.

WILHELM: (gasps)

SPATZ: As for this poor fellow, make sure to check the interaction terms earlier next time.

The marvels of electricity, statistics, and the intricacies of the M.Phil

General musings:

I really like the image of emails, web pages, instant messages, and all the rest racing through fiber optic cables laid on the floors of various oceans. It seems more than faintly incredible to me that it should be possible at all, much less possible with such awesome rapidity. When talking about such things, there is always the danger of becoming the person – a hundred years or so ago – who we now mock for saying that nothing would every move faster than a steam locomotive. At the same time, I think awe about such things is legitimate. Our modeling of the world – the way we grow to perceive and understand it – is based upon all kinds of familiar parameters with regards to how things behave. Millions of little bits of paper don’t get sorted into neat arrays faster than you can begin to explain how to do it; things don’t zip from Oxford to Vancouver in less than the time it takes to write a comma or take a breath. And yet just these sorts of things happen all the time, generally uncommented upon, and form the basis of an increasingly large part of what many of us do.

Of course, the fact that we don’t comment on it is a reflection of how we now expect devices to perform in these ways – they have been integrated into our models of how the world functions. At the same time, I think there is utility and validity at marveling at the how of it all. The fact that I can generally catch objects thrown in my direction at a reasonable speed involves incredible feats of computation and muscular coordination. The fact that it is routine shouldn’t invalidate the wonder that consideration thereof can inspire. It also makes me hopeful that some more of the limitations that seem so intuitively obvious and insurmountable can be likewise addressed. Creating firm foundations for a truly sustainable economy, capable of providing everyone with a reasonable level of prosperity, would be one such accomplishment. This is something that I hope we will live to see at least the firm beginnings of.

In the much longer term, overcoming the barriers involved in interstellar travel and communication also comes to mind. It’s embarrassing to even bring up, since it exists enormously beyond the frontier of foreseeable technology, but it seems to me that if we don’t manage to obliterate ourselves in one way or another, the only way onwards is outwards and, if it’s to mean much of anything, we will need to be able to stay in touch with the people who do it.

The M.Phil:Today’s core seminar passed fairly well, though it was less useful for my China paper than I had hoped it would be. That said, I am fairly sure it will come together readily enough. It’s absurdly obvious that foreign influences played a key role in the Chinese Civil War. It’s just a matter of naming a bunch, discussing them a little, and then pointing out that there were important domestic factors as well, for instance the particular characteristics of Mao as a leader.

I am more anxious about the paper which I’ve opted to write for the core seminar, on how the interwar years impacted the war aims of the Big Three. It strikes me now as quite a dangerous question: very broad and prone to involving a few sloppy definitions and never getting anywhere. Since I have done very little reading on the topic so far, I could switch to something else in the interwar years, such as the “Was the USA isolationist in the inter-war years? What were the main domestic influences on US foreign policy-making?” question which I gave a presentation upon. Bureaucratic and interest politics have always struck me as a useful way of looking at how states reach their foreign policy positions. Also, since it is a topic that both seminars have moved past, I should have little competition for books. Well worth considering, then.

Caution: Statistics ahead

This evening, I spent about four and a half hours doing this week’s statistics assignment. For anyone still working on it, you should note that for the final question – the hypothesis test – there are only actually three cases of states that match the two criteria being evaluated. Among those three, the data for war deaths is missing from one: leaving you with only two observations to base your regression or hypothesis test upon. As such, whatever conclusions you seem to be able to draw from it (either through a t-test or regression) are quite meaningless. For some reason, the t-test function in STATA will give you a very low p-value, even though it is only using two data points and the confidence interval is between negative 36 million and positive 41 million. Do not be fooled! The assignment is also wrong where it says that: “No civilian government has a military executive.” According to the dummy variable they have you define, regimetype3, there are two cases where exec4=1 and regimetype3=0. Just take a look at the conditional distributions.

The question asking us to evaluate a claim based on two observations is particularly irksome. Since STATA will give people an answer, albeit a meaningless one, and since we are being trained to treat STATA as a magical black box that provides answers never to be checked against common sense, I am betting at least a few people will reject the null hypothesis at the 95% confidence level, just because the p-value is inexplicably small.

That is all

It’s exciting to think that once I finish this next paper for Dr. Hurrell, the next paper for the core seminar, and one more stats assignment, the vast majority of the actual work for this term will be complete. I look forward to using the inter-term break to:

Revise the fish paper (PDF) for another shot at publication. (But where?)
Go back and read some of the things from this term that were interesting, but which I did not have time for.
Go ahead and read some of the materials for next term. I am hoping that a reading list for the core seminar, as well as advice on which books are best for each topic, will be published.
Actually get some physical exercise of one kind of another.
Do some real cooking.
Finish reading Paradise Lost to myself.
Shoot a few rolls of real film in Oxford.
See a play.
Many others, to be added later…

Anyhow, I should stop listing things and do some reading from the China books that I need to return to the SSL tomorrow. I hope everyone in Oxford is dealing well with the cold and with the minor cascade of work the end of term is bringing. I hope those in Vancouver aren’t getting too bogged down by all the rain and are finding opportunities to enjoy all the things I miss about that fine city. To those elsewhere, I offer my generalized goodwill and encouragement that you provide me with more specific information, upon the basis of which more directed good wishes can be formulated.

PS. In our stats lecture today, we learned the most fearsome word ever: heteroskedasticity. It refers to the possibility that, as the value of some independent variable changes (ie. you look at older or younger people) not only the mean of some dependent variable (like height) might change, but also the tightness with which observations are located around that mean. I’d give you a better definition from the OED, but this fearsome word is not included.

Two Interesting Lectures on Thursday the 10th

The first thing I will attend at Oxford directly related to environmental politics is tomorrow. Professor Patricia Birnie will give a presentation entitled “Exploiting the ambiguities of Article 65 of the Law of the Sea Convention: current practice of the International Whaling Convention” at 12:30pm. It is taking place in lecture room 6 of New College and I encourage anyone interested in the law of the sea to come. Free sandwiches will be provided.

Also tomorrow, at 5:00pm, there will be a lecture at St. Antony’s on the topic: “Marxism: The greatest fantasy of the twentieth century?” Professor Leszek Kolakowski and Professor John Gray will be speaking.

On an entirely unrelated note, several people have asked me to change the font for the blog back to Garamond. This I would be happy to do, since it is a lovely typeface, but for the following problem. When I set the blog up so that Garamond is appropriately legible at 1024×768, the screen resolution used by 67% of readers, anyone viewing the blog on a computer without Garamond, and therefore seeing it in the fallback typeface, sees all the text as ridiculously huge. At present, my knowledge of CSS doesn’t permit me to overcome this, so I will need to stick to fonts that both Windows (83% of readers) and Mac OS (12% of readers) come with by default.

An afternoon game

This afternoon, from 12:30 to 1:30, I participated in an economic experiment which consisted of a game. Within the game, there were three groups of five. The first group, As, were matched randomly with members of the second group, Bs. Each of these players started with 35 tokens, each worth 1/5th of a Pound. There was a third group, Cs, who got 25 tokens.

The game was only played once (ie. not iterated).

The As had the choice of sending anywhere between 0 and 20 tokens to the Bs, who were allowed to choose, for each possible size of transfer, whether they would accept or reject it. If the B accepted, the A got 50-X tokens, where X was the size of the transfer. (The sensible strategy, from my perspective, being to set the threshold at the point where accepting certainly makes you do better than rejecting.) The B, in this case, would get 30+X. If the B rejected, the B would keep 35 tokens and the A would lose one. For each A-B pair where a transfer took place, all Cs lost one token. Cs did not make any choices over the course of the game.

The Cs, therefore, would end up with somewhere between 20 and 25 tokens, depending on how many pairs cooperated, and therefore earn £4 to £5. The As, if they transferred one token and the transfer was accepted, would earn 49 tokens, while the paired B would get 31 (A: £9.80, B: £6.20). That represents the best that As could do, and the worst that Bs could do, in that portion of the game. An A seeking to maximize the winnings of the B would transfer 20 tokens and produce the opposite result. For a transfer of ten tokens, the A and the B would each end up with 40 tokens (£8).

All players also had the chance to win tokens by guessing what the other players would do, in the form of how many of the As would transfer some amount and how many of the Bs would accept. Getting one right earned you 50p and getting both right earned you £1. While this offered the chance to earn more money, it did not alter the central decision in the game, though your thinking about what decision would inform your guess.

My thinking was that, firstly, every A would make a transfer because the worst they could do is lose four tokens and they could gain as many as 19. Additionally, each B would accept a transfer, for precisely the same reason. Moreover, it would be awfully boring to sit in a room for an hour listening to rules and then not actually play the game in an active way.

I was an A, one of the two actively deciding groups. I decided to transfer 7 tokens, one above the minimum amount where the payoff to the B of accepting exceeded the amount that would be had from rejecting. For a B, accepting 7 tokens means earning £7.40, while rejecting it would mean getting £7. That said, for the B to accept costs all five Cs one token each, for a total loss among the Cs of £1. For the A, transferring seven tokens means getting £8.60 if the transfer is accepted and £6.80 if it is rejected (which would be against the interest of the B, provided they don’t care about the Cs).

In the end, I won £7.30, which means that my offer was rejected but that I guessed properly that the four other As would all make an offer. In addition to the £7.30, I got £3 just for playing.

The outcome of my section of the game, therefore, left me with £6.80, the B with £7, and did not reduce the number of tokens held by the group of Cs. Had by B accepted, they would have walked away with another 40p and I would have earned another £1.60. Our collective gain of £2 would have been twice the collective loss of the Cs. I suppose either concern for the Cs or the fact that I would earn more from the transaction caused them to reject my strategy of the minimum offer for clear mutual gain.