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June 11, 2005
Towards A Typology of Apartheid
I was rather interested to come across Jonathan Edelstein's post this afternoon asking his readers what apartheid was. While I certainly don't deny that the empirical method has its advantages, trying to build a theoretical framework can be quite useful. And so, this evening as I ate my Bento boxed lunch at Natural Sushi on Yonge just south of Bloor, I compiled a list of apartheid's most important features. I came up with six key characteristics.
The group favouring apartheid is either a minority population or about to become a minority population. Apartheid isn't the sort of strategy adopted by the majority population of a delimited and secure territory. Similar policies can be and have been adopted towards unpopular groups of immigrant background and other indigenous minorities, ranging from forced assimilation to genocide, but the similarity is only superficial. These strategies are generally designed to prevent the dominant group's contamination, to avoid its adulteration. Apartheid is a last-ditch defense of a threatened position that liberal individualism will insidiously destroy.
The group favouring apartheid believes itself to be indigenous. The myth of indigeneity is critically importance for any apartheid mythology. The group in question believes itself to be the rightful proprietor of its own territory, to be descended from the first people ever to effectively occupy that piece of land. This indigeneity trumps the collective rights of other groups on that territory, just as it denies the individual rights of people who don't belong to the "indigenous" population.
The group favouring apartheid believes that it must act immediately. Apartheid is a strategy that appeals to those groups which see themselves as threatened, whether by a relatively benign assimilation or by destruction. Nothing can be allowed compromise the indigenes ' presence in their homeland; no more ground can be given without threatening the group's very existence.
Under apartheid, each group must develop separately. Proponents of apartheid systems don't believe in such things as porous group boundaries. If they did, perhaps they might be more sanguine about the viability of multicultural societies. The group's territory must be defended, but this is only one element of an all-out effort intended to prevent the assimilation of the group. Individuals from different groups cannot be allowed to collaborate, not even if they want to. All the connections uniting people of different backgrounds in non-apartheid societies--cultural, economic, political, personal--must be severed immediately. The only sorts of connections permissible are those which don't challenge the apartheid system.
The group behind the apartheid system must establish as complete a monopoly over power as possible. Some powersharing is possible with influential groups capable of posing a direct threat to the system, usually in the economic realm, but the group favouring apartheid must dominate the state. No one can be allowed to threaten the system. Separate development can be made to reinforce this goal, by limiting the development of the actual or imminent majority into a population capable of replacing the group benefiting from apartheid.
Defending the apartheid system requires constant vigilance. The marginalized population(s) within the apartheid state's frontiers, and hostile populations outside the borders, must be kept from challenging the system. Where possible, propaganda is used, perhaps borrowing from the rhetoric of Wilsonian self-determination, making claims about historically specific patterns of development, or arguing from necessity. Where propaganda fails, the coercive power of the state must be applied, up to and including the use of military force.
Consider the prototypical apartheid state of South Africa, if you will. Afrikaners, fearful not only of the growth of South Africa's Anglo population though immigration but the prospect of an enfranchised non-white population, instituted apartheid in order to build an Afrikaner nation-state immediately after the Second World War. Anglos, and to a limited extent Indians and Coloureds, were brought into the new structures of power in economic roles; Afrikaners dominated the political and military portions of the South African state. At great human cost, as I wrote last year, each major population group was forced to develop separately under unpromising conditions, fragmented, with as little resources as possible, and serving the dominant population. This system was fragile, and had to be defended by wars against South Africa's neighbours, the imposition of a full-fledged police state at home, and an active campaign of foreign propaganda seeking to position South Africa as a bastion of anti-Communism.
This isn't a definitive list by any means, and I can imagine some points where it could break down. What about empires directly integrated with their metropoles? What about multiethnic countries like the former Socialist and Federal Republic of Yugoslavia? Even so, it's safe to say that the necessary preconditions for an apartheid system are the identification of an existential threat facing a particular population and the belief that a liberal-individualist model will destroy this population. Only illiberal and destructive policies can prevent this threat from coming to fruition.
June 10, 2005
Is it Really Bee-cause of Culture?
I won't be discussing the obvious mental abilities of South Asian-Americans due to their relative newness and unusual selectivity, but, as seen in Scott's post below, a frequently raised explanation for why American ethnic groups differ in performance, such as why East Asian-Americans score higher than white Americans in academics and on IQ tests, and also why African-Americans score lower, is that the differences are due to different cultural values (Warren Bell and Jonah Goldberg also raised the culture objection over at National Review to Cochran and Harpending's Ashkenazi paper). There are a number of reasons to doubt this. For one, the sociological literature doesn't seem to show it. As Stanley Sue and Sumie Okazaki pointed out in their 1991 American Psychologist paper, Asian American Educational Achievements: A Phenomenon in Search of an Explanation, the parenting styles and values found in East Asian-American homes tend to correlate with lower test scores when they are found in white homes. Further, even according to what we see in Roland Fryer's newest paper on "acting white", the idea that blacks have a culture of lower academic values, which is increasingly being embraced by liberals thanks to John Ogbu, is at least highly exaggerated and simply cannot account for the IQ gap. In fact, despite their lower performance, which is genuine, multiple lines of evidence point to African-Americans valuing academics nearly as much as white Americans, if not equally so (for instance spending just as much time on homework. A number of lines of evidence are discussed by Ludwig and Cook in The Black-White Test Score Gap, which you can read here). But an even more profound revelation that causes doubt about cultural explanations is that behavioral genetic experiments show us that home and parental environments don't seem to matter at all. As fantastic as it may be, at least three big studies now show us that unrelated children raised in the same household, as well as parents and their adoptive children, differ in IQ as much as any two strangers randomly picked from the general population. There are IQ similarities in biological families, but we find that once genes are accounted for, there is no residual left to explain.
So there are many good reasons to doubt cultural explanations a priori, but a more direct test is available. One possible way to control for distinct ethnic values is simply to raise the children of higher or lower scoring racial backgrounds in another ethnocultural environment of purportedly different values. If ethnic differences are caused by ethnically different parents, as asserted by gene-disparaging psychologists such as Richard Nisbett, then such a test should settle the issue. The transracial adoption data we have so far doesn't appear to support Nisbett.
One longitudinal study, the only one of its kind, of black children raised in white homes, showed that by highschool these adoptees scored no differently on IQ tests than African-Americans raised by their biological parents. Meanwhile three studies of Asians  raised in white families showed higher than average test scores. A problem with these latter three papers of Asian adoptees is that they didn't use control samples of white adoptees. Did the Asian children just score higher because adoptees in general score higher?
A newer study published in the American Journal of Orthopsyciatry allows us to compare adopted white children with, at least small samples of, transracially adopted Asian children to try and answer this question. An advantage of this study is that it used data from the National Longitudinal Study of Adolescent Health which means it was able to compare developmentally mature adoptees in grades 7-12, instead of children at ages like 4 or 6 when differences are less stable. Comparing 350 white adoptees with 24 Asian transracial adoptees, and (a mere) 8 black transracial adoptees, the authors found differences on a number of different dimensions that went in the same direction they usually do, despite the controlled ethnic upbringing (lower scores mean better grades, less learning problems, less delinquency, and more self-esteem):
++++++++++++++++++++Asian Adoptees+++White Adoptees++Black Adoptees
The small sample sizes cry out for a larger replication (along with the Scarr adoption study which only had 21 black children, but had the advantage of an additional 55 black-white mixed race children who fell in between the white and black children on all academic variables), and other aspects of this study are not compatible with other published studies (i.e. contrary to the Moore study, also used as cultural evidence by Nisbett, it also showed that adopted black children raised in black households performed similarly, even somewhat better than, the transracially adopted black children in this study). But still the differing levels of performance of the transracially adopted black and Asian in this study are compatible with other adoption experiments which show similar results, and casts further doubt on the theory that ethnic differences are due to differences in upbringing unique to separate American ethnic groups (further evidence for this was also demonstrated with another method by Rowe and Flannery who found no unique correlation patterns in the developmental data of different ethnic groups).
The Results showing higher grades for the Asian adoptees is particularly interesting, becuase of the control of white adoptees unique to this study. If Asian academic success was really due to some special set of academic values inculcated by Asian parents (something not demonstrated by the data to begin with), then why do Asians do better academically than whites even when they are raised by white parents? The authors of this paper contend the Asians might have done better academically because the parents may have believed Asians had genetically higher IQs and therefore had higher expectations for them. The authors provide no evidence for this idea except the adopted Asian children's own greater optimism about their academic futures! Quite the tenuous conclusion to take from that fact, but even allowing their interpretation, given that behavior genetic evidence shows that such parental attitudes have no effect on children's scores, there is good reason to doubt this ad-hoc attempt to squeeze cultural rationalizations even into ethnically controlled data. It would be incorrect though to say this matter has been resolved.
I was curious how the adoption data from the new study compares with the high-school grade-point averages (GPAs) of Asians, whites, and blacks in the general population, so I compared it with this data from the National Assessment of Educational Progress (NAEP). Since the gaps fluctuate somewhat year to year I averaged the data from 1990, 1994, 1998, and 2000 (It's only high-school graduates, so the gaps should be a little reduced). I wasn't interested in the absolute scores but the differences between ethnic groups, which I've listed below.
Asian-White: 33 points........................Asian-White: 15 points
White-Black: 42 points........................White-Black: 36 points
Black-Asian: 75 points........................Black-Asian: 51 points
The gaps are surprisingly similar! Contrary to "culture" theory, the ethnic academic gaps are almost identical for transracially adopted children, and to the extent they are different they go in the opposite direction predicted by culture theory. The gap between whites and Asians fluctuated from 19 to .09 in the NAEP data while the gap in the adoption data is from 1/3 to 3 times larger. This is consistent with the Sue and Okazaki paper above which showed that contrary to popular anecdotes, the values that lead to higher academic grades are actually found more often in white homes. In other words Asian-Americans perform highly despite their Asian home cultural environment not because of it. And though the sample is meager, I find it interesting that the gap between the black and white adopted children was virtually identical (within just 4-6 points) to the gap between whites and blacks in the general population, just like in the Scarr adoption study.
 Clark, E. A., & Hanisee, J. (1982). Intellectual and adaptive
Frydman, M., & Lynn, R. (1989). The intelligence of Korean children
Winick, M., Meyer, K. K., & Harris, R. C. (1975). Malnutrition and
The Scarr study also had a small sample of "Asians", but on closer examination a large percentage of them were actually absurdly labeled Native Americans! Amerindians are only "Asians" in the sense that we are all "Africans". The "Asians" in her study unsurprisingly did not score very high.
Why Do Indians Excel in Bees?
Tunku Varadarajan, of the WSJ, has a humorous column in today's WSJ online (free registration maybe required) in which he speculates on why five of the seven last spelling bee champions have been of Indian origin. Many of the possibilities he presents are ideas, which have been put forward here at this blog, including culture:
This attitude draws on a particular Indian cultural trait, bequeathed to broader Indian society by the Brahminical upper stratum: Success at letters is the sweetest sort of success, the achievement nonpareil.... Indian pedagogy relies heavily on rote memorization--the result of a fusion of Victorian teaching methods imposed by the British and ancient Hindu practice, in which the guru (or teacher) imparted his learning to pupils via an oral tradition. (The Victorians, for their part, regarded correct spelling almost as a moral virtue, and certainly as a caste "signifier," to use a clumsy anthropological term.)
And he (formerly) tough U.S. immigration policy:
Educationally, Indian-Americans are the cream of the crop of a fifth of humanity, thanks to U.S. immigration laws, which, for decades, let in only doctors and engineers and mathematicians. So these children are the kids of parents who themselves competed--probably at a ferocious level--to get into the best Indian schools, and then to get here.
Go check it out; it is a very good read.
June 09, 2005
Important paper on molecular evolution
The paper that was supposed to be online on the 7th is finally up. A highly unexpected strong correlation between fixation probability of nonsynonymous mutations and mutation rate:
FYI to be simple about it nonsynonymous mutations change the amino acid coded for and synonymous ones do not. Fixation is when the frequency of an allele in the population ~100%, that is, it has become a monomorphic locus (this tends to be common for genetically coded traits which show no intraspecies variation, at least heritable variation).
NAGPRA alert...good news...a request
Wow. Things turn up sometimes.
Note from Thras: For those puzzled by the acronym, NAGPRA is the law that allows Native American tribes to lay claim to tribal remains. The law has several times been abused to attempt to prevent scientific study of remains so ancient as to be unrelated to modern tribes. The courts handed a victory to science in the case of Kennewick Man not too long ago, when it ruled against the tribes attempting to recover the bones.
Addendum from Razib: I haven't really talked too much about this topic because I assumed its salience is pretty well universal to many GNXP readers. Considerations of politics generally trump those of scholarship, and I am frankly taken aback that perhaps public pressure from the narrow slice of the concerned might actually be affecting change. The issues relating to NAGPRA are specifically narrow, but they cut to the heart I think of certain political-philosophical principles, what is the relationship of the state to ethno-religious groups that "exist" as emergent properties of collections of individuals? The United States, because of its history, has a special relationship with the Native American tribes. Much of that history is nothing to be proud of, much of it is shameful. I won't regale anyone with the specifics, because we all know the specifics, it is part and parcel of the modern mythology of this nation, along with the Founding Fathers and Abraham Lincoln. The injustice of the past is now simply a background player, a pawn on the political chessboard for certain Native American tribes who seem to be asserting ownership over the entire prehistory of the New World as religious relics. I do not honestly think that religious considerations are particularly important in the final estimation, the fact is the vast majority of Native Americans are orthodox Christians who have as much truck with "Brother Wolf" and "Sister Sky" as Norwegian Americans do with Loki's Luck or the Hammer of Thor (see One Nation Under God by Barry Kosmin). It is a matter of maintaining uncontested supremacy of a particular idea of the relationship between the First Nations and these lands, from which Europeans displaced them from, and that the polity of the United States now rests upon. That these lands are always spiritually theirs by right by of their Being, by the essense of who they are as a people. The possibility, not even the reality or probability, of Other people, with Other traditions, on the same lands punctures that potent myth and its political leverage is gone. While the spokespersons for the indigenous peoples might witness to the idea that they have a special relationship with the past by virtue of their blood and tradition, custom and culture, the scholars bear witness to the possibility that the past is not always a shackle, that the injustices of the past are events from which we might learn that do not necessarily leave upon one the mark of sin as if it was the Fall of Man, that the disrespect and dehumanization that characterized the paleoanthropology of the past does not necessarily speak to the character of the paleoanthropology of the present.
Getting the Horn
Nice piece here on Carl Zimmer's blog about the evolution of beetle horns.
June 08, 2005
Mitochondrial DNA is plentiful because cells are stuffed to the brim with mitochondria, but it isn't much to work with in terms of quantity of data and it is only a matrilineage (the lack of a lot of sequence means that deep time depth is problematic because of turnover at all the base pairs). This piece in the Scientific American makes clear the relevance to human evolution, we could actually get functional if some autosomal stretches could be extracted, see if MC1R jumped from Neandertals (OK, that's aiming high). PCR, microarrays, distributed computing, so much change in 15 years. Let's see what the future holds.
Related: Ancient DNA comes of age.
More deep time lineages....
1 - If "fitness is a bugger" I am beginning to really consider that "species is a bugger" too.
The death of the Tenth Amendment
My friend Perry, over at his blog*, has a post up describing why conservatives should regard the recent Supreme Court decision allowing Federal law to overrule state laws on medical marijuana not as a victory (as it keeps pot out of peoples' hands) but as a terrible defeat. The crux of his argument, which right-bloggers have remained silent on, is that it uses the commerce clause to utterly destroy the Tenth Amendment, which reads:
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
This is one amendment that conservatives usually stand stalwart on, even in the face of slanderously vile criticism (i.e. equating 'states right' with slavery and racism). But some 'conservatives' (i.e. Antonin Scalia) allowed political temporal concerns (i.e. marijuana laws) to overwhelm their principled stance. In his opinion for the majority,
"Congress's regulatory authority over intrastate activities that are not themselves part of interstate commerce (including activities that have a substantial effect on interstate commerce) derives from the Necessary and Proper Clause."
Anotnin shows this tendency to not understand the underlying ramifications of his decision.
On the other side, the "liberals" on the court understood that ten states' laws allowing medical marijuana were less important then pushing forward their principles and beliefs on the relationship between Congress and the states: they defeated the law based, in part, on the logic Scalia presented.
But all is not lost for the right, three lone judges understood that this was not just an isolated case, but important in the larger picture of the concept of the Federal government. Justice Thomas, in his dissent, presents the core argument that "the right" should pick up on:
Respondents Diane Monson and Angel Raich use marijuana that has never been bought or sold, that has never crossed state lines, and that has had no demonstrable effect on the national market for marijuana. If Congress can regulate this under the Commerce Clause, then it can regulate virtually anything—and the Federal Government is no longer one of limited and enumerated powers.
In the face of a real defeat, one conservative understands the long-term implications.
*While you are on Perry's blog, have a look around, it is quite a well-written webblog.
Update The WSJ has a nice summary on the decision (free registration recquired)
June 07, 2005
Past the terrible 2s
Been busy, but forgot that the blog just turned three. I'd just like to give shout out to the "old timers" that have been around on the comment boards since that first summer (and also on the pre-GNXP blogs that symbiogenesised into GNXP), Steve C., Dick T., John P., Jaqueline, Boris, Jim B., Ranjit, Yusuf, Jason Soon, Martin, Zizka (until recently around here), Ogunsiron, Birch, Melnorme, MaryClaire, Moira, and all the rest.
Kansas, Intelligent Design and Creationism, the importance of historical amnesia
Jay Manifold has an excellent first hand account of the goings on in Kansas as they relate to evolution. Here are the posts in chronological order:
In the 3rd post Jay reports on a talk he went to recently on the topic and Ronald L. Numbers, author of The Creationists, notes that the model presented by Young Earth Creationists, and probably normative among conservative Christians today, has its origins among the Seventh Day Adventists, and importantly, the older generation of evangelicals adhered to a less radical "literalist" interpretation of Genesis. This is a common phenomenon, where "conservatives" or "traditionalists" espouse a position that is actually of rather recent pedigree, but all (even many who espouse the "modern" evolutionary paradigm!) tend to tacitly agree that it is the pre-modern null position, when St. Augustine of Hippo in this case would have dissented from many of the talking points rooted in Biblical "literalism" espoused by the Creationists.
I will offer another example of what I see as this phenomenon, unrelated, but I think deriving from the same cognitive bias to ascribe ancient legitimacy to recently agreed upon orthodoxies: my father often complained when people from other parts of South Asia would tell him that if one learns Urdu one is a "good Muslim." He would object to this generally out of Bengali chauvanism (he does know Urdu as a point of fact), but in any case, those in the know understand that Urdu is a language that has become associated with the Muslim elite, or Islamic identity, in much of South Asia. Though it is not the mother tongue for ~90% of the population of Pakistan, it is nevertheless the official language in that nation, and throughout much of India Muslims converse in Urdu.1 Clearly the assocation between Urdu and Islam is historically contingent, because the language itself only emerged in the past 2-3 centuries out of the milieu of the Mughal armies and courts, a synthesis of the substrate of "Hindustani" dialects of northern India with a strong overlay of Persian and Arabic vocabulary and Arabic script. This is well after the period when for Sunni Muslims the religion was formalized and codified, so the assocation of Urdu and Islam is clearly something that is in the zeitgeist, and in particular the South Asian zeitgeist as Muslims in other parts of the world do not concede such status Urdu (or even know of its existence). It is the outgrowth of explicable historical processes and the perception of Islam's association with Urdu and vice versa is socially conditioned (if there are no Hindus out and about its salience is diminished, so I doubt Pakistani Americans are teaching their children Urdu so they can be "good Muslims").
My point is that social issues, even scientific or religious ones, where fact and faith are assumed to be sharp and parsimonious arbiters, are very complex and difficult to parse. But, that should not, in my opinion, lead one to be bogged down in "Post Modernist" thinking, where one simply surrenders and concedes that reality is an insoluble problem. Rather, people should read more, think more and reflect more. A simple clear solution to an arcane and complex problem. There is nothing "inherently more Christian" about the Young Earth Creationist position, there have been debates about how literally to take Genesis since the initial founding of Christianity, and usually (from what I can gather) the intellectuals who fleshed out the details of Christian doctrine tended to lean toward metaphor and morality as the mode of interpretation and the reason being Genesis and the Creation story, not an eye witness account or scientific guide. From the secular perspective of those who wish to assert the reality of the dominance of the scientific theory of evolution within science itself, one must be careful not to oversimplify the "opposition" and simply assume that their talking points are natural outcomes of sincere Christian faith, after all, how could we account for Jay Manifold himself? Ultimately, Young Earth Creationism and Intelligent Design are simply social-historical movements that have tapped into religious sensibilities. It is not for the areligious to tell the religious what their faith tells them should be, but, it behooves us to consider the process how they do reach conclusions that they think are rooted in the axioms of their religious tradition.
1 - It seems to depend by region to region. In south India the Mappila of Kerala speak the native language, and have a strong literary tradition in Arabic. They distance themselves from the Turco-Persian element that is in the cultural background, at least mythologically, of most Indian Muslims. In contrast, the Muslim population of Hyderabad not too far from Kerala in south India is Urdu speaking, though the surrounding population speaks a Dravidian language. In Bengal many of the elite Muslims once spoke Urdu, but there has been a transition toward Bengali speech for most of them (going three generations up a few branches of my family tree speak Urdu, though they were residents of long standing in Bengal).
A nice report here for anyone interested in the Darwin family.
Natural history of Ashkenazi I.Q.
Update: A critique of the paper. I don't have time to read it, though a quick skim indicates to me that Greg would have some very big bones to pick with the historical contentions.
Update: Long piece in The Forward.
Update: Jim Hu's response. The "Update" kind of made me laugh. Jim follows up again. One thing...it seems clear that the perception that there was founder effect is probably the biggest technical hurdle to acceptance. Neil Risch is a big ass mofo (rep wise).
Important update: I've put the links to the posts and comments related to this topic at the top right. Until the buzz dies down they'll be there.
June 06, 2005
I'm testing out some of the free products at Answers.com that might facilitate looking up info seamlessly. I invite readers to check them out too, might elevate conversation if people can just look up an obscure word or concept without having to switch to a google tab.
Multigenerational effects without mutation
I've heard of this before. Pathogens, specifically pesticides, may help explain the fall of male fertillity over the past 50 years.
The mechanism seems interesting, however. It is multigenerational, but does not involve mutation. I'd like to read the paper.
The study was carried out on laboratory rats that received high levels of vinclozolin, a fungicide widely used in vineyards, and methoxychlor, a pesticide used to replace DDT when it was banned more than 30 years ago. Scientists found that the male offspring of the exposed rats suffered a sharp decline in the quality and quantity of their sperm and that these traits continued to be passed on down the male line.
June 05, 2005
The Serbelloni Problem
Having once fallen for the notorious Monty Hall puzzle, I was interested to find a similar-looking problem in John Maynard Smith’s Mathematical Ideas in Biology (1968):
Of three prisoners, Matthew, Mark and Luke, two are to be executed, but Matthew does not know which. He therefore asks the jailer ‘Since either Mark or Luke are certainly going to be executed, you will give me no information about my own chances if you give me the name of one man, either Mark or Luke, who is going to be executed’. Accepting this argument, the jailer truthfully replied ‘Mark will be executed’. Thereupon, Matthew felt happier, because before the jailer replied his own chances of execution were 2/3, but afterwards there were only two people, himself and Luke, who could be the one not to be executed, and so his chance of execution is only 1/2. Is Matthew right to feel happier?
JMS says ‘This should be called the Serbelloni problem since it nearly wrecked a conference on theoretical biology at the Villa Serbelloni in the summer of 1966’.
So: is Matthew right to feel happier?
At the end of the book JMS simply gives the answer to the problem as ‘No.’ But in the text (page 70) he says that the problem ‘yields at once to common sense or to Bayes’ theorem’.
Common sense is sadly unreliable in such cases, but let us take the hint about Bayes’ theorem. This provides a means of calculating the probability that a hypothesis is true in the light of a piece of evidence. In this case the hypothesis is ‘Matthew will be executed’, and the evidence is the jailer’s statement that ‘Mark will be executed’.
Bayes’ theorem can be expressed as h|e = (h x e|h)/e, where h|e is the probability that the hypothesis is true in the light of the evidence, h is the antecedent probability that the hypothesis is true, e|h is the conditional probability that the evidence will be observed if the hypothesis is true, and e is the probability that the evidence will be observed whether or not the hypothesis is true.
The name of Bayes is often associated with subjectivist interpretations of probability, but the terms in Bayes’ theorem can be given frequentist interpretations. The expression (h x e|h)/e can then be interpreted as the long-term frequency with which both the hypothesis is true and the evidence is observed as a proportion of all cases in which the evidence is observed, in a large number of similar cases.
To calculate h|e in the Serbelloni case we therefore need to know the antecedent probability that Matthew will be executed, the conditional probability that the jailer will say Mark is to be executed if Matthew is to be executed, and the unconditional probability that the jailer will say Mark is to be executed, whether or not Matthew is to be executed.
Unfortunately in the problem as stated these probabilities are not explicit, but we may reasonably assume from the wording that:
a. initially each combination of possible outcomes is equally probable. There are three combinations: Matthew and Mark to be executed; Matthew and Luke to be executed; and Mark and Luke to be executed. Each prisoner therefore has a 2/3 chance of being executed and a 1/3 chance of surviving. Therefore h = 2/3
b. If Mark and Luke are both to be executed, the jailer will give Matthew the name of one of them at random, with probability 1/2
c. the jailer will not lie.
With these assumptions, e|h is 1/2. The condition h is fulfilled if Matthew and Luke are to be executed, or if Matthew and Mark are to be executed. By assumption these events are equally probable. If Matthew and Luke are to be executed, the jailer cannot tell Matthew that Mark is to be executed (since the jailer does not lie). If Matthew and Mark are to be executed, the jailer is bound to say that Mark is to be executed. The conditional probability e|h is therefore (1/2 x 0) + (1/2 x 1) = 1/2.
The unconditional probability of e is also (coincidentally) 1/2. There are two circumstances in which the jailer will say that Mark is to be executed: either, with probability 1/3, Matthew and Mark are to be executed, in which case e has a probability of 1, or, also with probability 1/3, Mark and Luke are to be executed, in which case there is a probability of 1/2 that the jailer will choose to give Mark’s name. The total probability of e is therefore (1/3 x 1) + (1/3 x 1/2) = 1/2.
Putting the various components together, we get h|e = (2/3 x 1/2)/1/2 = 2/3. The antecedent probability of 2/3 that Matthew will be executed therefore is not changed by the information he is given, and he is wrong to feel happier.
This may seem at first sight inconsistent with the Monty Hall puzzle, where the probabilities do change when Monty opens one of the doors. But the two cases can be reconciled if we consider the probability that Luke will be executed. Suppose for example that Matthew wants to place a bet on who will survive, with the proceeds to go to his widow if he does not survive himself. Initially there is an equal 1/3 probability that each of the prisoners will survive. But if Matthew persuades the jailer into giving him Mark’s name as described in the Serbelloni problem, then the probability that Luke will survive increases to 2/3, and Matthew (or rather his widow) will stand to gain by betting on Luke’s survival rather than his own (given the same betting odds), since Matthew himself still only has a 1/3 chance of survival. This can also be shown using Bayes’ theorem, but I leave that as an exercise for the reader!
Added on June 7:
- draw three lines of equal length (say, 2 inches) in pencil. These can represent the number of times each of the three outcomes (Matt/Mark, Matt/Luke, Mark/Luke) will occur in a large number of similar cases
- now rub out parts of the lines representing those cases where the jailer does not say that Mark is to be executed. This means you have to rub out the whole of the Matt/Luke line and half of the Mark/Luke line.
- you are left with the whole of the Matt/Mark line (2 inches) and half of the Mark/Luke line (1 inch), totalling 3 inches. These represent the posibilities remaining after the jailer's announcement. Mark is executed in all of these cases, Matt in 2/3 of them, and Luke in 1/3, which is consistent with the Bayesian conclusion.
As a matter of historical interest, the Serbelloni problem seems to pre-date the Monty Hall puzzle. The latter became notorious around 1990, though I have found a reference to it in the 1980s. But the Serbelloni problem goes back at least to 1966, the date of the conference. However, in a slightly different form it is also to be found in a puzzle by Martin Gardner in 1959. In Gardner's version the prisoner and the jailer have an argument about whether he should give him the information.