skew in Facebook friend-count distribution at various levels of intimacy

Social relations can can be modeled as a hierarchy of intimacy.  Among much larger sets of contacts or acquaintances, most persons maintain only a small number of close friends.  A recent analysis of Facebook data found:

although the average Facebook user has 130 friends, they only communicate directly with four of those people in any given week. Direct communication includes likes and comments on their posts, posts on their wall, chat conversations, video calls, and private messages.

People I talk to are always surprised at how low the number is – only four people per week, and only six people per month. What’s more, the majority of people in these small groups remains consistent from week to week – for example, our partner, our closest friends and family.

Facebook data also show considerable skew in the number of friends.  Consider Facebook users who have been on Facebook at least 6 months and have logged in at least 80% of days during the past 6 months.  Among those Facebook users, consider the number with whom a given user has “reciprocally exchanged communication explicitly directed towards alter at least twice in a month.”  The median number of these close friends for a given user is 3, but the mean number is 6.3.  Those figures indicates considerable skew in the distribution of the number of close friends.  In fact, 25% have eight such close friends, 10% have 17, and 5% have over 25.  The volume of communication with these close friends also has considerable skew: the median number of communications per close friend per month is 19, while the mean is 60.2.[*]  Similar skew occurs across every level of friend intimacy.

Heterogeneity in social capabilities and differences in friendship investments spread the friend-count distribution.  Some persons are better at socializing than others, either through natural or technological advantages.  These capability differences support differences in friend counts across persons.  But another possibility is differential investment in communication.  Text messaging has surpassed voice calls in part because text message requires less relational effort than real-time voice calls.  Marking a “like” on a friend’s post requires much less relational effort than comforting a grieving friend.  Those with more friends may be less invested per friend, even with a similar volume of direct communication per friend.

Understanding the economics of social relations is important for understanding communication industry developments.  Identifying within the friend-count distribution spread the different effects of communication-capability heterogeneity and differential per-friend investment would contribute to that understanding.

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skew in friends and communication by level of closeness (Excel version).  For a model of levels of relational closeness, see Sutcliffe, Alistair, Dunbar, Robin, Binder, Jens and Arrow, Holly (2012), “Relationships and the social brain: Integrating psychological and evolutionary perspectives.” British Journal of Psychology, 103: 149–168. doi: 10.1111/j.2044-8295.2011.02061.x


[*] Pp. 170-1 in Kraut, Robert E. and Rosenn, Itamar (2012), “Comment on relationships and the social brain: Integrating psychological and evolutionary perspectives.” British Journal of Psychology, 103: 169–173. doi: 10.1111/j.2044-8295.2011.02074.x

visual poetry: a Hellenistic "coronis" epigram

Ancient Greek epigrams typically have a speaking object directly addressing the viewer/reader.  For example, an epigram engraved on a memorial stone at Thermopylae commemorated a Spartan army that fought there to the last man against an invading Persian army.  The epigram declares:

Stranger, go tell the Spartans
That we lie here
True, even to the death
To our Spartan way of life.

The literary conceit is to charge someone unaware of the battle with the momentous task of conveying the news, while the existence of the memorial itself testifies to both the news’ importance and reception.

By the Hellenistic period, epigram had become a highly refined literary form.  Epigrams never to be engraved in stone were written to circulate in books among the literary elite.  Epigrams such as those about Myron’s Cow and Medea intricately interrelated visual and verbal effects.[1]  Beneath an often playful surface, epigrams were allusive, self-reflective, conscious of epigrammatic predecessors, and communicatively complex.  Consider, for example, this epigrammatic representation of cleverly interpreting a non-verbal epigram:

Let me see whose death this stele reports.  But I see
no writing engraved anywhere on the stone,
just nine dice, tossed, of which the first four
bear witness to the throw called Alexander,
the next four the ephebe throw, the bloom of youthful maturity,
and this one shows the lowest throw, the Chian.
Do they announce: “A man who proudly ruled with the sceptre
and was in the bloom of youth came to naught”?
No, that’s not it, but I think that now I shoot my arrow
straight at the target, like a Cretan bowman.
The dead man was a Chian, he had acquired the name
of Alexander, and he died in ephebic youth.
How well someone has said with voiceless dice that the young man
died through recklessness, his life stacked and lost. [2]

As this epigram explains, the straight-forward interpretation is not it.  The details tell and ring poetically.

An obscure book curse appears to be a highly literary Hellenistic epigram.  At the end of a relatively unimportant third-century papyrus roll appears the text:

I am the coronis, guardian of letters.
The reed pen wrote me, the right hand and knee.
If you should lend me to someone, take another in exchange.
If you should erase me, I will slander you to Euripides.
Keep off! [3]

Medieval and early modern book curses typically are formulaic and not highly literary.[4]  With a speaking object engaged in direct address, this Hellenistic-era book curse belongs to the more creative genre of epigram.  The existing literature on Hellenistic epigram seems to have overlooked it.  Yet it has considerable literary merit.

This Hellenstic epigram includes subtle visual poetry.  The epigram is obviously multi-voiced.  The coronis, a textual symbol that marks the separation or end of major sections in ancient Greek papyri, speaks “I am the coronis.”  But the book roll is the reference in the line, “If you should lend me to someone, take another in exchange.”  The best literary division of the voices is to have the coronis as a separating voice speaking the first and last lines.[5]  That’s visual poetry that parallels the coronis’ visual work of separating.  That work is expressed verbally, in the context of poetic dynamism, as guarding and “keep off.”

The reference to Euripides has considerable literary weight.  The book roll contains a copy of books three and four of the Iliad.  Homer was the most celebrated poet in the Hellenistic world.  Euripides in the Hellenistic era was popularly known through solo actors, probably including celebrity pantomimes, performing dramatic highlights from his tragic plays.[6]  To the literary elite, that popularization of Euripides was probably equated to destroying Euripides’ literary value.  Threatening to “slander you to Euripides” for erasing Homer’s Iliad might well be a literary allusion and response to the post-classical shift in the popular marketplace for poetry.[7]

The epigram has other noteworthy literary features.  A book owner might lend a valued book to a friend as a special favor.  The phrase “take another in exchange” places lending a book in a context like that, common in the ancient world, of exchanging political hostages to secure an agreement among hostile powers.  “The reed pen wrote me, the right hand and knee” figures the scribe through metonymy expanding from the reed pen to the scribe’s right hand and knee to the scribe’s whole person.  That representation suggests a dedicated, professional scribe.

The person who inscribed the epigram and the copy of the Iliad wasn’t doing elite literary work.  The catalog entry for the manuscript describes the script as “rough, ugly uncial.”  Moreover, within the text,“mistakes in orthography and copying are common.”[8]  Just above the epigram, which is written on a separate sheet at the end of the roll, the writer apparently wrote three coronides, which increase in figural complexity from left to right.[9] Moreover, this literary text is written on the back (verso) of a bureaucratic papyrus — a tax-assessment document.  Compared to parchment, which was also in use in the third century, papyrus is relatively cheap.  This epigram has been preserved in a low-value copy.

This epigram almost surely originated in an earlier, elite literary parchment.  The epigram refers to erasing the text.  Relatively few rewritten papyrus rolls have been found.  Erasing the back side of a papyrus roll that contains on the front side a bureaucrat text is completely improbable.  A reference to erasing the text would make sense within an expensive, original-use parchment roll.  The epigram’s high literary sophistication points to an elite literary audience.  A luxurious copy of the Iliad for a literary patron is probably the original context for this epigram.

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Update: more general information on marking the end of books in the ancient world.  Here’s another coronis epigram:

I, the coronis, announcing the final lap, the most trustworthy guardian of the enclosure of written sheets, proclaim that Meleager has brought his labour to an end, having gathered all the works from all lyric poets into one collection and having wrapped them into this roll. And that from flowers he has twined together one poetic wreath worthy of remembrance from Diolces. And, curled in coils like the back of a snake, I am sitting here enthroned beside the conclusion of his learned work.

Palatine Anthology, 12.257, trans. p. 16-17 n.35, in Schironi, Francesca. 2010. To mega biblion: book-ends, end-titles, and coronides in papyri with hexametric poetry. Durham, N. C.: American Society of Papyrologists (via Roger Pearse).

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[1] On Myron’s Cow, see Squire (2010).  Asterius of Amasea, a late-fourth-century Christian bishop, provides an insightful example and perspective on ecphrasis.

[2] Antipater of Sidon 32 GP (=AP 7.427, trans. Gutzwiller), quoted in Meyer (2007) pp. 207-8.

[3]  From Papyrus 136, held in The British Library.  The text in Papyrus 136 appears to have a rectilinear arrangement of eight lines with the last word on an additional line. See Drogin (1983) p. 56, Plate 17 (image of papyrus sheet). Trans. Haines-Eitzen (2000) pp. 109-10, which also provides the Greek.  The arrangement of the Greek text above is my interpretation of the sense of the original text.  See subsequent discussion above. Drogin (1983) pp. 55, 57 provides alternative translations.

[4] See examples in Drogin (1983).

[5] Haines-Eitzen (2000) p. 110 gives the coronis only the first line.  Drogin (1983) p. 57 gives the “colophon” the first two lines.

[6] Hall (2002) pp. 13-8.

[7] Book 3 of the Iliad pits Paris and Menelaus in man-to-man combat.  Aristotle’s Poetics associates tragedy and epic, describes tragedy as superior to epic, and names Euripides as the greatest of tragic poets.  The above epigram may also be alluding to these literary-critical references.

[8] To find the catalog entry, search the British Library’s Catalog of Archives and Manuscripts using the terms “papyrus 136 Iliad tax” (without quotes).

[9] Drogin (1983) p. 56, Plate 17, provides a photo of the relevant papyrus section.


Drogin, Marc. 1983. Anathema!: medieval scribes and the history of book curses. Totowa, N.J.: Allanheld, Osmun.

Haines-Eitzen, Kim. 2000. Guardians of letters: literacy, power, and the transmitters of early Christian literature. Oxford: Oxford University Press.

Hall, Edith. 2002.  “The Singing Actors of Antiquity.” Pp. 3-38 in Easterling, Patricia E., and Edith Hall. 2002. Greek and Roman actors: aspects of an ancient profession. Cambridge, U.K.: Cambridge University Press.

Meyer, Doris. 2007. “The Act of Reading and the Act of Writing in Hellenistic Epigram.” Pp. 187-210 in Peter Bing & Jon Steffen Bruss (edd.). Brill’s Companion to Hellenistic Epigram Down to Philip. Leiden: Brill, 2007 (Brill’s Companions in Classical Studies).

Squire Michael. 2010. “Making Myron’s cow moo? Ecphrastic epigram and the poetics of simulation.”  American Journal of Philology. 131 (4): 589-634.

COB-70: bureaucracy triumphed over Bolsheviks

Cindzmarauli, Stalin's favorite bottle of wine

In an important and insightful recent article, Tatiana Yu. Borisova has shown the enduring importance of bureaucracy.  She shows that “old bureaucratic means of writing and distributing legislation to the local soviets” became dominant within months after the Bolshevik revolution in Russia in 1917.  The Bolsheviks adopted internationally standard bureaucratic language, including “a particular syntax (complex syntactical constructions), a particular vocabulary (conservative and filled with special terminology), and a system of broad formulations.”  This scholarship indicates the need for deepening and intensifying the reconstruction of socio-economic systems worldwide by coalitions of expert bureaucratic organizations committed to overcoming the worsening economic crises and fiscal imbalances that threaten the unity of governing bodies that are crucial to the continuing welfare of the people, especially women, children, and the disabled, who face grave danger from forces attacking the foundations of equitable and self-governing states.

In other bureaucratic news, Max Zografos was fired from Microsoft.  Among other problems, he failed to appreciate the importance of meetings:

Microsoft culture expects you to be in meetings. Calendars need to be decorated with sufficient colourful blocks, to signal over-activity.

Dig a bit deeper and you’ll realise that Microsoft meetings are a way to diffuse and evade responsibility for decisions. Yes – let’s spend weeks and weeks “reviewing with stakeholders.” It’s so much safer that taking swift decisions ourselves. The company places no trust on the individual to make the right decision on their own.

Since being fired, Mr. Zagrofos states that he has “Never been so content, fit, and healthy.”  While that may be true, as exemplary bureaucrats, we hate to see anyone get fired.  The lesson is obvious: schedule and attend many meetings, and maintain your position.

Yahoo’s top manager has decided, “It’s time for Yahoo! to move forward, and fast.”  From a bureaucratic perspective, that sounds bad.  However, the plans for moving forward involve a corporate reorganization.  That’s bread-and-butter bureaucratic work.  In 2009, a prior Yahoo CEO also did a reorg to help Yahoo move faster and become more customer-focused.  Hence Yahoo’s bureaucratic specialists should be well-prepared to implement this reorg.

Bureaucrats need to stick together, or they risk falling like dominoes.  Consider media developments in Britain:

Some journalists shrug at the news that BBC local radio may lose its station managers. Bon voyage, bureaucrats! But shrugs turn to shivers when it emerges that the corporation’s next director general need never have made a programme, or indeed edited anything. And now Johnston Press, commanded by a former BBC digital wizard, begins to abolish editors for individual papers themselves, merging and melding from Edinburgh to Leeds as though they were, well, managing local radio stations.

Managing and editing is critical, generic bureaucratic work.  When one manager or editor falls, others face increased risks.  The only solution is to advocate for an increased number of managers and editors.

That’s all for this month’s Carnival of Bureaucrats.  Enjoy previous bureaucratic carnivals here.  Nominations of posts to be considered for inclusion in next month’s carnival should be submitted using Form 376: Application for Bureaucratic Recognition.

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Reference: Borisova, Tatiana, The Legitimacy of the Bolshevik Order, 1917-1918: Language Usage in Revolutionary Russian Law (March 20, 2012). Higher School of Economics Research Paper No. 05/LAW/2012.  Available at SSRN: or

deadly sex discrimination in Titanic chivalry myth reporting

April 15, 2012, was the centennial of the sinking of the Titanic.  Coincidentally, five days before that centennial, two authors posted online a working paper, “Every man for himself: Gender, Norms and Survival in Maritime Disasters.”  The next day their employer described that working paper in a press release entitled “Titanic is an Exception among Disasters at Sea.” By the next day, the Associated Press (AP) was distributing this news under the title “Researchers: Titanic was an exception, male {sic} chivalry on sinking ships is ‘a myth’.”  The Washington Post, the NY Daily News, the Globe and Mail (Toronto, Canada), and other leading news sources ran the AP article on that same day.  By the centennial of the Titanic’s sinking, about 300 online news sources from Malta to India to Australia were running this news.

In reporting this news, major news organizations mislead their readers, presented absurd statements, and furthered grotesque sexism.  The news stories reported that “two Swedish researchers … economists Mikael Elinder and Oscar Erixon of Uppsala University” did an “82-page study.”  That “study” was the working paper posted online five days before the Titanic’s centennial.  The main text of the working paper spans six pages.  The news reports described the working paper as if it were objective, authoritative scholarly research. To encourage readers to remain ignorant of its credibility, none of the news stories linked to the working paper.  News reports thus presented as scholarly research what would be better understood as a tendentious media gambit.

Recognizing grave weaknesses in the story of the working paper / press release should not have been beyond the capabilities of a professional journalist.  For example, the press release states:

It is expected that the crew should rescue passengers, but our results show that captains and crew are more likely to survive than passengers.

That’s a non sequitur.  Consider the relationship between the two independent clauses.  Is it necessary for the captain and crew to be more likely to die in order for them to work to rescue passengers?  Try to think of any other factors besides helping passengers that would be relevant to the differential survival of the captain and crew (hint: experience at sea and swimming ability).  The bottom of the news report includes a quote from a ship captain making this obvious point. The news story presents the captain’s statement merely as another viewpoint, rather than as reasoning that seriously undermines the value of paying any attention to the working-paper’s “findings.”

The news article presented statistics to impress and factually dominate the reader, but not statistics that usefully and accurately inform.  See if you notice a problem with these two statistical statements from the news article:

  • Out of the 15,000 people who died in the 18 accidents, only 17.8 percent of the women survived compared with 34.5 percent of the men.
  • Of the 1,496 people that perished with the Titanic, 73.3 percent of the women and 50.4 percent of the children survived compared to only 20.7 percent of the men.

These statistics make no sense.  How could a share of the persons who died have survived?  The above first sentence of statistical gibberish apparently is based on these sentences in the working paper:

Table 2 reports tests of each of the 6 hypotheses conducted in separate regressions, as well as together in one regression. We find that the survival rate of women is 16.7 percentage points lower than, or about half of (17.8% vs. 34.5%), that of men.[1]

Here a survival rate is described as a percentage apparently related to hypotheses tested in regressions.  The meaningfulness of those numbers depend on a vast array of other assumptions and specifications in the working paper’s analysis.  Most of those assumptions were not statistically supported.  In short, the working paper is also filled with statistical gibberish.[2]

full set of sinking ships
sinking ships authoritatively discriminating against men
persons on ships
persons perished
% perished
persons on ships
persons perished
% perished

Those interested in the truth start with understanding simple facts.  While the working paper failed to provide a summary table of deaths by sex, such a table can be constructed from the working paper with some additional work. In the working paper’s set of sinking ships, 60% of the males and 68% of the females on the sinking ships died.  To what extent does that death-share difference reflect differences in seafaring experience and relevant physical skills?  The working paper didn’t evaluate that issue.  Even if men did privilege women on sinking ships, a higher share of men could still survive if they had more sea experience and better swimming ability.

Nearly twice as many males died on the sinking ships as did females. That fact points to sex-differentiated exposure to risk.  Women have been shielded from significant risks to which men are subject.  For example, in contrast to wide-ranging efforts to promote gender equity in the workplace, men still predominate in the most dangerous jobs.  In the U.S. in 2006, the dead person in 92% of workplace fatalities was a man.  Among U.S. soldiers on active duty in 2008, men outnumbered women by about six to one.  Among U.S. soldiers killed in Iraq, men outnumbered women about forty-two to one.

Authoritative discrimination against men on sinking ships is associated with a higher share of men perishing and a lower share of women perishing. For those sinking ships in which the captain ordered that women and children go first into the lifeboats, 71% of the males perished, while 51% of the females perished.  On sinking ships in which the captain is known not to have ordered sex discrimination for the evacuation, the shares perishing were nearly the reverse: 50% of males and 70% of females.  Thus an accurate and meaningful finding can be uncovered: on sinking ships, authoritative sex discrimination against men has deadly effects on men.[3]

The working paper and the press release presented these facts much differently.  Following a similar statement in the working paper, the press release declared:

On the ships where the captain gave the order ‘women and children first’, the difference in survival rates between men and women is lower. But women survived to a higher extent than men only when this order was enforced by the threat of violence.

This indicates an important role of leaders in the face of disasters. It is, however, unusual for captains to give such an order. [4]

The European Union was explicitly founded as a society in which “non-discrimination … and equality between women and men prevail.”[5]  Uppsala University in Sweden seems to support leaders threatening violence against men to uphold sex discrimination against men on sinking ships.  Underscoring its commitment to sexism and anti-male bigotry, the working paper’s title describes not privileging women and children as “every man for himself.”

In a disaster, many ordinary men may have a gut sense of their equal worth as human beings.  They may act accordingly.  That doesn’t mean that men would not or do not help some others deserving of help.  But, in extraordinary circumstances, many ordinary men may reject their categorical disposability.

In ordinary circumstances, men tend to accept their disposibility without protest.  That’s modern chivalry.  The communicative success of the Uppsala University working paper testifies to the enduring significance of such chivalry.

Universities and major media can help to guide societies to the secure shores of justice and truth.  Many today, especially in Europe, are now far out at sea.  Don’t follow an inhumane and untruthful order into the blue void.  Seek your own saving way!

Women's Titanic Memorial, Washington DC

Data: set of sinking ships, with characteristics and sex-differentiated death totals (Excel version)

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[1] Elinder & Erixson (2012) p. 6.

[2] The quality of the statistical work in Elinder & Erixson (2012) appears to me to be so low as to not merit attention. Its hypothesis are laughably ill-formed, its framework of hypothesis testing is not credible (do you really believe that those hypotheses were formulated independent of the data? What does that imply for the interpretation of statistical tests?), the results are incompletely reported, the data have not been posted, the model forms chosen are not well justified and tested, etc.  The main value of Elinder & Erixson (2012) is to intimidate untrained readers and obscure simple facts.  While Elinder & Erixson (2012) has not undergone peer review, many peer-review publications present false results.  The institutional problems that Begley & Ellis (2012) identify in preclinical cancer research are even worse in economic research.

[3] The data in Elinder & Erixson (2012) do not consistently distinguish adults and children.  Because the number of young children is probably relatively small, males and females are reasonable proxies for men and women.

[4] In their concluding main section entitled “Discussion,” Elinder & Erixson (2012), p. 8, states:

Most notably, we find that it seems as if {sic} it is the policy of the captain, rather than the moral sentiments of men, that determines if women are given preferential treatment in shipwrecks. This suggests an important role for leaders in disasters.

[5] See Treaty of the European Union, Article 2.


Begley, C. Glenn, and Lee M. Ellis. 2012. “Drug development: Raise standards for preclinical cancer research.” Nature. 483 (7391): 531-533.

Elinder, Mikael and Oscar Erixson. 2012.  “Every man for himself: Gender, Norms and Survival in Maritime Disasters.” Uppsala Universitet, Department of Economics, Working Paper 2012:8.

Update:  The Proceedings of the National Academy of Sciences of the United States of America (PNAS) received the paper for review on May 2, 2012, approved it on June 29, 2012, and published it on July 30, 2012.  It was published as Elinder, Mikael and Oscar Erixson. 2012. “Gender, social norms, and survival in maritime disasters.”  doi:10.1073/pnas.1207156109  The publication in PNAS generated another round of coverage in major news sources.  While the second round of press reporting seems to have avoided obvious statistical blunders, the reporting provided no critical perspective on the article’s claims.

The peer review of the paper did little to improve it.  The criticisms above still apply.  PNAS published online a supporting dataset with the article.  The organization of the dataset, which shows no regard for informative data structure, is further reason to doubt the article’s tendentious statistical analysis.

Here’s an example of the article’s scientific veneer:

A small survival disadvantage for women is difficult to interpret, as it can either indicate that the WCF norm has helped women from a potentially larger disadvantage or that the norm has not been upheld. However, if we observe a substantial survival disadvantage of women we regard it as evidence that compliance with the WCF norm is exceptional in maritime disasters. (p. 1)

Note the technical-normative babble “compliance with the WCF norm” and “the norm has not been upheld.”  The actual issue is whether passengers and crew valued women’s lives and children’s lives above men’s lives.  This paper strives to make that gender inequality into a norm for which society demands compliance.  In the historical shipwreck sample, men are likely to differ significantly from women in sea-survival skills and physical capabilities.  With regard to isolating the quantitative extent to which men helping women affects men’s and women’s differential survival, the article offers little actual quantitative evidence.  Instead, the article states: “if we observe a substantial survival disadvantage of women we regard it as evidence…”  The observed facts aren’t actually evidence of the authors’ claim; the authors merely “regard it as evidence.” I regard this article as evidence that junk statistical work, if appropriately tendentious, gets published quickly in PNAS.