why social networks are overrated (a 3+ when they are at best a 2)

One reason I believe that “fundamental values” constrain our valuations, however loose such constraints may often be, is that I have been fortunate to witness and participate in two intellectual revolutions that have clearly improved our understanding of the world.  In each case, I had early exposure to a new “science” that was something of a fringe movement.  But as the successes of the science became undeniable, it was widely embraced and established as the new common wisdom.

The first of these revolutionary sciences is one many readers may find trivial due to its subject matter, but may be the clearest example of scientific advance that I know of.  I’m referring to Sabermetrics, the set of methods introduced by Bill James and his colleagues to analyze the performance of baseball players and teams.  With his sharp, unsentimental eye and his vast gifts for framing problems and devising simple but ingenious approaches to addressing them, James subjected common wisdom in the baseball community to scientific analysis and showed its deep flaws.  I still remember the day I happened upon the 1984 Baseball Abstract at Brown Bookstore (as Jenn knows, I grew up in Providence, RI) and sat there for hours as my eyes were opened by James’s revolutionary and clear-sighted mode of analysis.  I subsequently ran into many others of my generation who had had the same epiphany.  And while at the time, the Sabermetrics community took pride in its counterculture identity, it is amazing in hindsight how quickly it overturned the establishment.  As Michael Lewis relates in his bestseller Moneyball, Oakland A’s general manager Billy Beane used Sabermetrics to arbitrage between price and value (e.g., by leveraging the Sabermetric insight that the ability to draw walks was a greatly undervalued skill), and thereby helped his impoverished team to compete with richer teams for over a decade– until the rich folks adopted Sabermetrics as well.

I had a second epiphany 6-7 years after that first one.  It occurred as I was walking in front of my Columbia dorm, Wien Hall.  I had been reading Burt’s (1982) Towards a Structural Theory of Action and mulling over his theory of structural autonomy, which he measured in social-network terms and applied to a market setting– in particular, the flow of exchange between sectors of the US economy, as captured in input-output tables.  The eureka moment was when I “realized” that this was all a market was– repeated flows of exchange between actors.  Whereas the market had once been something of a mysterious abstraction in my mind, it was now something “concrete” (a mantra for early network analysts, if there ever was one!).  If one wanted to see and understand a market, all one needed to do was to find the actors/nodes and the trades.  And if one wanted to understand which actors would be more successful in the market, one needed but to identify the actor’s position in the network of exchange that constitutes a market.  Moreover, the immense power of this perspective was that it could seemingly be used to understand and analyze a wide variety of otherwise abstract features of social life.  For instance, what is a social role if not a pattern of relationships between its incumbents and others?  What is a group or organization if not just a set of nodes and a set of relations among such nodes?  Where indeed does the identity of an individual person lie, if not in her relations to others?  As Harrison White wrote in Chains of Opportunity (1970: 5): “Consider how an impostor is exposed.”  (I used this as the epigraph of my 1999 AJS paper).  The idea is that your identity is a function of how others relate to you.  You can say you are the messiah, but what matters is whether others agree, as reflected in their relationships with you.  A real messiah has a very different network from a false one.

And as with the case of Sabermetrics, what was once a minor, brash subfield at the time I encountered it (though further along, at least in sociology) has since diffused widely to become a very popular mode of analysis, not only in the social sciences (spreading even to economics, which we used to caricature as “hopelessly atomistic”!) but in the natural sciences and even in the social and business world (Web 2.0!!).  As the details of this movement are well-known to orgtheory readers, I will not rehearse them here.  Suffice it to say that there has been an incredible boom of interest in and use of social networks. It is not far-fetched to describe a social networks boom, a mania.. or even, dare I say, it a “bubble”– in the specific sense that it is now overvalued relative to what it can reasonably deliver.

Why would I suggest such heresy?  Well, there are several reasons, but I want to spare you another zillion-word post.  Let me zero in on one key reason.

One of the features of social network analysis that is at once a great strength and a great danger is that network diagrams are highly evocative.  In teaching and presenting network material, I have found that if I put up a picture of a network and start spinning a story about it, even untutored audiences follow along easily and they tend to accept the network as an accurate characterization of the actors and the social structure they inhabit.  This is great, but the problem is that any such presentation tends to bake in all kinds of assumptions that should always be questioned.  Many of these issues are well-known among long-time practitioners, though are generally not appreciated by novices: (a) how to specify the boundary of the network [i.e., which are the set of nodes that are at risk for having a tie]?; (b) how to deal with different perceptions of the presence or absence of a tie?; and (c) how to deal with the fact that there are  infinite ways of defining a tie, each of which produces a different image of the network?  I review these issues and some related ones [with cites to key sources] in this essay.

The aforementioned issues are daunting, though they can often be handled well-enough to do a reasonably useful social network analysis (SNA).  But there is an additional issue that, I contend, renders SNA rather impotent.  And more generally, it points to the limits of what interaction through networks can achieve.

In a sense, the issue I have in mind is a version of the third problem listed above– i.e., how do we define what a link is.  Note that this is not really a problem if we focus on dyads.  What constitutes a dyad?  Well, as long as we are able to distinguish two entities from one another and say that they have some sort of relationship with one another, we then basically have a dyad.  But the term “network” implies more than two actors.  And as Simmel taught us, things get both much more interesting and more challenging when we go from dyads to triads (after that, the issues tend to be qualitatively the same, even if quantitatively different).  Quoth Simmel:

[On the one hand…] Points that cannot be contacted by the straight line are connected by the third element, which offers a different side to each of the other two, and yet fuses these different sides in the unity of its own personality.  Discords between two parties which they themselves cannot remedy, are accommodated by the third or by absorption in a comprehensive whole.  Yet [on the other hand…] the indirect relation does not only strengthen the direct one.  It may disturb it.  No matter how close a triad may be, there is always the occasion on which two of the three members regard the third as an intruder.  The reason may be the mere fact that he shares certain moods which can unfold in all their intensity and tenderness only when two can meet with out distraction: the sensitive union of two is always irritated by the spectator.  It may also be noted how extraordinarily difficult it is for three people to attain a really uniform mood—when visiting a museum, for instance, or looking at a landscape—and how much more easily such a mood emerges between two.  A and B may stress and harmoniously feel their m, because the n which A does not share with B, and the x which B does not share with A, are at once spontaneously conceded to be individual prerogatives located, as it were, on another plane.  If, however, C joins the company, who shares n with A and x with B, the result is that (even under this scheme, which is most favorable to the unity of the whole) harmony of feeling is made completely impossible. Two may actually be one party, or may stand entirely beyond any question of party.  But it is usual for just such finely tuned combinations of three at once to result in three parties of two persons each, and thus to destroy the unequivocal character of the relations between each two of them (emphasis added).”

— pp. 135-6 from Kurt H. Wolff (trans., ed. and introduction). 1950. The Sociology of Georg Simmel. The Free Press: Glencoe, IL.

What an amazing summary of both the power and limits of networks.  On the one hand, adding a third to a dyad can serve as a source of balance and can, more generally, be the basis for a unified collectivity that is greater than the sum of its parts.  But on the other hand, how the heck do we get everyone on the same page, and when is it reasonable to assume that they are?  To see the challenge here, let’s focus on the analytic problem that Simmel poses– i.e., that if you have three people– A, B, and C– you may have three different types of relationships— A-B is of type m; A-C is of type n; and B-C is of type x.  (Apparently, Simmel had never heard of the letter o?)  If this is the situation, wherein lies the network?  Rather than anything that can really be called a triad, what you have is a collection of three dyads.  In order to call it a network, we must be able to say that the links are of the same type throughout the network.

(One might object and say that early social network analysts were fond of stacking different types of relations and analyzing the stacked matrix.  That’s true to a point, but the only way one can justify this practice is through the assumption that the different types of relations could be all treated as realizations of a comparable type of tie.  Otherwise, stacking cannot be justified.)

Ok, so maybe this is not such a big deal.  After all, SNA is a huge industry now and in order to be as successful as it has been, it must be succeeding at finding tie criteria that are meaningful across an entire network.  No doubt.  And this is why I myself am an SNA practitioner.  Great insights about social structure and how it affects outcomes we care about can be learned by making such assumptions and analyzing the networks they imply.

And yet, there are some really interesting, very important interactions which simply cannot be reduced to a common type across dyads without losing what is essential to them.  In particular, note that in order to specify a common criterion to draw links throughout a population, one must eliminate anything that is particular to the actors involved.  That is, the link cannot have “indexical” properties such that it means something different depending on who is on either side of it.  Thus, if A and B have an AB type relationship; B and C have a BC type relationship and so on, we are back to Simmel’s problem.  It must instead be the case that there is a common type, and this implies that anything particular to the parties involved is removed. 

But this seemingly innocuous requirement means that some very important interactions do not occur through networks and cannot be captured by SNA.  In the remainder of this post, I’ll briefly discuss two examples: (a) gossip; and (b) common knowledge.

a. Gossip

Gossip is the lifeblood of any social system.  We are constantly talking about one another behind one another’s backs.  And this information is generally not “idle” but is used to make decisions how we will interact with that person.  You would think that the analysis of the spread of gossip would be ideal for SNA.  After all, how does gossip spread if not through networks? 

This was certainly the assumption held by a prominent social network analyst, who gave a seminar I attended a few years ago.  At the seminar, he discussed how he had collected SN data based on asking members of a community who their confidants are.  He then related that the network was fully connected, and suggested rather smugly that the joke was on his respondents.  They thought their secrets were safe with their friends; but those friends had other confidants, and so on.  As a result, the confidences spread (becoming “gossip” in the process), till everyone knew. 

But is this really how things work?  No.  The key thing about gossip is that it encodes network information.  It is not simply sensitive information.  It is sensitive information about the speaker’s relationship to a third party, and the utterance conveys something about the speaker’s relationship to her interlocutor.  Put differently, gossip is an offer of conspiracy by the speaker to the interlocutor, where the conspiracy targets the third-party.  And there are as many conspiracies as there are dyads in a network.  The problem though is that while there are many such dyads, it is not clear that there are any triads, in Simmel’s sense.  That is, A and B may gossip about C; A and C may gossip about B; and B and C may gossip about C– and these conspiracies remain stable and separate.  It is again like they are three types of relationships (type AB for talking about C; type AC for talking about B, etc.).  I would urge the reader to introspect and see whether this is not how much of your social life is conducted.  We are constantly talking with others about third-parties and saying different things in those conversations from what we say when the second-parties become third-parties, and so on.  In short, to say that A confides in B and B confides in C does not imply that anything A tells B will end up in C’s ears.  It might under some circumstances.  But it often will not.  And more generally, insofar as the links between actors are based on communications that refer to specific others (in the network), they are indeed “indexicals” and thus cannot be regarded as members of the same type.  There is thus no triad, just a set of (AB, BC, and CA) dyads– in which the content of each tie involves the third party!

There is obviously a lot more one can say about this issue.  But I will stop here at just giving a taste of the problem, and move on to the second one.

b. Common Knowledge

To see the second problem, assume for the moment that that the various members in a gossip network do in fact betray one another’s confidences.  I tell you something confidential about myself, you then (turn it into gossip) by relating it to someone else, and so on, until everyone in the network knows it.  (Of course, no one will tell it to me!)  Let’s make the example concrete.  Let’s say that I told you that I made up the data in one of my studies.  One might think that the cat is now out of the bag, and that I am now unmasked as a fraud.  Scandal!  My career is over!

Ah, but will there be a scandal?   Ari Adut’s deeply insightful work indicates that the answer is often ‘no.’  While it is now widely known that I am a fraud, it is not commonly known in the specific sense that each member of the network only knows that their contacts know, but they do not know that everyone knows.  This is again a fundamental difference between the dyad and the triad.  When A communicates with B in a dyad, we can say not only that a piece of information is now shared by both A and B, but that A and B know that they both know that piece of information.  And the same is true when B communicates with C– any information that passes between them is common knowledge.  However, when A passes on something to B, who passes on something to C, A and C will not know (for sure) whether they have the same information as one another.  And so on.  Everyone can have the same knowledge but not know that they have the same knowledge.  This is “pluralistic ignorance” (a term that is widely credited to Floyd Allport, with the earliest cite I have been able to find being from his 1924 book Social Psychology).  Centola, Willer, and Centola (2005) show how the failure of networks to convey what everyone knows (conveying only local knowledge instead, and thus fostering pluralistic ignorance) can systematically lead people to act counter to their true beliefs.  And Adut shows how widespread knowledge of an indiscretion can persist for a long time, with scandal erupting only when the information becomes publicized in such a way that it becomes common knowledge.  The knowledge that I’m a fraud can become widely disseminated, but this knowledge has no effect on my fate unless it is publicized in such a way that it becomes common knowledge.  (See also Rodrigo Canales‘s research for how the distinction between private and public beliefs is crucial for understanding how institutional entrepreneurs emerge and endogenous institutional change can happen even when there is apparent convergence on a set of beliefs that support the status quo).

I discussed another example of networks failing to convey common knowledge in my last post— i.e., how knowledge that we were in a bubble was widely dispersed, but only became actionable knowledge with the emergence of the ABX indexes, which provided a vehicle that allowed private beliefs to be publicized and become common knowledge (Rodrigo C subsequently pointed me to this paper with a terrific natural experiment of this effect). Indeed, I now believe that my epiphany back in front of Wien Hall was based on a relatively impoverished view of markets.  Markets cannot be fully captured in the pattern of exchanges in the system.  Rather, a crucial part of market functioning is the system of communication that conveys the information in such exchanges (e.g., prices and other matters relevant to decision-making).  It really matters whether there is an institution like the Walrasian auctioneer (who makes prices visible to all, and thus common knowledge) or whether prices and other terms are negotiated dyadically. 

And in some of my current work (drawing on a joint project with Shelley Correll and Cecilia Ridgeway, based in part on their terrific 2006 SF paper on consensus and the creation of status beliefs), I argue that such coordination through common knowledge is crucial to the production and reproduction of identity.  In short, it is misleading to suggest (as have those of us who have described networks as “prisms”) that an actor’s identity is a function of their position in network structure.  For such relationships to convey identity to all parties who might coordinate on the basis of such an identity, there must be some system of  communication that makes such network information publicly visible.

I could go on and on about the importance of common knowledge in getting actors to coordinate their action (see in particular, Chwe’s wonderful 2001 book Rational Ritual: Culture, Coordination, and Common Knowledge).  The key point for this post is that insofar as coordination requires common knowledge, networks built up on dyadic communication links are systematically unable to produce such coordination because they are poor at conveying common knowledge.  If we are just interacting dyadically, we cannot know (for sure) what is transpiring in other interactions and so cannot know the distribution of knowledge.  In this sense, it is again the case that each link has indexical properties.  What is touted as a triad (or more) is often no more than a set of dyads.  (*Footnote below)

To be clear, I think that much happens through networks, as conventionally understood, and that SNA is a very useful framework.  But I hope you can see now why I think it has some important limitations, and these limitations pertain to what SNA was supposed to be so good at– capturing social structure beyond the dyad.  It’s not that it cannot do that.  But because a network must be composed of links of the same type, there are certain key types of information that are not well conveyed by networks– (a) information about others; and (b) information about what others know.

A coda:

This is my last post for orgtheory.  I’d like to thank my gracious hosts for giving me this space and for being patient with me, as I overstayed my welcome a bit while trying to find the time for this last post.  (The’ll swear that this is not true, but it is!)  Thanks guys!

I’d also like to say again that while I welcome any and all comments, I will only respond if I think the interchange can be productive.  If you wish to engage further with me, please just email me.


An objection to to the limitation concerning common knowledge is that in fact, networks often allow for one-to-many communications [I have it on good authority that this is how Facebook works…], which creates common knowledge among all those who participate in such communications.  For instance, if you put A, B, and C in a room then they will all know what they have all discussed, right?  Sure, but then you have just changed the meaning of what we mean by network.  You have overlaid on top of the dyadic relations a separate structure that marks the three parties as privy to the same communications.  You can call this a network if you like [I guess, Facebook does] but is something very different from what we conventionally mean by a network– i.e., a set of nodes joined by links.  The point here is that these are different animals regardless of what you call them. 

That this distinction has not been sufficiently appreciated may be seen in the fact that traditionally [see especially Breiger’s classic “The Duality of Persons and Groups”] network analysts have taken co-presence data [as in the classic dataset from Gardner et al. 1941 study Deep South] and tranformed it into conventional network data, thus eliminating the eliminating the possibilty of knowing who shares knowledge about what others know.  For instance, such a transformation sees two events with A, B, and C attending as equivalent to three events with A-B, B-C, and A-C attending.  Those are very different, at least when it comes to the production of common knowledge.  Note however, that analyzing co-presence data with Galois Lattices retains this distinction, and would seem to have more promise for modeling the production of common knowledge.

Written by EWZS

November 14, 2008 at 5:07 am

Posted in uncategorized

13 Responses

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  1. While it is now widely known that I am a fraud, it is not commonly known

    The difference between common knowledge and an open secret is extremely important, as you say. It’s the point of the saying (is it just a saying? I don’t know the origin of it) that a secret is something you can only tell one person at a time. An open secret is not quite the same thing as pluralistic ignorance, though. In pluralistic ignorance (as you say) people have the same knowledge but aren’t aware that they do so. With an open secret people are often aware (or strongly suspect) that everyone else has the same bit of information they do, but it has not been or cannot be shared in a way that would make it common knowledge. So, for instance, you don’t have to read many good classic novels before coming across a situation of the kind you describe — “if you put A, B, and C in a room then they will all know what they have all discussed, right?” — where much of the drama is sustained by the fact that, in spite of the direct interaction between the parties, some convention of communication prevents the transformation of open secrets into common knowledge.

    Chwe’s book is terrific, btw.



    November 14, 2008 at 6:51 am

  2. I am a little more optimistic about network theory and its prospects. I often wish social network theory was more integrated into introductory sociology courses instead of the usual ramble of history of sociology, social theory, and the holy trinity of “gender, race, and class”. The lack of current concepts or foundations within introductory sociology classes makes it feel very outdated, boring, and unrigorous.

    I think SNA clearly has its limits, but I think it should exploited to its full potential. Nearly all of sociology that has been published in the journal Science has been led by SNA, with much of it by figures such as Duncan Watts. The forefronts of many subfields of sociology have involved themselves with SNA in many ways. Medical sociology (such as Jefferson High School’s sex network, one of the more memorable publications in AJS) is close to public health and epidemiology; economic sociology is close to social capital; political sociology is close to organizations and collective behaviour.

    Sociology’s decline can be averted if it rides the wave of SNA, but it chooses not to, for whatever reason. If anything, Obama’s victory is showing how relevant social networks are becoming, and how more relevant they will become. I think sociology should embrace SNA despite its limits, because I feel it’s probably the last chance of quantitative rigour we have.



    November 14, 2008 at 6:58 am

  3. Interesting post, with some nice points of caution about the over-promise of SNA in certain areas. The example of “common knowledge” I found especially appropriate.

    Without arguing against the main points of the post, here are a couple of thoughts I had after reading:
    1. The definition of “social network” used in the post seems more than a little restrictive to me. While it is absolutely true that most applications of SNA (and indeed, most theories) focus on only one or two types of ties, networks may certainl



    November 14, 2008 at 7:24 am

  4. Damn, that’s embarrassing. Cat hit keyboard.



    November 14, 2008 at 7:25 am

  5. Okay, thoughts I actually *meant* to post:

    IMHO, the definition of a social network used in the post seems a bit too restrictive for my tastes.

    For example, take the statements “If this is the situation, wherein lies the network?” and “In order to call it a network, we must be able to say that the links are of the same type throughout the network.” Perhaps I mistake your meaning, but isn’t the triad you refer to a classic example of a multiplex network? Why must a network have to involve only a single type of tie?

    The way I have always understand network analysis is that it is merely a collection of techniques for studying patterns of interdependencies; in the context of social groups, such interdependencies can easily (as you point out yourself, when discussing the idea of network-wide “broadcasts,” and triads as unique entities from collections of dyads) involve multiple types of ties and social processes occurring at multiple levels of analysis (monadic, dyadic, triadic, etc.)

    The problem with the idea of social networks as multirelational, multilevel interdependencies is not a conceptual one in my mind, merely practical. Analyzing multirelational networks can be hard. Analyzing networks from a multilevel perspective is also hard. (Again, perhaps I am misunderstanding your point in the quoted lines.)

    The solution to some of the issues you bring up is, I think, to stop thinking about social networks as mere collections of actors who share one type of tie or a collection of independent dyads, but as a particular realization of a combined set of social *and cognitive* interdependencies. (I don’t know if this last point would be controversial on a soc blog, but given your stated interests in network cognition, perhaps not.) Some examples that come to mind of this more general approach to network analysis include work by people like Philippa Pattison and Garry Robins on analyzing social network “neighborhood” effects and work by people like Kathleen Carley integrating traditional “social” networks with various types of cognitive networks, such as cognitive social structures and shared mental models.



    November 14, 2008 at 8:35 am

  6. Forgive me, but I don’t really get this.

    A. A tie between A & B isn’t *really* the same as a tie between B & C.
    At the risk of misinterpreting your point, I’m reading this as stating that measurement error applies to networks, and that gaps exist at each stage between the theoretic construct, its observable manifestation, and the empirical measure. These issues are real and can compromise research, but apply to any empirical research, whether “natural” or “social.” Why is this particularly worse for SNA research?

    B. Common Knowledge: Much of SN research topics and findings have little if anything to do with common knowledge. I agree that an exclusively structural approach is likely to be incomplete/insufficient explanation of common knowledge, but this argument may be applied to many topics. Why is this a test for the success or applicability of SNA?



    November 14, 2008 at 6:57 pm

  7. A comment about the ‘gossip’ and ‘common knowledge’ bits: the difference between knowledge being transferred and common knowledge does not lay only in the structural setting (i.e. dyads versus triads), but also in the actual information that is communicated. Human-to-human interactive exchange of information, such as in face to face conversation, frequently includes not only an exchange of information, but also the exchange of meta-information. So, when a piece of gossip is transferred, person A would frequently (even, typically) tell B who else knows, how sensitive the information is, etc. In fact, information and meta-information are so deeply intertwined in such communication that a piece of gossip, for example, is likely to lose much of its value without it. By the way, when it comes to markets, the inclusion of meta-information in transaction related information is what makes many of the transactions possible, and what differentiates computer-centred markets from human-centred ones. So, I agree completely with the need of a Walrasian Auctioneer, but I think that what such an auctioneer does, among other things, is not only to make prices commonly available, but also to enrich bids and asks with the all-important meta information (how stressed is the buyer/seller, hints to what’s coming in the book, etc.). That comment aside, I like the post very much and agree with the general sentiment that sometimes too much explanatory burden is being placed on the narrow shoulders of SNA (to be slightly poetic about it).



    November 15, 2008 at 10:21 pm

  8. Thanks for the comments. A few of you seemed to think I was down on SNA. I’m not. My point that that there are some important interactions/communications that cannot be said to occur through networks that are built up from dyadic interaction.

    A few other notes:

    Kieran: Thanks for the very helpful clarification that there is a range of possibilities from pluralistic ignorance about X and common knowledge about X, with intermediate cases essentially being ones where everyone suspects that others know X but are less than 100% confident that X is widely known.

    Brian: A is not a measurement issue. It’s a conceptual issue. I’m saying that insofar as every dyad involves a different kind of interaction, there simply is no network. More refined measurement will not help.

    Yuval: Nice observations about meta-information.



    November 16, 2008 at 12:11 am

  9. (35 hours is a long time in the blogosphere…)

    “A is not a measurement issue. It’s a conceptual issue. ”
    and yet:
    “the analytic problem that Simmel poses– i.e., that if you have three people– A, B, and C– you may have three different types of relationships– A-B is of type m; A-C is of type n; and B-C is of type x. … In order to call it a network, we must be able to say that the links are of the same type throughout the network.”

    Precisely. A “network” approach to gossip must abstract from m, n and x and claim, for the purposes of analysis, that they are similar enough to be treated as the same. This would also apply to ties of friendship, advice, trust, etc. One question is whether these ties are *really* the same. This is an epistemological question that could similarly be levied in individual analyses and beyond (e.g., Is it fair to claim 2 different people are *really* the same race?) Another question is whether the admittedly problematic abstraction (and are there any unproblematic abstractions?) is useful? Do analyses based on the abstraction(s) produce useful insights?

    Forgive me for presuming that we’d agree the answer is yes.

    In something of a digression, I would also agree that much of SNA has been too constrained by a focus on dyads, and that trying to represent other collective arrangements (triads and more) as mere aggregations of dyads may hinder the progress of our understanding of network dynamics. The concept is consequentially tied to its representation.



    November 17, 2008 at 4:43 pm

  10. Well, I *guess* I can forgive you, Brian. :->

    I do agree that such an abstraction *can* be useful. What I was pushing against was the assumption that it is always useful. In fact, it can often be highly misleading.



    November 17, 2008 at 4:50 pm

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