On Godwin’s Law: A Statistical Analysis on the Distribution of Nazi Analogies in Online Discussion

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On Godwin’s Law: A Statistical Analysis on the
Distribution of Nazi Analogies in Online Discussion
Alex Miller
alex@miller.im
November 2013
Abstract
Godwin’s Law is a well known internet adage about the prevalence of analogies
to Nazi Germany in online discussions. Though Godwin’s Law can be shown to be
mathematically true by a triviallly universal proof, this does not account for the per-
ceived frequency of Nazi analogies specifically by Godwin and others. The undertaking
of this research is to study the empirical distribution of online Nazi-comparisons by
examining the comments section of major online news outlets. It is shown that number
of comments until the first Nazi-comparison does not follow a geometric distribution
(as presumed by the trivial theory), but rather demonstrates power-law characteristics
above a specified threshold. The dataset in this study is shown to resemble a type
II Pareto (Lomax) distribution, though ways to improve this model are suggested in
conclusion.
1 Introduction
The social dynamics of online discussion fora have received increased media and research
attention in the past year. Perhaps the most well-known topic in recent discourse is the
University of Wisconson-Madison study [1] that prompted Popular Science to remove its
online discussion boards due to their effect on readers’ perception of their articles [2]. Results
such as this underscore the importance of understanding discussion dynamics not simply
from a statistical perspective, but also a social one.
One of the first and oldest observations about social behavior in online discussion threads
was formulated by Mike Godwin in 1990. In what has become known as “Godwin’s Law
of Nazi Analogies”, Godwin asserts: As an online discussion grows longer, the probability
of a comparison involving Nazis or Hitler approaches one [3]. Despite its tongue-in-cheek
characterization as a “law”, it is still surprising to find very little academic literature on this
subject. The current research attempts to formally study Godwin’s Law and its properties
in real online discussion fora.
Initially, Godwin’s assertion was less a “law” than an informal observation about the
prevalence of analogies to Nazi Germany in Usenet discussion groups. Nonetheless, Godwin’s
Law anectodally appears to hold true universally. Indeed, as discussed in [3], a key aspect
of Godwin’s Law is that it appears to hold true regardless of the topic of conversation (esp.
when references to Nazi Germany would be unexpected).
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As recalled in [4], Godwin’s intention behind his eponymous law was to to invent a
meme that would neutralize the “Nazi-comparison meme”. Quoting from Godwin himself
(in reference to his law):
Although deliberately framed as if it were a law of nature or of mathematics,
its purpose has always been rhetorical and pedagogical: I wanted folks who glibly
compared someone else to Hitler or to Nazis to think a bit harder about the
Holocaust.
Godwin’s goal is a worthy one. Though this study may betray his intention by studying
the law mathematically, it may also contribute to Godwin’s goal by laying the groundwork
for future research. Presently, no literature exists on the prevalence of Nazi-comparisons in
online dicussion. This prevents even the most essential questions about this subject from
being studied; namely, is Godwin’s Law succeeding as a “counter-meme”? Is the incidence of
Nazi-comparisons decreasing over time? Is it inversely related to awareness about Godwin’s
law itself?
The current research does not address these questions, but rather the more basic ones of:
(1) How accurate is Godwin’s Law (quantitatively) in real discussion fora? And (2) what is
the distribution of Nazi-comparisons in online discussion?
2 Background
2.1 Formalization & Terminology
Let us first formalize Godwin’s Law in the language of mathematical precision. Though
the statement, ”As an online discussion grows longer” can be interpeted as a reference to
an increasing quantity of words, characters, or digital memory correspoding to an online
discussion, we will instead refer a thread’s “length” as the integral number of entries or
comments in the discsussion. Furthermore, when referring to an entry that makes a “com-
parison involving Nazis or Hitler”, we will euphmistically call this a “Godwin positive” entry
or a “Godwin match”. Let us all refer to the number of comments in a thread until the first
Godwin match as the thread’s “Godwin length”.
2.2 Triviality
Presumably, Godwin’s Law is trivially true. Let l be the length of arbitrary thread and
assume the probability that a thread participant makes a Godwin positive comment is
greater than or equal to some p > 0 at all times. We can then think of each new comment
in the thread as a Bernoulli trial. The distribution of Godwin length will be bounded below
by a geometric distribution with parameter p. Let F (l) be the cumulative distribution of
the first Godwin positive comment in an arbitrary thread and let G(l) = 1 (1 p)
l
be
the theoretical lower-bound geometric distribution. Then Godwin’s Law may be proven
mathematically using the squeeze theorem:
1 F (l) G(l)
2
lim
l→∞
G(l) = 1
lim
l→∞
F (l) = 1
Of course, nothing about this argument has been unique to Godwin’s Law. The same
logic could apply be applied to to any arbitrary topic, so long as we assume that the
probability of it being mentioned is always greater than zero.
Indeed, Godwin’s Law has been criticized for this very reason. French blogger Brogol [5]
points out the apparent absurdity of Godwin’s Law (using roughly the same logic above)
by declaring his own law:
As an online discussion grows longer, the probability of finding a comparison
involving platypi approaches 1
Clearly, this observation has the potential to diminish the appeal Godwin’s Law as an
interesting subject. Thus, the over-arching goal of this research is not to simply ”prove”
Godwin’s Law, but rather demonstrate empirically that references to Nazi Germany in online
discussion are more common than those to an arbitrary subject (such as platypi). This task
is not fully accomplished in the present study, though the findings here are constructive in
informing future inquiries into the subject.
2.3 Related Literature
Much of the literature about Godwin’s Law is found in popular media outlets. These
articles are typically either a criticism of the universal ”ban” that Godwin’s Law pronounces
on mentioning Nazis ([6], Salon.com) or just commentary on the the prevalence of Nazi-
analogies in general discourse ([7], Reason.com).
Though there is apparently no strictly academic literature on the subject of Godwin’s
Law, there are numerous studies on the dynamics of online discussions. In [8], Mishne &
Glance undertook the task of studying comment sections in the whole blogosphere. Their
results demonstrated an approximately power law distribution in the overall length of weblog
discussion threads. In both [9] and [10], the authors studied the mechanisms by which the
distribution of various blog metrics (e.g., length, number of authors, post in-degree, thread
depth) arise. These results can be very instructive for explaining discussion meta-data, but
less so for analyzing the contents of online discussion.
3 Methodology
The data for this study were extracted from the comment sections following online news and
commentary articles. The sites used were www.cnn.com, www.npr.org, and abcnews.go.com.
All three domains are home to major national news organizations, each with thousands of
news articles and accompanying comment sections. Each website has daily stories on a
variety of subjects and significant readership (and consequent discussion participation).
To gather the data, each site was first crawled (using a third-party spider) to generate a
list of URIs with discussion sections. Each URI was then processed that scraped both the
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webpage content and the comment section (full description of this process will appear in a
forthcoming article). Comments were sorted chronologically and searched for matches from
the list of keywords below. This list was generated by considering the most salient subjects
pertaining to Nazi Germany and their most common misspellings (identified by data from
http://spellweb.com).
nazi
nazis
natzi
nazie
nazzi
adolf
hitler
hilter
hittler
hitlar
weimar
gestapo
gistapo
himmler
goebbels
goebells
goebels
fuehrer
fuhrer
third reich
3rd reich
third riech
3rd riech
third rike
3rd rike
holocaust
concentration
camps
concentration
camp
mein kampf
auschwitz
dachau
yellow badge
yellow patch
yellow badges
yellow patches
fuhrer
furher
holocost
holocoust
halocaust
holocuast
holacaust
holocause
hollocost
holicost
hallocaust
holcaust
holocast
holocust
holacuist
hulocost
haulocaust
haoulocaust
holucaust
holocauset
hholocaust
holicaust
aushwitz
auchwitz
auschwits
auschwiz
auschwtiz
auswitz
aushcwitz
auchwats
auschzites
auchwtiz
auschowitz
Each URI was processed and assigned a corresponding data-vector with the following
information:
Thread Length: Total number of comments in thread at time of observation
Godwin Match Index: The index of the first comment containing any keyword(:=0 if
no match found)
Match Context: 100 (±50) character comment context around keyword
Keywords found in page body: boolean value, TRUE/FALSE
4
TRUE was applied to the last entry for URIs for which any one of the keywords was
found outside of the page’s discussion section; these URIs were excluded from the final
dataset.
4 Data
A total of 20175 URLs were crawled between the three sites. Of these, 16043 URLs contained
discussions with 1 comment. Of this subset, 4716 threads contained a Godwin match.
Below is a summary of the this study’s dataset.
Table 1: Summary Data
Total URLs Processed 20175
Threads with 1 comment 16043
Total comments processed 10593454
Average Thread Length 659
Threads with 1 Godwin match 4716
Average Godwin Length 213
Table 2: Data by Source
www.cnn.com www.npr.org abcnews.go.com
Threads With 1 Comment 8468 6126 1507
Average Thread Length 4024 1507 555
Threads With 1 Godwin Match 3996 555 127
Average Godwin Length 236 73 138
For reference, Figure 1 shows the distribution of overall thread length (in log-log scale)
with the best-fit power law coefficient (in red). This distribution closely resemebles that
found by Mishne & Glance [8]. Both appear to approximiately follow a power law, with
slightly diminished quanitities of small values.
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Figure 1: Distribution of thread length in log-log scale with best-fit power law coefficient
Figures 2 and 3 represent the data corresponding to the subset of with Godwin matches.
Recall that a thread’s Godwin length is the number of comments until the first Godwin
positive entry.
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Figure 2: Distribution of Godwin length in log-log scale
Figure 3: Empirical cumulative distribution of Godwin length
Table 3: Summary of the Inverse Empirical Godwin Length CDF
l ECDF
1
(l)
.1 11
.2 26
.3 44
.4 66
.5 94
.6 138
.7 198
.8 307
.9 526
.95 817
.99 1675
5 Analysis
Upon first glance at Figure 2, the distribution appears to resemble that of a geomet-
ric/exponential random variable. However, this is seen to not be the case upon further
anlayis. See red CCDF line in figures 4 and 5 for the best fit geometric distribution. These
figures reveal the dataset evidentaly has a heavy-tailed distribution.
Though the data clearly deviates from a strict power law or Pareto distribution, its tail
does appear to follow a power law above a certain minimum value. Choosing an x
min
of
1000, and fitting the data using maximum-likelihood method yields a theoretical power law
distribution with parameter α = 3.56. The KS statistic between this theoretical power
distribution and the empirical distribution is 0.05689 with corresponding p-value of 0.656.
However, we can model the head of the distribution and account for its power-law tail
by considering the Lomax (Parteo type II) distribution:
PDF:
αλ
α
(x + λ)
α+1
CCDF:
h
1 +
x
λ
i
α
Using the MLE method, the estimated parameters for the data’s best-fit Lomax distri-
bution are α = 2.080, λ = 246.866. One can assess the accuracy of this distribution by
comparing CCDFs. The green line Figure 4 (on log-log scale) represents the best-fit Lomax
CCDF.
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Figure 4: CCDF functions in log-log scale. Legend:
BLACK: experimentally measured Godwin Length distribution;
RED: best fit exponential (i.e., geometric) distribution;
GREEN: Best fit Pareto distribution (type II)
The semi-log plot in Figure 5 better represents the tail behavior of the distributions.
As can be seen, the data’s distribution is heavy-tailed, though less so than the theorietical
Lomax curve.
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Figure 5: CCDF functions in semi-log scale. Legend:
BLACK: experimentally measured Godwin Length distribution;
RED: best fit exponential (i.e., geometric) distribution;
GREEN: Best fit Pareto distribution (type II)
Despite this deviant tail-behavior, the χ
2
goodness-of-fit test returns a p-value of 0.38.
This allows us to assume the null hypothesis at the critical value of .05.
6 Conclusions & Future Work
This research has shown that the Godwin length of the observed data is not accurately
modeled as a geometric random variable. Rather, power-law behavior was observed for
values 1000 and the entire sample set was plausibly modeled by the Lomax distribution.
Strictly speaking, the Lomax distribution should be used for continuous random vari-
ables. A straightforward way to to extend the current analysis is to start with a discrete
probably distribution, such as the zeta or Zipf. However, this approach will still need ac-
count for the non-power law behavior for small values. Cristelli et al. [11] have studied Zipf
distributions with the same general skewness as that in this study and propose a correction
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factor for small sample values. This approach is promising for both modeling and explaining
the power and non-power law behavior of the Godwin length distribution.
The data sources themselves may also deserve more scrutiny in future analyses. The
nature of national news and commentary websites (such as those used here) ensures a diver-
sity of article (and corresponding discussion) topics, though it is expected that the content
of the articles in this study was more political in nature than ”general” online content. It
is possible that the prevalence of Godwin positive comments is higher in politically-themed
discussions than general discussions. If this question were studied, the current research
would be a very useful basis for comparison.
Also not taken into consideration in this study was the effect of a thread’s topology on
the applicability of Godwin’s Law. The Disqus commenting platform employs a ”threaded”
commenting system (cf. [12]), which was entirely ignored in the current analysis in favor of
purely chronological ordering. Many questions could be asked about the incidence of God-
win matches among various other types of thread characteristics than simply length (e.g.,
comment depth, degree, etc.). Studying the distribution of “Godwin time” (the amount of
time passed between a thread’s first comment and its first Godwin match) instead of God-
win length may also be a more accurate representation of the data given the chronological
ordering.
As indicated by the many questions raised above, it is clear that many opportunities
exist for further study on Godwin’s Law. Being the first of its kind, this study will serve
as a basis for future research on the topic for the author and will hopefully be the same for
others.
7 References
1. Anderson, A. A., Brossard, D., Scheufele, D. A., Xenos, M. A. and Ladwig, P. (2013),
The “Nasty Effect:” Online Incivility and Risk Perceptions of Emerging Technologies.
Journal of Computer-Mediated Communication. doi: 10.1111/jcc4.12009
2. LaBarre, Suzanne. “Why We’re Shutting Off Our Comments.” Web log post. Popular
Science. 24 Sept. 2013. Web. http://www.popsci.com/science/article/2013-09/
why-were-shutting-our-comments.
3. Godwin, Mike. “Meme, Counter-meme.” Wired. Oct. 1994. Web. http://www.
wired.com/wired/archive/2.10/godwin.if_pr.html.
4. Godwin, Mike. “I Seem To Be A Verb: 18 Years of Godwin’s Law.” Jewcy. 30
Apr. 2008. Web. http://www.jewcy.com/arts-and-culture/i_seem_be_verb_18_
years_godwins_law.
5. Brogol. “En Finir Avec Le Point Godwin.” La Politeia. 2 Oct. 2010. Web. http://
lapoliteia.com/en-finir-avec-le-point-godwin-critique-de-la-loi-de-godwin/.
6. Greenwald, Glenn. “The Odiousness of the Distorted Godwin’s Law.” Salon. 1 July
2010. Web. http://www.salon.com/2010/07/01/godwin/.
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7. Weigel, David. ”Hands Off Hitler!” Reason.com. 14 July 2005. Web. http://reason.
com/archives/2005/07/14/hands-off-hitler.
8. Mishne, Gilad, and Natalie Glance. ”Leave a Reply: An Analysis of Weblog Com-
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com/www2006-workshop/papers/wwe2006-blogcomments.pdf
9. Kumar, Ravi, Mohammad Mahdian, and Mary McGlohon. ”Dynamics of Conversa-
tions.” Mahdian.org. Web. http://www.mahdian.org/threads.pdf.
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On-line Conversations.” HP.com. 2012. Web. http://www.hpl.hp.com/research/
scl/papers/comments/comments.pdf
11. Cristelli, Matthieu, Luciano Pietronero, and Michael Batty. ”There Is More than
a Power Law in Zipf.” Scientific Reports 2 (2012). DOI:10.1038/srep00812. http:
//www.nature.com/srep/2012/121108/srep00812/full/srep00812.html
12. omez, Vincenc, Hilbert J. Kappen, Nelly Litvak, and Andreas Kaltenbrunner. ”Mod-
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//www.quantware.ups-tlse.fr/complexnetworks2012/slides/kaltenbrunner.pdf
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