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

[email protected]

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

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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-

ments.” (2006). Web.http://www.ambuehler.ethz.ch/CDstore/www2006/www.blogpulse.

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.

10. Wang, Chunyan, Mao Ye, and Bernardo A. Huberman. ”From User Comments to

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. G´omez, Vincenc, Hilbert J. Kappen, Nelly Litvak, and Andreas Kaltenbrunner. ”Mod-

eling the Structure and Evolution of Online Discussion Cascades.” 26 July 2012. http:

//www.quantware.ups-tlse.fr/complexnetworks2012/slides/kaltenbrunner.pdf

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