Communications of the ACM

always appear in posts containing the protomeme itself, their πm,μ always equals 1. Finally, a low canonicity score is obtained when there are many words in the post and they have low πm,μ. If a post includes only one unusual word, its canonicity score is still high, because it is still composed mostly of the protomeme itself.

How canonicity is distributed in Reddit is reported in the online appendix. To test the connection between canonicity and popularity for posts using protomemes appearing on the front page the previous day, we create a rank binary variable φM that records whether or not the post was among the 5% best-scoring posts of the day. This is the target variable of the following logistic regression

φMl = α +β Γ(Ml,m) + um + εm.

This is the φ Model. Given a post M
containing protomeme m, the φ Model
estimates its probability of experienc-
ing a popularity spike on day i, after m
hit the front page on day i − 1. Note the
set of posts we include in the model is
still dependent on the l parameter. For
different l values the set of posts in-
cluded is different, because, for in-
creasing front page size, more pro-
tomemes hit the front page, and more
posts on the day after will thus be con-
sidered in the model.

Figure 3 reports φ Model’s βs for increasing l. For Reddit (see Figure 3a), β never takes values greater than −0.7, suggesting a noticeable and notable effect: high canonicity halves the odds of being a high-scoring post; for a deeper discussion see the online appendix. As we increase l, the canonicity effect gets weaker and weaker. This is expected, as we are considering the regression posts that might have not hit the front page. All β values in Figure 3a are significant (p < 0.0001). We thus expect a null result in Hacker News, given the result of the MAX Model covered earlier. Indeed, Figure 3b reports the effect of canonicity in Hacker News is zero, as no p-value reported for any l is less than 0.01.

We also run two Poisson mixed models with the same form of the φ Model, with the only difference being the dependent variable (in this case the post score) and the data included in them. In the Zero Model, we consider only the posts for which φMl = 0, while in the One Model we focus on the posts for which φMl = 1. In practice, the φ Model tells us the effect of canonicity on the odds of experiencing two popularity spikes in a row, while the One and Zero models reveal the score effect of canonicity on the posts that did and did not experience two popularity spikes in a row.

In the One Model, β has a negative sign (see Figure 4a); all βs are significant with p < 0.0001. If the φ Model told us that canonicity lowers the odds of experiencing two popularity spikes in a row, the One Model would tell us that if a post can nevertheless overcome those odds, it is additionally penalized with a worse score. In the Zero Model (see Figure 4b), β is positive and significant. For the unsuccessful posts in the Zero Model, canonicity has a positive effect. For robustness, we also ran a negative binomial model, resulting in similar estimates as the Poisson model (see the online appendix).

The discordance of β signs in the Zero and One models can be interpreted as a similarity between protomeme

We introduce the concept of canonicity of a post, measuring how much a post containing a protomeme m differs from the usual usage of m. A post is said to be canonic if it uses m as expected, without introducing elements not strongly associated with m itself. Consider, for example, a post M as a bag of words. Each word μ in the bag of words co-occurs with protomeme m with a given probability πm,μ. If m appears in 100 posts, and in 30 of them the post title also includes μ, then πm,μ = 0.3. The canonicity of M is calculated like this

Γ(M,m) = Σ∀/∈Μ πm,μ / |M|.

The formula means the canonicity of a post M is the average probability of its words to appear with the meme it contains. Note some posts contain no other word than the words of the protomeme m itself. For this reason, the formula includes the m words in M. Otherwise, such posts will have Γ(M,m) = 0/0, which is unacceptable. Moreover, posts including only a protomeme’s words must have Γ(M,m) = 1 because they use m in its purest form. Since the protomeme’s μs