Competition among memes in a world with limited attention

“Competition among memes in a world with limited attention” is a 2012 paper by L. Weng et al. that investigates the dynamics of memetic competition and epidemic spread using a toy simulation of Twitter.

Individual Twitter users were represented as nodes in a network. Each node held a queue of currently visible posts (their “screen”), and a queue of past posts (their “memory”). Users’ limited attention and limited interests were modeled by periodically removing posts from each queue.

Without considering qualitative or external factors in content and user activity, their simple model replicated the quantitative complexity of meme and user behavior found in empirical data: certain memes were found to win over other memes in lifespan and popularity, even when they are otherwise identical. This provides an argument against biological analogies, where for instance the intrinsic properties of viruses are vitally important to viral competition and evolution.

Background

Traditionally, the field of memetics uses biological analogies to explain memetic phenomena. Early memetic works in particular adopted a replicator-centric view of evolution, in which selfish replicators (genes) are the primary units and agents of evolution. Among the assumptions of this view is that genes compete with other genes by way of natural selection, where qualitatively beneficial traits encoded by the gene are favored over others. A limited degree of mutation, which modifies these qualitative traits, is a key driver behind the diversity of gene behaviors.

This replicator-centric view of memes was dominant from the original publication of The Selfish Gene up to the early 2000s, when critics found in part that biological hypotheses were not rooted in sufficient data. In parallel, starting in the 2000s empirical memeography grew as a field that could challenge the previously dominant assumptions of memetics. By neglecting qualitative traits and mutation in its model, this paper directly challenges biological analogies using empirical data.

Empirical Observations

The paper notes several empirically observed memetic phenomena found in existing research. In these observations, hashtags were used as a proxy for identifying memes in a post.

• Limited attention: The breadth of memes tweeted by a user is limited, and independent of the total number of memes on the platform.
• User interests: The memes tweeted by a user are similar to their previously tweeted memes. Past behavior can, in part, predict future behavior.
• Heterogeneous behavior: Measurements of meme lifespan, popularity, user activity, and breadth of user attention show large quantitative differences between memes and users. For instance, certain memes are orders of magnitude longer-lived than others. A small fraction of memes account for a large portion of all posts, and a small fraction of users generate most of the traffic.

By modeling the first two points in a Twitter-like network, the authors hoped to recover the quantitative differences in meme and user behavior.

Model structure

The paper used an agent-based model in which Twitter users were represented as autonomous nodes in a static directed graph: each user-node was unidirectionally connected to a predetermined set of other user-nodes. The user-nodes communicated by sending (tweeting or retweeting) instances of memes (hashtags) to downstream nodes (followers). Not simulated were the intrinsic properties of each meme, memetic mutation, and other functions of Twitter e.g. favorites.

A user-node held two FIFO queues:

• Screen: Posts currently visible to the user, received from upstream nodes
• Memory: Posts that the user previously sent to downstream nodes

Where each post was an instance of a meme, and each queue could contain multiple posts of the same meme.

At each step, a user could either generate a post with a new meme, generate a post with a meme from memory, or retweet a post on their screen.

Limited Attention

Each user-node paid attention to a meme when they tweeted or retweeted a post containing the meme. Limited attention was modeled by removing posts from a user’s memory or list after some time. This memory mechanism is based on the Yule-Simon model.

Model Parameters

The paper used four parameters to tune the model. The first three were fitted to data; the latter was normalized to 1 by default.

• p_n – Novelty of the system, or the probability that a user generates a new meme
• p_r – Retweet activity, or the probability that a user pays attention to a given post
• p_m – Strength of user interests, or the probability that a user tweets a meme from memory
• t_w – Time window factor, or the amount of time each post remains on a user’s screen or memory

A longer time window is identified with less competition, as each meme has more chances to be retweeted by each user.

Results

The paper found that limited attention and user interests in a Twitter-like toy network are sufficient to reproduce the observed diversity in meme lifespan, popularity, and user activity. This diversity depends on a properly tuned time window factor t_w: simulations with longer time windows (t_w > 1) displayed less differentiation among meme and user behavior (e.g. lower difference in popularity), whereas shorter time windows (t_w < 1) could not generate long-lived memes. Without limited attention (t_w >> 1) or user interests (p_m = 0), the model failed to reproduce empirical observations.

Qualitative and exogenous characteristics of memes and users are not ruled out as important factors in meme propagation, but are not necessary to reproduce the investigated phenomena.