Competition-Induced Criticality in a Model of Meme Popularity

Abstract

Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at criticality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent α < 2, unlike preferential-attachment models), similar to those seen in empirical data. DOI: 10.1103/PhysRevLett.112.048701 PACS numbers: 89.65.-s, 05.65.+b, 89.75.Fb, 89.75.Hc When people select from multiple items of roughly equal value, some items quickly become extremely popular, while other items are chosen by relatively few people [1]. The probability P n ðtÞ that a random item has been selected n times by time t is often observed to have a heavytailed distribution (n is called the popularity of the item at time t). In examples where the items are baby names [2], apps on Facebook [3], retweeted URLs or hashtags on Twitter [4-6], or video views on YouTube [7], the popularity distribution is found to scale approximately as a power law P n ∼ n −α over several decades. The exponent α in all these examples is less than two, and typically has a value close to 1.5. This range of α values is notably distinct from those obtainable from cumulative-advantage or preferential-attachment models of the Yule-Simon type-as used to describe power-law degree distributions of networks, for example [8-11]-which give α ≥ 2. Interestingly, the value α ¼ 1.5 is also found for the power-law distribution of avalanche sizes in self-organized criticality (SOC) models [12,13], suggesting the possibility that the heavy-tailed distributions of popularity in the examples above are due to the systems being somehow poised at criticality.In this Letter, we present an analytically tractable model of selection behavior, based on simplifying the model of Weng et al. [14] for the spreading of memes on a social network. We show that, in certain limits, the system is automatically poised at criticality-in the sense that meme popularities are described by a critical branching process [15]-and that the criticality can be ascribed to the competition between memes for the limited resource of user attention. We dub this mechanism "competitioninduced criticality" (CIC) and investigate the impact of the social network topology (degree distribution) and the age of the memes upon the distribution of meme popularities. We show that CIC gives rise to heavy-tailed distributions very similar to the distributions of avalanche sizes in SOC models [16,17], even though our competition mechanism is quite different from the sandpile paradigm of SOC. This Letter may, therefore, be of interest in other areas where SOC-like critical phenomena have been observed in experiments or simulations, such as economic models of competing firms [18,19], the evolution and extinction of competing species [20][21][22], and neural activity in ...

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