Modeling individual attention dynamics on online social media

TL;DR

The paper addresses how an individual's attention decays when faced with many social stimuli, proposing a minimal analytical model in which attention allocation depends on the total duration of interactions rather than their count or participant activity. By deriving $P(t^*)$, the probability that a comment is rewarded on day $t^*$, from the daily comment flow $n(t)$ and the thread duration distribution $P(T)$, the authors show that, for an exponential decay $n(t)$, $P(t^*)$ is independent of $N$ and $\eta$, and can be obtained by averaging over $T$ as $P(t^*)=\sum_{T=t^*}^{T_m} P(t^*|T)P(T)$. They validate the model using Change My View (CMV) data from Reddit, demonstrating that the predicted $P(t^*)$ matches the observed distribution, and that the model also reproduces inter-reward statistics such as $P(\eta^*)$, $P(\tau)$, and $P(m)$. The work provides a microscopic perspective that complements macroscopic attention studies and suggests extensions to other online contexts, with potential applications to email management and collaborative work platforms. The approach lays a foundation for renewal-theory analyses and permits incorporating heterogeneous fitness distributions to capture more nuanced attention dynamics.

Abstract

In the attention economy, understanding how individuals manage limited attention is critical. We introduce a simple model describing the decay of a user's engagement when facing multiple inputs. We analytically show that individual attention decay is determined by the overall duration of interactions, not their number or user activity. Our model is validated using data from Reddit's Change My View subreddit, where the user's attention dynamics is explicitly traceable. Despite its simplicity, our model offers a crucial microscopic perspective complementing macroscopic studies.

Figures (6)

• Figure 1: (a) Inset: Probability distribution of number of rewarded comments $P(n^*)$ in threads with $N = 100$ and $T = 33$, for different values of $n_0$. Symbols correspond to numerical simulations, red lines correspond to the binomial distribution. We used $\omega = 1$, $P(\eta) = 1$, $\lambda = 3$, and number of threads $V = 10^6$. Main: Probability distribution of reward days $P(t^*)$ considering a power-law distribution $P(T)$, for different values of exponent $\delta$, see Eq. \ref{['eq:T_powerlaw']}. Dashed lines following the predicted asymptotic behavior for $t^* \to 1$ ($P(t^*) \sim \mathrm{const.}$) and $t^* \to \infty$ ($P( t^*) \sim (t^*)^{-\delta}$) are included. We used $n_0 = 100$, $\lambda = 3$, $T_0 = 30$, and number of threads $V = 10^6$. (b) Inset: Normalized global time series $N(t)/C$ displayed in semi-log scale, representing the proportion of comments posted in CMV on day $t$. Main: Probability distribution of reward days $P(t^*)$ observed in CMV. Red symbols correspond to the real results, solid line corresponds to numerical results obtained from Eq. \ref{['eq:numerical']}.
• Figure 2: (a) Probability distribution $P(\eta^*)$ of number of comments posted by a single user that have been rewarded. (b) Probability distribution $P(\tau)$ of elapsed days between two consecutive rewarded comments in threads. (c) Main: Probability distribution $P(m)$ of elapsed comments between two consecutive rewards of a single user. Insets: Nonlinear regression of a stretched exponential performed in $P(m)$ with exponents $\beta = 0.52 \pm 0.02$ (CMV) and $\beta = 0.56 \pm 0.02$ (model). We show the results obtained from both CMV and the model, represented by red and blue symbols, respectively. Very similar results are obtained by running the model with different initial conditions. We used a logarithmic binning where bins are sized like the Fibonacci sequence vigna2013fibonacci. We used $n_0 = 200$ in Eq. \ref{['eq:prob1']}.
• Figure SF 1: Number of rewarded comments as a function of the number of comments posted for every receiver in CMV. Every point depicted in a random color corresponds to a different user.
• Figure SF 2: Mean value (a) and standard deviation (b) of the number of comments posted by receivers in CMV as a function of the number of rewarded comments. Solid lines correspond to linear regressions in logarithmic scale: $\mu = \mathcal{C}_\mu (\eta^*)^{\nu_\mu}$ with $\mathcal{C}_\mu = 66.51 \pm 1.07$ and $\nu_\mu = 0.91 \pm 0.02$, $\sigma = \mathcal{C}_\sigma (\eta^*)^{\nu_\sigma}$ with $\mathcal{C}_\sigma = 115.28 \pm 1.13$ and $\nu_\sigma = 0.68 \pm 0.03$.
• Figure SF 3: Empirical probability distributions of (a) total comments of threads $P(N)$, (b) duration of threads $P(T)$, and (c) activity of users $P(\eta)$ in CMV. Red lines correspond to spline interpolations, blue symbols correspond to rejection sampling generation.