How often should I access my online social networks?

Daniel Sadoc Menasch\'e; Eduardo Hargreaves; Giovanni Neglia

REVIEW 3 major objections 4 minor 39 references

How often should I access my online social networks?

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A user's best check-in rate for a social feed is $\mu^* = \lambda\left((K/c)^{1/(K+1)} - 1\right)$, balancing new posts against access cost; the formula holds for chronological feeds while ranked feeds deliver measurably less value.

desk verdict A correct and simple closed form for optimal access frequency under FIFO timelines, but the practical answer is conditional because the paper's own Facebook data show real feeds violate the no-repeat assumption. read the letter →

arxiv 1908.04811 v1 pith:R6LMZA7G submitted 2019-08-13 cs.SI

Eduardo Hargreaves , Daniel Sadoc Menasché , Giovanni Neglia This is my paper · ORCID

classification cs.SI

keywords valueofaccessoptimalratesocialnetworktimelinesPoissonprocessNewsFeeduserutilityageinformationsampling

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Users who want to stay informed face a trade-off: check a social network too often and most accesses return no new posts; check too rarely and posts pile up beyond what one can read. This paper claims that this trade-off has a unique optimal access rate, and that the optimum is given by a simple closed-form expression when content arrives as a Poisson process, inter-access times are exponential, and each timeline has fixed size. The core result is that the utility-maximizing rate is $\mu^* = \lambda\left((K/c)^{1/(K+1)} - 1\right)$, where $\lambda$ is the posting rate, $K$ the number of posts visible per access, and $c$ the cost of an access. The authors validate the underlying value-of-access formula against measurements from a large social platform, and find that a chronological feed matches the model while the platform's ranked feed delivers fewer new posts than predicted. If correct, the paper gives users and platforms a quantitative target for how often feeds should be refreshed.

What carries the argument

The engine of the argument is the value-of-access (VoA) metric, defined as the expected number of new impressions per timeline view. The model treats the number of posts created between accesses as a Poisson random variable truncated at $K$, and then integrates over the exponential inter-access distribution to obtain Eq. (12). This closed form is what turns the optimization into a one-variable calculus problem: differentiating $U(\mu)$ gives $\partial U/\partial\mu = K(\lambda/(\lambda+\mu))^{K+1} - c$, and setting it to zero produces the optimal rate $\mu^*$ in Eq. (17). The same expression also yields the limiting behaviors the paper discusses: as $K\to\infty$, $\bar{V}\to\lambda/\mu$, and as $\mu\to 0$, $\bar{V}\to K$.

What would settle it

Run a controlled experiment with a reverse-chronological feed in which posts arrive as a Poisson process with known rate $\lambda$, the user's inter-access times are exponentially distributed with known mean $1/\mu$, and each view shows at most $K$ posts; if the measured mean number of new posts per access disagrees with $(\lambda/\mu)(1-(\lambda/(\lambda+\mu))^K)$ beyond sampling error, the central claim fails.

Watch

Extended reading notes

Core claim

The paper's central discovery is a closed-form expression for the expected number of new posts a user sees per access — the 'value of an access' — and the optimal access rate that follows from it. Under Poisson content generation with rate $\lambda$, exponentially distributed times between accesses with mean $1/\mu$, and a timeline that shows at most $K$ posts, the value of an access is $\bar{V} = (\lambda/\mu)(1 - (\lambda/(\lambda+\mu))^K)$. Assuming a per-access cost $c$, the utility per unit time is $U(\mu) = \mu\bar{V} - c\mu$, and the maximizing rate is $\mu^* = \lambda\left((K/c)^{1/(K+1)} - 1\right)$. The paper's measurements, taken by observing what a set of automated accounts actually saw on a major platform, show that a reverse-chronological feed reproduces the model's values, while the platform's ranked feed shows repeated posts in top positions and therefore yields a lower value of access than the model predicts for the same parameters.

Load-bearing premise

The whole result assumes a timeline that shows new posts first and repeats old posts only when there are no novelties; a ranked feed that puts repeated posts at the top breaks that assumption, and then the predicted value of access and the optimal rate no longer describe what the user gets.

Editorial extensions

If this is right

A user who can estimate the posting rate $\lambda$, the number of posts $K$ they can actually consume per visit, and the cost $c$ they attach to an access has a concrete number to aim for: $\mu^* = \lambda\left((K/c)^{1/(K+1)} - 1\right)$.
Because $\mu^*$ grows linearly with $\lambda$, busier content streams justify more frequent checking, but the marginal gain of each extra check shrinks as $K$ grows; in the saturated regime, larger timelines lower the optimal check-in rate.
The model predicts that any feed that repeats already-seen posts instead of showing all available novelties will deliver a lower value per access than the user's optimal plan assumes, so the user either scrolls further or checks more often to reach the same utility.
The two operating regimes the paper identifies — where the value of access is limited by the posting rate $\rho = \lambda/\mu$ versus by the timeline size $K$ — give platform designers a criterion for when recommender filters help and when they just add overhead.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An implicit corollary of the optimization is that a platform can manipulate a user's access rate by adjusting how often it repeats posts: lowering the observed value per access raises the $\mu$ that maximizes utility, which may be exactly why ranked feeds bury novelties.
Because the formula separates $\lambda$ and $K$ from the user's internal cost $c$, observed access behavior could in principle be inverted to estimate $c$ for a given user, turning the model into a measurement tool for attention-budget studies.
The derivation assumes exponential inter-access times; extending it to general renewal processes would replace the factor $(\lambda/(\lambda+\mu))^K$ with a Laplace-transform term, a testable generalization the paper does not pursue.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: Eq. (12) and Eq. (17) are correct, useful, and not something I have seen in the prior work. Under Poisson content generation, exponential inter-access times, and a K-post timeline filled with new posts before repeats, the expected number of new impressions is (lambda/mu)(1 - (lambda/(lambda+mu))^K), and maximizing utility mu*Vbar - c*mu gives mu* = lambda((K/c)^(1/(K+1)) - 1). That is a nice back-of-envelope for screen-time tools, and the derivation is clean.

The paper earns credit for honesty in the empirical section. The trace-driven FIFO simulation matches the model, and the Facebook News Feed measurements show the model overpredicts VoA. The paper attributes this to News Feed position bias and reports that at K=10 Facebook shows about 5 new posts instead of the 10 the model expects. That is a real, useful empirical finding. The later note that real dropped posts can reappear in subsequent accesses in the 15

The soft spots are real but not fatal. The biggest is that Assumption A2 is exactly what fails on Facebook's ranked feed, so the optimal rate in Eq. (17) is not yet an answer to the title question for Facebook as it runs. The paper acknowledges this gap in Section VII, but the abstract and Section IV present the result more confidently. Because News Feed lowers the marginal value of frequent accesses, the formula likely recommends checking too often on ranked feeds. That is a load-bearing caveat, but it is openly documented.

Smaller issues: lambda is estimated from the same trace used for validation, the simulation plots have no error bars, and no data or code are released. These are fixable and standard reporting gaps. The citation pattern is fine: the paper builds on the authors' earlier FIFO/TTL timeline work and says so.

Verdict: this deserves peer review. It is a compact, correctly derived idealization with an honest empirical comparison. I would want revision to add artifacts, uncertainty quantification, and a prominent statement that Eq. (17) applies to FIFO/no-repeat timelines, not to ranked feeds as they currently operate.

Referee Report

3 major / 4 minor

Summary. The paper proposes an analytical model for the value of an access (VoA) to an online social network, defined as the expected number of new (previously unseen) impressions in a timeline. Under assumptions of Poisson content generation at rate λ, exponential inter-access times with mean 1/µ, timeline size K, and a timeline that displays new content before repeats (Assumptions A1–A3), the authors derive a closed-form expression for VoA (Eq. (12)) and then solve a utility-maximization problem U(µ)=µV̄−cµ to obtain an optimal access rate µ* (Eq. (17)). The model is parameterized with Facebook data and compared against trace-driven FIFO simulations and against measurements from Facebook bot accounts that use the actual News Feed. The paper reports that the model matches FIFO timelines well but overestimates VoA under Facebook News Feed, which exhibits position bias by repeating posts. The authors conclude that News Feed reduces VoA and that the model provides insights into optimal access rates.

Significance. If the modeling assumptions hold, the paper makes a useful analytical contribution: it provides simple closed-form expressions for the expected number of novel impressions per access and for the optimal access rate, with transparent dependence on content generation rate, timeline size, and access cost. The VoA metric is intuitive and could serve as a building block for comparing personalization algorithms. The empirical observation that Facebook's News Feed repeats posts in top positions is also valuable and consistent with prior work on position bias. The derivation from assumptions to Eq. (12) and Eq. (17) appears correct, and the paper does not fit the VoA formula to data, so the central result is not circular. However, the title question concerns real social networks, and the practical answer is limited by the FIFO-timeline assumption that the paper's own measurements show is violated by News Feed; this is a substantial caveat on the applicability of the headline result.

major comments (3)

[Section II-B (Assumption A2) and Section III-C] The central practical claim, the optimal access rate in Eq. (17), is derived under Assumption A2 that the timeline displays as many new posts as possible before repeating old content. However, the paper's own Facebook measurements (Section III-C, Figure 2) show that the News Feed violates A2: repeated posts appear in top positions, and for K=10 the measured VoA is about 5 instead of the model's 10. Because the measured VoA is below the model's prediction, the marginal benefit of an extra access (Eq. (16)) is overestimated for ranked feeds, and hence the optimal µ* from Eq. (17) is likely too high for actual Facebook timelines. The acknowledgment in Section VII that the model does not consider all impacts of News Feed does not fix this, because the title question is about real online social networks. I recommend either restricting the domain of the optimal-rate result to FIFO or chronological timelines, or extending the model to account for position bias, e.g., by adding a parameter that captures the fraction of repeated impressions in top positions.
[Section IV, Eq. (17)] The optimization analysis omits the feasibility condition for the stationary point. The derivative at µ=0 is ∂U/∂µ|₀ = K − c, so the interior maximum given by Eq. (17) exists only when c < K. For c ≥ K, the utility is decreasing for all µ ≥ 0 and the optimal solution is the boundary µ* = 0. As written, Eq. (17) can produce negative or infeasible access rates when c ≥ K, and the numerical examples in Section V use c=1 with K ≥ 2 but do not state the condition. The authors should present the piecewise solution and the condition explicitly; otherwise the optimization claim is incomplete.
[Section III-A and III-C] The empirical validation is weakened by in-sample parameter estimation and by the lack of uncertainty quantification. The value λ=4.487 is estimated from the same Facebook trace against which the model is compared in Figure 1(b), so the close agreement is not a predictive test. No confidence intervals or error bars are reported for the measured VoA values in Figures 1(b) and 2. In addition, the FIFO simulation procedure described in Section III-A is not a faithful implementation of the model's inter-access process: snapshots are built by selecting a reference post uniformly at random from all posts and taking its K−1 immediate predecessors, which forces access times to coincide with post-creation times rather than following the assumed exponential or deterministic interval distribution. This can bias the simulated VoA and the apparent agreement with Eq. (12). The authors should either describe a direct event-driven simulation of the assumed access process or justify why the uniform-reference-post scheme is equivalent.

minor comments (4)

[Section III-C, paragraph on position bias] The sentence 'This finding reveals that Facebook Facebook creates a position bias' contains a duplicated word 'Facebook'; it should read 'Facebook creates a position bias'.
[Section II-C, Eq. (2)] The definition of V would be clearer as V = min(A, K) under the assumption that the timeline is filled with new posts only up to its capacity.
[Section V-A, Figure 4 discussion] The text writes 'V (ρ, K) = ρ' and 'V (K, ρ) = K' using V for the expectation; for consistency with the notation introduced in Section II, these should be V̄, the expected value of access.
[Abstract and Section III-C] The abstract claims the results indicate 'the predictive power of the approach,' but the validation is in-sample and the News Feed measurements show the model overestimates VoA; a more cautious phrasing would better match the evidence.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the VoA formula and optimal access rate are derived from stated assumptions, not fitted; the empirical validation is in-sample but the optimization result is self-contained.

full rationale

The derivation chain is transparent: Eq. (2)-(5) compute the conditional expected new impressions under the Poisson generation assumption, Eq. (8) averages over the exponential access interval, and Eq. (12) is the closed form. Substituting (12) into the utility definition (13) gives (14), and differentiating with respect to mu yields the first-order condition (16) and the optimal rate (17). None of these equations is fitted to the value-of-access measurements; the model's parameters are K, lambda, and c, and VoA is a derived quantity. The only empirical parameter, lambda=4.487, is measured from the same Facebook trace later used for comparison in Fig. 1, so the 'predictive power' language overstates the strength of the validation: this is an in-sample model check, not an out-of-sample forecast, and the FIFO simulation embeds assumption A2 by construction. That caveat concerns the empirical validation, not the logical derivation. The citations to the authors' prior work [16], [17] are contextual and do not supply any uniqueness or existence theorem on which Eq. (17) depends. Therefore there is no self-definitional, fitted-input, or self-citation-based circularity in the paper's central claim.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The model rests on four stated modeling assumptions (Poisson generation, FIFO-like display, exponential revisits, linear utility). The only empirical parameter is λ, estimated from the same Facebook data used for validation; cost c is chosen arbitrarily for numerics. No new physical or algorithmic entities are postulated.

free parameters (3)

λ (content generation rate) = 4.487 posts/hour (estimated from Facebook API data, Section III-A)
Aggregate content creation rate; used to evaluate Eq. (12) and Eq. (17). Estimated from the same election-period data, so validation is in-sample for this parameter.
K (timeline size) = 10 in trace validation; varied from 1 to 50 in FTE comparison
Maximum number of impressions per timeline. It is an exogenous design parameter, not estimated from data, but the VoA formula and optimal access rate depend on it.
c (cost per access) = 1 (chosen by hand for numerical examples, Section V-B)
Cost per access; treated as an input parameter in the optimization, not estimated. The reported optimal rates in Figures 5 assume c=1.

assumptions (4)

domain assumption Content is generated according to a Poisson process with aggregate rate λ (Assumption A1, Section II-B).
Load-bearing for the closed-form VoA and optimal access rate; the paper's own trace simulation shows real post generation is not exactly Poisson, and deviations are visible in Figure 1(b).
domain assumption The timeline always displays as many new posts as possible and uses repeats only to fill space (Assumptions A2 and A3, Section II-B).
This makes VoA equal to min(A,K) with A the number of posts generated in the interval. Facebook News Feed violates it, as the paper's FTE measurements show.
domain assumption The interval between user accesses is exponentially distributed with rate µ for the main closed-form result (Section II-E).
Required for Eq. (12) and the optimal µ* formula; deterministic access gives a different, integral form.
ad hoc to paper User utility per time is linear: U(µ)=µV̄-cµ, with c a constant cost per access (Section IV, Eq. (13)).
A modeling choice, not derived from data; the paper notes that more complex cost functions are future work.

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Cite this review

Pith. "Pith review of How often should I access my online social networks?." pith.science (2026). https://pith.science/paper/R6LMZA7G

@misc{pith2026190804811,
  author       = {Pith},
  title        = {Pith review of: How often should I access my online social networks?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R6LMZA7G}},
  note         = {Machine review of arXiv:1908.04811}
}

read the original abstract

Users of online social networks are faced with a conundrum of trying to be always informed without having enough time or attention budget to do so. The retention of users on online social networks has important implications, encompassing economic, psychological and infrastructure aspects. In this paper, we pose the following question: what is the optimal rate at which users should access a social network? To answer this question, we propose an analytical model to determine the value of an access (VoA) to the social network. In the simple setting considered in this paper, VoA is defined as the chance of a user accessing the network and obtaining new content. Clearly, VoA depends on the rate at which sources generate content and on the filtering imposed by the social network. Then, we pose an optimization problem wherein the utility of users grows with respect to VoA but is penalized by costs incurred to access the network. Using the proposed framework, we provide insights on the optimal access rate. Our results are parameterized using Facebook data, indicating the predictive power of the approach.

Figures

Figures reproduced from arXiv: 1908.04811 by the authors.

**Figure 2.** Model (squares) compared against the measured VoA (tr [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** ECDF for the number of posts viewed versus the number o [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Sensitivity analysis: impact of different paramete [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Sensitivity analysis: impact of different paramete [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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