Scaling Participation in Complex Systems

• Scaling participation is the challenge of preserving meaningful engagement and interpretability as systems grow in size, complexity, and diversity.
• It encompasses methods from participatory design in AI and democratic decision-making to operational scheduling in distributed services and diagnostic measures in quantum systems.
• Practical applications span large-scale user involvement in federated learning, modular AI architectures, and democratic infrastructures, highlighting trade-offs in governance, cost, and scalability.

“Scaling participation” denotes a family of problems concerned with what happens when participation must remain meaningful under changes of scale: more users, larger constituencies, broader deployment domains, longer time horizons, higher-dimensional state spaces, or larger many-body systems. In the recent literature, the phrase appears in at least four technically distinct senses: the extension of participatory design from local settings to large sociotechnical infrastructures; the prediction, scheduling, proof, or incentive alignment of participation in distributed systems; the empirical scaling of turnout and representation in democratic decision-making; and the mathematical study of participation factors, inverse participation ratios, and participation entropy under changes of units, basis, or system size (Hochwarter et al., 2020, 1711.02150, Borghesi et al., 2013, Xia et al., 2024).

1. Meanings and scope of the term

In the surveyed literature, “participation” does not name a single object. It ranges from stakeholder agency in design processes to client engagement in federated learning, citizen turnout in local elections, and basis-dependent localization measures in nonlinear dynamics and quantum many-body systems. The common problem is not semantic identity but preservation of interpretability under expansion, aggregation, or rescaling.

Domain	Meaning of scaling participation	Representative papers
Participatory design and AI governance	Extending meaningful participation from local settings to large, multi-site, or foundation-model-based systems	(Hochwarter et al., 2020, Sloane et al., 2020, Suresh et al., 2024)
Distributed services and infrastructures	Sustaining, scheduling, predicting, or proving participation as users, peers, or clients join, leave, or contribute	(Kamal et al., 2016, 1711.02150, Chaidos et al., 2023, İşler et al., 11 Nov 2025, Lu et al., 2016, Feng et al., 5 Jun 2026)
Democratic decision-making	Explaining how turnout and representation scale with constituency size	(Borghesi et al., 2013)
Dynamical and quantum systems	Defining participation factors or participation entropies that remain meaningful under rescaling, basis choice, or thermodynamic limits	(Xia et al., 2024, Misguich et al., 2016, Zhang et al., 2019, Frey et al., 2023, Heinrich et al., 13 Mar 2026)

A plausible implication is that “scaling participation” functions less as a unified theory than as a recurrent structural question: how to preserve agency, interpretability, or diagnostic value when the object of participation is no longer local.

2. Participatory design, machine learning, and foundation models

In participatory design, scaling participation refers to enabling participatory design to operate in “large-scale, multi-site, platform-based information systems and infrastructures,” rather than only in “small, local, in-house projects” (Hochwarter et al., 2020). The paper on managed communities analyzes this problem through a healthcare case in which a vendor organizes a yearly user conference and fee-based “HealthSoftWare Academy” courses. These arrangements are treated as mechanisms for “generification work”: turning local requirements into a product that “can travel” across many organizations. Their power structure is analyzed through four mechanisms—agenda, participants, scope, and resources—showing that large-scale participation is materially shaped by who sets topics, who can afford to attend, and what is deemed discussable (Hochwarter et al., 2020).

A more critical literature argues that participation cannot be treated as a scalable design fix for machine learning. “Participation is not a Design Fix for Machine Learning” distinguishes participation as work, participation as consultation, and participation as justice, and warns that ML systems often rely on the first two while rhetorically invoking the third (Sloane et al., 2020). The paper names this dynamic “participation-washing”: the use of participation language to legitimize systems whose extractive logics, decision rights, and governance structures remain unchanged. Its central claim is that participatory design is “necessarily situated and context-dependent,” whereas the dominant ML ideal is “context-independent scalability,” so attempts to standardize participation as a reusable module tend to dilute earlier gains as products scale beyond the original context (Sloane et al., 2020).

The same tension becomes sharper with foundation models. “Participation in the age of foundation models” argues that it is intractable for impacted communities to meaningfully shape a model intended to be universally applicable (Suresh et al., 2024). The proposed response is a three-layer architecture. The “foundation” layer contains the base model; the intermediate “subfloor” layer develops shared technical infrastructure, norms, and governance for a grounded domain; and the “surface” layer concerns a specific downstream task. The “subfloor” layer is designed to scope the range of harms to consider, create more concrete avenues for deliberation, and avoid duplicative effort by scaling input across relevant use cases. The paper illustrates this architecture with clinical care, financial services, and journalism (Suresh et al., 2024).

These works converge on a negative and a positive thesis. The negative thesis is that participation does not scale frictionlessly when what must be governed is generic, context-disconnected, and centrally controlled. The positive thesis is that scaling becomes more plausible when participation is re-situated in domain-grounded infrastructures and long-term governance arrangements rather than in one-off consultations or universally applicable rulesets. This suggests that the central design problem is not simply enlarging participation numerically, but relocating it to the level where collective agency remains tractable.

3. Operational participation in distributed infrastructures and AI systems

A separate body of work treats participation as an operational quantity to be predicted, scheduled, incentivized, or certified. In smart-city IoT management, participation is the extent to which citizens use and engage with services through smart-device usage, media consumption, GUI feedback, and ongoing interaction with regulatory and emergency services (Kamal et al., 2016). “Non-Parametric Bayesian Rejuvenation of Smart-City Participation through Context-aware Internet-of-Things (IoT) Management” defines two key requirements: “unwrapping of contexts, which are relevant” and “scaling up (over time) of participation.” It models observed participation $\mathbf{X}$, latent contexts $\mathbf{Z}$, and parameters $\theta$ through $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$, with posterior $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$. The non-parametric Bayesian construction is used to let the number of contexts grow with data, and the empirical assessment combines 71 participants, controlled lab measurements, and acceptability-based smartphone feedback (Kamal et al., 2016).

In cloud-hosted multimedia conferencing, scaling participation means keeping the conference size elastic as users join and leave while meeting QoS constraints (1711.02150). The ADS mechanism formalizes this as an ILP with two application-level parameters: $\theta$, the maximum acceptable delay for a participant to join, and $\delta$, the IaaS provisioning lag. The objective is to minimize a time-weighted capacity cost while guaranteeing enough capacity for arrivals and active participants. The heuristic runs in $O(n\cdot(\theta-\delta))$ time and, in simulation, its resource provisioning cost is within 18% of optimal for OPPD and within 35% of optimal for MMOG workloads, while a greedy baseline has lower QoS violation cost but substantially higher resource cost (1711.02150).

In permissionless blockchains, the problem is strategic participation under stochastic eligibility (Chaidos et al., 2023). The basic game has participation cost $\alpha$, reward $r$, threshold $\mathbf{Z}$0, and eligibility probability $\mathbf{Z}$1. In the homogeneous case with $\mathbf{Z}$2, the all-in profile is a Nash equilibrium if and only if

$\mathbf{Z}$3

The paper extends this to retraction and universal-payment regimes and shows that universal payments can sustain participation but require strictly higher total expenditure than eligibility-based rewards for the same equilibrium target (Chaidos et al., 2023). Here scaling participation means designing reward mechanisms so that large populations do not collapse into abstention or free riding.

In federated learning, the problem is auditable participation under privacy constraints. “FedPoP” introduces nonlinkable proof of participation without a public ledger and without extensive computations, while remaining compatible with secure aggregation (İşler et al., 11 Nov 2025). The system combines threshold signatures on the trained model with an OPRF-based proof using a group witness. In the prototype, FedPoP adds 0.97 seconds of per-round overhead atop securely aggregated FL and allows a client to prove participation to a third party in 0.0612 seconds, while preserving anonymity and unlinkability (İşler et al., 11 Nov 2025).

In unstructured P2P networks, dynamic peer participation is a topology-maintenance problem. E-SRA maintains a limited scale-free overlay with user-defined exponent $\mathbf{Z}$4 and hard cut-off $\mathbf{Z}$5 under both joins and leaves, using local PUSH and SHUFFLE operations and no global information (Lu et al., 2016). The average number of update messages per node lifetime is bounded by $\mathbf{Z}$6, and the resulting topologies improve flooding and normalized flooding efficiency relative to competing growth models (Lu et al., 2016).

The most explicitly participatory AI proposal in this operational sense is “Scaling Participation in Modular AI Systems” (Feng et al., 5 Jun 2026). It constructs collaborative systems out of 61 contributed models, uses a default pool of 32, and evaluates 14 collaboration methods across API-level, text-level, and weight-level composition. The resulting participatory systems outperform monolithic and/or non-participatory baselines by up to 15.4% across 15 tasks, improve by 28.78% on average as the number of contributors scales from 2 to 32, benefit from contributor diversity by 13.8% on average, and solve over 15% of problems where all individual models fail (Feng et al., 5 Jun 2026). In this setting, participation is itself the scaling resource: more contributors, more model diversity, and more composition mechanisms increase system capability.

4. Democratic participation and representation

One of the clearest quantitative uses of the term concerns turnout and representation in local democracy. “Universal size effects for populations in group-outcome decision-making problems” studies local elections and the number of democratic representatives across scales (Borghesi et al., 2013). For turnout, the core variable is the logarithmic turnout rate

$\mathbf{Z}$7

where $\mathbf{Z}$8 is the number of registered voters, $\mathbf{Z}$9 the number of actual voters, and $\theta$0 the number of abstainers. Across 21 local elections in 10 countries, the conditional mean is well fitted by

$\theta$1

with $\theta$2 for 8 out of 10 countries, while the conditional variance follows

$\theta$3

with $\theta$4 (Borghesi et al., 2013).

The same paper finds that the number of democratic representatives scales as

$\theta$5

with $\theta$6 approximately one-third across municipal councils, regional chambers, and national lower houses. For national lower chambers in 181 democratic countries, the empirical relation is $\theta$7, while continent-specific exponents remain near $\theta$8–$\theta$9 (Borghesi et al., 2013). The authors interpret the parallel exponents $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$0, $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$1, and $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$2 as evidence for a hierarchical internal structure in which each constituency of size $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$3 is divided into about $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$4 subgroups with $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$5.

The paper’s phenomenological model links abstention to a voter’s perceived distance from the rest of the constituency. An agent’s inclination is written as

$$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$6

where $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$7 is a hierarchical group idiosyncrasy, $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$8 is the depth of the agent in the constituency hierarchy, and $$p(\mathbf{X},\mathbf{Z}) = p(\mathbf{X}\mid \mathbf{Z},\theta)p(\mathbf{Z}\mid\theta)$$9 is a national field (Borghesi et al., 2013). This gives a direct formalization of scaling participation as a size effect: turnout per capita declines with constituency size in a universal logarithmic form, while representation rises sublinearly. A plausible implication is that democratic participation at larger scales is mediated less by atomized individuals than by nested collective structures.

5. Participation as a scaling-sensitive diagnostic in dynamical and quantum systems

In nonlinear dynamical systems, participation refers to the contribution of state variables to modes. The classical linear participation factor is

$$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$0

where $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$1 and $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$2 are right and left eigenvectors of the linearized dynamics (Xia et al., 2024). The key issue is scaling ambiguity: if $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$3 and $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$4, then the combined factor $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$5 controls whether participation is uniquely defined. The paper proves that linear participation factors in mode $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$6 are unique if and only if the corresponding $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$7 is unique, whereas nonlinear participation factors generally require that all $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$8 be fixed. It also shows that linear participation factors are invariant under diagonal scaling of state variables—changing physical units does not alter $$p(\mathbf{Z}\mid \mathbf{X}) = p(\mathbf{X},\mathbf{Z})/p(\mathbf{X})$$9—but nonlinear participation factors are sensitive to unit changes through the normal-form coefficients (Xia et al., 2024). In this literature, “scaling participation” is literally the problem of how mode scaling and state scaling enter the formulas.

In many-body quantum systems, participation is often measured by inverse participation ratios. For the XXZ spin chain in the Ising basis, the paper defines

$\theta$0

where $\theta$1 is the mean infinite-time return probability to a randomly chosen basis state (Misguich et al., 2016). The scaling of $\theta$2 distinguishes phases: $\theta$3 in the gapped phase, $\theta$4 in the integrable gapless phase, and $\theta$5 appears to saturate to a constant in the non-integrable gapless phase with next-nearest-neighbor interactions (Misguich et al., 2016). The associated entropy function $\theta$6, defined through $\theta$7, describes how rare high-IPR states dominate $\theta$8 in the gapped regime.

The same logic appears at the many-body localization transition. In the disordered quantum Ising chain, participation entropy is defined from the many-body IPR as

$\theta$9

with the study focusing on $\delta$0 (Zhang et al., 2019). Finite-size scaling of $\delta$1 yields $\delta$2 and $\delta$3, in agreement with the critical point and exponent extracted from entanglement entropy, supporting the interpretation of the MBL transition as a localization transition in many-body configuration space (Zhang et al., 2019).

When exact Hilbert-space fragmentation is present, ordinary basis IPRs become insufficient, because states can be extended inside disconnected blocks. “Probing Hilbert space fragmentation and the block inverse participation ratio” introduces

$\delta$4

where $\delta$5 projects onto a fragmented block (Frey et al., 2023). The paper uses perturbation theory around the fragmented limit to define an effective block structure and finds that the resulting block IPR yields a boundary between fragmented and nonfragmented regimes compatible with level statistics and bipartite entanglement. Its scaling analysis indicates that a finite region around the exactly fragmented limit is dominated by approximate fragmentation even in the thermodynamic limit, suggesting that fragmentation constitutes a phase (Frey et al., 2023).

In monitored quantum circuits at measurement-induced criticality, participation entropy becomes a dynamical critical observable. “Critical behaviors of magic and participation entropy at measurement induced phase transitions” finds that both participation entropy and stabilizer entropy exhibit critical slowing down: their saturation time scales linearly with system size along the critical line separating a low-entanglement spin-glass phase from a paramagnetic phase (Heinrich et al., 13 Mar 2026). The bipartite participation mutual information shows logarithmic scaling behavior similar to entanglement entropy, while in a hybrid random quantum automaton the appropriate scaling variable is $\delta$6 with $\delta$7 (Heinrich et al., 13 Mar 2026). Across these studies, scaling participation is inseparable from basis choice, block structure, and the asymptotic regime under consideration.

6. Recurrent tensions and controversies

Several controversies recur across these otherwise disparate literatures. In participatory AI and ML, the main dispute concerns whether participation can be made scalable without becoming extractive. One line of work argues that context-independent scaling of participation produces participation-washing and hidden labor extraction (Sloane et al., 2020). Another shows that managed communities can discover common needs across user bases but may “legitimatise in a pseudo-democratic way the exclusion of the particular,” putting core participatory design values at risk (Hochwarter et al., 2020). Work on foundation models sharpens this tension by arguing that a universally applicable base model is too detached from context to be meaningfully governed by impacted communities, motivating the domain-specific “subfloor” as a compromise between local control and non-duplicative scale (Suresh et al., 2024).

In quantitative systems, the central controversy is not power but invariance. Nonlinear participation factors can cease to be well-defined under arbitrary mode or state scaling unless precise $\delta$8-conditions are imposed (Xia et al., 2024). Standard IPRs may fail to detect fragmented structure unless the diagnostic is lifted from microscopic basis states to blocks (Frey et al., 2023). Participation entropy at monitored criticality scales differently from its purely unitary counterpart, so the meaning of “slow” or “extended” participation depends on the circuit class and critical regime (Heinrich et al., 13 Mar 2026).

A further recurring theme is trade-off. In conferencing, lower resource cost can come with higher QoS violation cost, as the ADS heuristic outperforms a greedy baseline in resource efficiency while the greedy policy has the lowest QoS violation cost (1711.02150). In blockchain participation games, universal-payment schemes can maintain participation under imperfect observability but do so at strictly higher total expenditure than more discriminating reward mechanisms (Chaidos et al., 2023). In federated learning, auditable participation can be achieved without public ledgers and without extensive computations, but only through additional cryptographic structure layered atop secure aggregation (İşler et al., 11 Nov 2025).

Taken together, these works suggest that scaling participation is never purely an expansion problem. It is a problem of preserving the meaning of participation—agency, incentive compatibility, uniqueness, or diagnostic sharpness—under the very transformations that make systems large, generic, or compositional.