A Computational Systems Model of Justice-Centred Multi-Level Governance for Human Flourishing Under Bounded Non-Exploitation

1. Introduction

1.1. The Challenge of Multi-Level Governance

Contemporary governance problems—climate change, pandemic response, migration, digital regulation, financial stability—are inherently multi-level. Households, communities, municipalities, provinces, nation-states, regional blocs, and global institutions act in coupled ways. Yet the dominant formal models in political economy and public choice treat governance as occurring at a single level, typically the nation-state.

The multi-level structure matters because it creates opportunities for jurisdictional exploitation: a higher level imposing uncompensated costs on a lower level, a powerful state extracting from a weaker one, a present generation depleting the capabilities of a future one. These are governance failures arising from asymmetric power, incomplete representation, and the absence of enforceable reciprocity. Most formal models either assume them away or permit them when aggregate welfare improves—endorsing arrangements that are efficient but unjust.

1.2. The Computational and Systems Perspective

This paper adopts a computational systems approach. Governance is modelled as a complex adaptive system with multiple interacting levels, feedback loops, and emergent dynamics. It builds on six traditions:

• Systems theory and cybernetics (Ashby, 1956; Beer, 1972; Meadows, 2008).
• Polycentric governance (Ostrom, 1990, 2010; McGinnis, 1999).
• Institutional economics (North, 1990; Acemoglu & Robinson, 2012).
• Capability theory (Sen, 1999; Nussbaum, 2011).
• Eudaimonic well-being research (Ryan & Deci, 2001; Seligman, 2011).
• Contemporary justice theory (Rawls, 1971; Fraser, 2009; Young, 1990; Pettit, 1997; Gardiner, 2011).

1.3. The Justice Gap

Bounded non-exploitation is not coextensive with justice. A system can satisfy it perfectly while remaining unjust in at least five respects:

• Distributive injustice below the exploitation threshold.
• Procedural exclusion without extraction.
• Recognition injustice without resource harm.
• Corrective neglect of ended but unremedied harm.
• Intergenerational depletion through voluntary transactions.

These are the normal form of structural injustice in multi-level systems: harm that operates below the threshold of detectable exploitation, through background institutions and accumulated advantage.

We therefore extend GSM with justice as a sixth capability cluster—productive, fragile, multi-level, and contestable.

1.4. Core Contributions

1. A multi-level governance architecture. GSM-J formalizes $L$ interacting levels with coupled jurisdictions, vertical and horizontal interaction decomposed into cooperative and exploitative components, and cross-level information flows with fidelity matrices.

2. Justice as a governance capability. Justice is decomposed into five dimensions with a signed interaction matrix, embedded in the state space, and coupled to the other five capabilities. This shifts justice from an evaluative afterthought to an endogenous state variable.

3. An enforcement and accountability architecture. Four justice constraints—bounded non-exploitation, dimension-specific floor, vulnerability-sensitive non-exploitation, and dimension-wise vertical alignment—are complemented by a dimension-specific accountability mechanism and a policy-intervention projection operator with designated authority, multi-channel implementation cost, finite horizon, and passive recovery.

4. A conditional normative framework. Normative parameters (weights, floors, prioritarian coefficients, subsidiarity, coupling coefficients, intervention weights) are explicit, representable, and swappable. The model predicts consequences; it does not derive values.

5. An open-source implementation. The gsm-governance Python library implements the full model and a scenario protocol that supports ablation, sensitivity analysis, and empirical extension.

1.5. The Normative Status of GSM-J

GSM-J is a conditional model, not a normative theory. Given specified normative parameters, the model predicts systemic consequences. Its contribution is to make those parameters explicit, contestable, and swappable. Users who reject prioritarianism can set ${\delta }_d={\gamma }_d$; users who reject intergenerational weighting can set $w_I=0$; users who reject floors can set $J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d=0$. Each choice produces a different model, and each choice’s consequences are inspectable.

The architecture constitutes a candidate framework for a computational theory of normative governance systems: a formal apparatus in which normative commitments are explicit parameters, systemic consequences are derivable, and the space of possible governance regimes is explorable by simulation. GSM-J does not resolve normative disagreement; it structures it.

2. Theoretical Foundations

2.1. Human Flourishing

We adopt a eudaimonic, multi-dimensional, capability-based conception of flourishing: the ongoing realization of a good human life, comprising subjective well-being, meaning and purpose, growth and mastery, autonomy and agency, relationships and belonging, health and vitality, character and virtue, engagement and play, and contribution and transcendence. Flourishing is relational, ecological, lifelong, and imperfect.

2.2. Bounded Non-Exploitation

Let $E_{ij}\left(t\right)\in {\mathbb{R}}_{\ge 0}$denote the exploitation index: the uncompensated, non-trivial sacrifice imposed by jurisdiction $i$on jurisdiction $j$at time $t$, for $i$’s benefit. The bounded non-exploitation constraint states:

$$E_{ij}\left(t\right)\le {\tau }_j\mathrm{or}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}_{ij}\left(t\right)\ge E_{ij}\left(t\right)\forall i,j,t$$

where ${\tau }_j$is jurisdiction $j$’s tolerance threshold and ${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}_{ij}$is the compensation vector transferred from $i$to $j$.

2.3. Why Non-Exploitation Is Not Sufficient for Justice

Bounded non-exploitation is negative and dyadic. Justice is broader as shown in Table 1.

A system can satisfy bounded non-exploitation perfectly while remaining profoundly unjust. Non-exploitation is therefore necessary but not sufficient for justice.

2.4. Justice as a Governance Capability

Justice is:

• Productive — it enables trust, voluntary compliance, information sharing, and long-horizon cooperation.
• Fragile — it can be eroded by short-term optimization, power concentration, and exploitation of vulnerable populations.
• Multi-level — realized or violated at household through global levels.
• Contestable — what counts as just is a matter of normative disagreement.

This conception draws on Rawls (1971), Sen (1999), Nussbaum (2011), Fraser (2009), Young (1990), Pettit (1997), and Gardiner (2011). It is pluralist in recognizing multiple irreducible dimensions and prioritarian in weighting improvements to the worst off more heavily.

3. The Computational Model: GSM-J

3.1. Levels and Units

Let $l\in \left\{1,\dots ,L\right\}$index governance levels, $L=6$, then Six levels are modeled, from household to global commons, each with a representative unit. The multi-level structure is what creates the possibility of jurisdictional exploitation and cross-level justice obligations, as shown Table 2.

Let $i\in {\mathcal{I}}^{\left(l\right)}$index jurisdictions at level $l$; $\mathcal{N}\left(i\right)$denotes same-level neighbors; $i^{\pm 1}$denotes parent and child units.

3.2. State Vector

Each jurisdiction $i$ at level $l$ carries:

$${\mathit{x}}_i^{\left(l\right)}\left(t\right)={\left[A_i,C_i,S_i,T_i,L_i,J_i\right]}^{\left(l\right)}\left(t\right)\in {\left[0,1\right]}^6$$

including accountability (A), institutional competence (C), social cohesion (S), strategic continuity (T), adaptive learning (L), and justice (J). Justice is the newly added sixth cluster; the other five are inherited from the General Governance Success Model, as detailed in Table 3.

3.3. Justice Capability Cluster

$$J_i^{\left(l\right)}\left(t\right)={\left[J_i^D,J_i^P,J_i^R,J_i^C,J_i^I\right]}^{\left(l\right)}\left(t\right)$$

where each of J^D, J^P, J^R, J^C, and J^I represent one dimension of justice capability, as detailed in Table 4.

Scalar aggregate:

$$J_i^{\left(l\right)}=\sum _{d\in \left\{D,P,R,C,I\right\}}{w}_d\hspace{0.17em}{J}_i^{d,\left(l\right)},\sum _d{w}_d=1,\mid w_d\ge 0$$

Weights are not derived from the model; users must specify and justify them.

3.3.1. Justice Dimension Interactions: ${\mathit{M}}_{\mathit{J}}$

Justice dimensions interact—not always synergistically. The signed interaction matrix $M_J\in {\mathbb{R}}^{5\times 5}$captures both.

$${\mathcal{C}}_J^d\left({\mathit{J}}_i\right)=\sum _{e\ne d}{m}_{de}{J}_i^e\left(1-J_i^d\right)$$

where $m_{de}\in \left[-,m_{\mathrm{m}\mathrm{a}\mathrm{x}}+m_{\mathrm{m}\mathrm{a}\mathrm{x}}\right]$is the signed coefficient from $e$to $d$, and $\left(1-J_i^d\right)$is a saturation factor.

Synergy entries (positive).

Table 5. Synergy entries in the justice interaction matrix M_J.

Entry	Theoretical claim
$m_{PR},m_{RP}$	Procedural voice and recognition reinforce each other
$m_{DP},m_{PD}$	Distributive security and procedural participation reinforce each other
$m_{DC}$	Distributive capacity enables corrective remedy
$m_{CR},m_{RC}$	Corrective remedy and recognition mutually reinforce
$m_{IP}$	Intergenerational concern extends procedural inclusion

Table 5. Synergy entries in the justice interaction matrix M_J.

Entry	Theoretical claim
$m_{PR},m_{RP}$	Procedural voice and recognition reinforce each other
$m_{DP},m_{PD}$	Distributive security and procedural participation reinforce each other
$m_{DC}$	Distributive capacity enables corrective remedy
$m_{CR},m_{RC}$	Corrective remedy and recognition mutually reinforce
$m_{IP}$	Intergenerational concern extends procedural inclusion

Tension entries (negative).

Table 6. Tension entries in the justice interaction matrix M_J.

Entry	Theoretical claim
$m_{ID},m_{DI}$	Present-oriented distribution displaces future investment
$m_{CD}$	Large corrective transfers draw from present distributive resources
$m_{PI},m_{IP}^{-}$	Present participation crowds out future representation

Table 6. Tension entries in the justice interaction matrix M_J.

Entry	Theoretical claim
$m_{ID},m_{DI}$	Present-oriented distribution displaces future investment
$m_{CD}$	Large corrective transfers draw from present distributive resources
$m_{PI},m_{IP}^{-}$	Present participation crowds out future representation

The net coefficient for each ordered pair is the sum of synergy and tension contributions. Default values in gsm-governance are set to theoretical priors; empirically, $M_J$is estimable.

3.3.2. Estimation Protocol for ${\mathit{M}}_{\mathit{J}}$

Signed coefficients introduce an overparameterization risk. For five dimensions, $M_J$contains 20 off-diagonal coefficients. Three constraints discipline estimation.

Constraint 1 — Bounded support. $m_{de}\in \left[-,m_{\mathrm{m}\mathrm{a}\mathrm{x}}+m_{\mathrm{m}\mathrm{a}\mathrm{x}}\right]$, default $m_{\mathrm{m}\mathrm{a}\mathrm{x}}=0.30$.

Constraint 2 — Sign priors. Each coefficient receives a sign prior ${\sigma }_{de}\in \left\{+,-,\pm ,0\right\}$from §3.3.1. Priors are informative but not binding.

Constraint 3 — Symmetry regime. Two regimes are available:

• Symmetric ($m_{de}=m_{ed}$): 10 free parameters. Appropriate for small samples.
• Asymmetric ($m_{de}\ne m_{ed}$): 20 free parameters. Appropriate when directional hypotheses are of interest and data permit.

Estimation strategy. A hierarchical Bayesian dynamic factor model:

• Observation model. Observed indicators $J_{i,t}^d$ = latent $J_{i,t}^d$ + ${\epsilon }_{i,t}^d$, $\epsilon \sim \mathcal{N}\left(0,{\sigma }_d^2\right)$.
• State evolution. Latent justice follows §4.2 with coupling ${\mathcal{C}}_J^d$ depending on $M_J$.
• Priors on$M_J$. Truncated Gaussians centered on sign-prior means with small scale when the sign is definite, larger when contested.
• Partial pooling. Jurisdiction-specific $m_{de}^{\left(i\right)}\sim \mathcal{N}\left(m_{de}^{\mathrm{group}},{\tau }_{de}^2\right)$.
• Identification. At least one exogenous shock per jurisdiction affecting a subset of dimensions; sufficient temporal variation; sign restrictions to break reflection and permutation symmetries.
• Inference. Particle filter or EKF with importance resampling; MCMC or variational inference for posterior.

Fallback. When users lack panel data, default theoretical priors should be used explicitly, and results reported under at least two alternative priors (all-positive vs. mixed-sign) for sensitivity.

3.3.3. Operationalizing Recognition Justice

$$J^R={\displaystyle \frac{1}{3}}\left(R^{\mathrm{dom}}+R^{\mathrm{exc}}+R^{\mathrm{assim}}\right)$$

Table 7. Components of recognition justice (J^R).

Component	Definition
$R^{\mathrm{dom}}$	Non-domination: absence of arbitrary interference
$R^{\mathrm{exc}}$	Non-exclusion: inclusion in the community of peers
$R^{\mathrm{assim}}$	Non-assimilation: tolerance of difference

Table 7. Components of recognition justice (J^R).

Component	Definition
$R^{\mathrm{dom}}$	Non-domination: absence of arbitrary interference
$R^{\mathrm{exc}}$	Non-exclusion: inclusion in the community of peers
$R^{\mathrm{assim}}$	Non-assimilation: tolerance of difference

Measurement protocols in Appendix C.

3.4. Exploitation Index

$$E_{ij}\left(t\right)=\sum _d{E}_{ij}^d\left(t\right)$$

Table 8. Components of the exploitation index (E_ij).

Component	Measurement
$E_{ij}^D$	Net resource transfer relative to fair-share benchmark
$E_{ij}^P$	Asymmetry in decision-making influence
$E_{ij}^R$	Assimilation pressure; dignity violations
$E_{ij}^C$	Unremedied harm from prior exploitation
$E_{ij}^I$	Depletion of future-oriented capital

Table 8. Components of the exploitation index (E_ij).

Component	Measurement
$E_{ij}^D$	Net resource transfer relative to fair-share benchmark
$E_{ij}^P$	Asymmetry in decision-making influence
$E_{ij}^R$	Assimilation pressure; dignity violations
$E_{ij}^C$	Unremedied harm from prior exploitation
$E_{ij}^I$	Depletion of future-oriented capital

Non-exploitation in one dimension does not imply non-exploitation in another.

3.5. Compensation Mechanism

$${\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}_{ij}\left(t\right)={\left[{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}^F,{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}^I,{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}^R,{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}^{Reg},{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}^{Fut},{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}^{Rest}\right]}_{ij}\left(t\right)$$

Table 9. Components of the compensation vector (Comp_ij).

Component	Primary Target
Fiscal transfers	$J^D$
Infrastructural investment	$J^D,J^C$
Representational inclusion	$J^P,J^R$
Regulatory constraint	$J^P,J^R,J^I$
Future-oriented transfer	$J^I$
Restitutional benefits	$J^C$

Table 9. Components of the compensation vector (Comp_ij).

Component	Primary Target
Fiscal transfers	$J^D$
Infrastructural investment	$J^D,J^C$
Representational inclusion	$J^P,J^R$
Regulatory constraint	$J^P,J^R,J^I$
Future-oriented transfer	$J^I$
Restitutional benefits	$J^C$

Adequacy: ${\lambda }_j\cdot {\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}_{ij}\left(t\right)\ge E_{ij}\left(t\right)$, with ${\lambda }_j\in {\left[0,1\right]}^6$.

3.6. Justice Constraints

3.6.1. C1 — Bounded Non-Exploitation

$$E_{ij}\left(t\right)\le {\tau }_j\mathrm{or}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}_{ij}\left(t\right)\ge E_{ij}\left(t\right)\forall i,j,t$$

3.6.2. C2 — Justice Floor

$$J_i^{d,\left(l\right)}\left(t\right)\ge J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d\forall i,l,d,t$$

Philosophical foundation. Three traditions converge on a moral minimum: sufficientarianism (Frankfurt, 1987; Crisp, 2003; Shields, 2012), capability thresholds (Nussbaum, 2000, 2011), and human rights frameworks (UDHR, 1948).

Table 10. Default justice floors ($J_{min}^d$) by dimension.

Dimension	Default $J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d$	Justification
$J^D$	0.30	Maximin floor at ~30% of capability-adjusted median
$J^P$	0.25	Minimal procedural rights
$J^R$	0.25	Non-domination threshold
$J^C$	0.10	Minimal restorative commitment
$J^I$	0.20	Weak sustainability

Table 10. Default justice floors ($J_{min}^d$) by dimension.

Dimension	Default $J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d$	Justification
$J^D$	0.30	Maximin floor at ~30% of capability-adjusted median
$J^P$	0.25	Minimal procedural rights
$J^R$	0.25	Non-domination threshold
$J^C$	0.10	Minimal restorative commitment
$J^I$	0.20	Weak sustainability

Defaults are placeholders for deliberation.

3.6.3. C3 — Vulnerability-Sensitive Non-Exploitation

$$\mathrm{If}{J}_j^{\left(l\right)}\left(t\right)<J_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{agg}},\mathrm{then}{E}_{ij}\left(t\right)=0\forall i$$

This closes a gap in C1: a jurisdiction below the justice floor may have a low tolerance threshold and thus be exploited legally under C1. C3 prohibits this, encoding a prioritarian commitment.

3.6.4. C4 — Vertical Justice Alignment (Subsidiarity)

C4 is a non-regression principle, not uniformity.

Dimension-level formulation (default).

$$J_i^{d,\left(l\right)}\left(t\right)\ge \varphi \cdot J_i^{d,\left(l-1\right)}\left(t\right)\forall d$$

This prevents a parent from satisfying C4 in aggregate while eroding one dimension below the child’s level. The aggregate form is available as C4Mode.AGGREGATE.

4. Dynamics

4.1. Capability Dynamics

Each capability evolves according to dynamics calibrated to its functional role. Full specifications are in gsm-governance.

4.2. Justice Dynamics

$${\displaystyle \frac{d{J}_i^d}{dt}}=\underset{\mathrm{internal}}{\underbrace{g_d\left({\mathit{x}}_i\right)}}+\underset{\mathrm{exploitation}/\mathrm{compensation}}{\underbrace{h_d\left(\mathit{E},\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\right)}}+\underset{\mathrm{coupling}}{\underbrace{{\mathcal{C}}_J^d\left({\mathit{J}}_i\right)}}+\underset{\mathrm{diffusion}}{\underbrace{\eta \sum _j{A}_{ij}\left(J_j^d-J_i^d\right)}}-\underset{\mathrm{decay}}{\underbrace{{\kappa }_d{J}_i^d}}$$

Internal:

$$g_D={\alpha }_D{A}_i{C}_i,g_P={\alpha }_P{A}_i{L}_i,g_R={\alpha }_R{S}_i{A}_i,g_C={\alpha }_C{A}_i,g_I={\alpha }_I{T}_i{L}_i$$

Exploitation/compensation:

$$h_d=-{\beta }_d\sum _{i^{\text{'}}\ne i}{E}_{i^{\text{'}}i}^d+{\beta }_d^{\text{'}}\sum _{i^{\text{'}}\ne i}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}_{i^{\text{'}}i}^d$$

Corrective restorative:

$${\displaystyle \frac{d{J}_j^C}{dt}}+={\alpha }_C^{\mathrm{rest}}\sum _i{E}_{ij}\left(t\right)\cdot {\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}}_{ij}\left(t\right)$$

4.3. Cross-Level Accountability (Dimension-Specific)

Let $m_i^{d,\left(l\right)}\left(t\right)={\mathrm{m}\mathrm{i}\mathrm{n}}_{j\in \mathcal{C}\left(i\right)}{J}_j^{d,\left(l-1\right)}\left(t\right)$denote the minimum value of dimension $d$across jurisdiction $i$’s children. Then:

$$A_i^{\left(l\right)}\leftarrow A_i^{\left(l\right)}+{\lambda }_c\left[{\overline{m}}_i^{\left(l\right)}-A_i^{\left(l\right)}\right]-\sum _d{\lambda }_p^d{\left[J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d-m_i^{d,\left(l\right)}\right]}^{+}$$

where ${\overline{m}}_i^{\left(l\right)}={\displaystyle \frac{1}{\mid \mathcal{D}\mid }}{\sum }_d{m}_i^{d,\left(l\right)}$is the average of dimension-specific minimums.

Default values. ${\lambda }_c=0.15$. Dimension-specific penalties:

Table 11. Default dimension-specific accountability penalties (${\lambda }_p^d$).

Dimension	${\lambda }_p^d$
Distributive	0.30
Procedural	0.30
Recognition	0.45
Corrective	0.20
Intergenerational	0.35

Table 11. Default dimension-specific accountability penalties (${\lambda }_p^d$).

Dimension	${\lambda }_p^d$
Distributive	0.30
Procedural	0.30
Recognition	0.45
Corrective	0.20
Intergenerational	0.35

Elevated penalties for recognition and intergenerational justice reflect the view that these dimensions are systematically under-enforced. This is a normative choice, not a derivation.

Properties. No masking across dimensions; non-trivial coupling; consistency with C4. A child with high distributive justice and low recognition justice triggers the recognition penalty even when the aggregate is adequate.

4.4. Justice Suppression of Exploitation

$${\displaystyle \frac{d{E}_{ij}}{dt}}-=\mu \cdot \min \left(J_i,J_j\right)\cdot E_{ij}$$

5. Welfare Function

5.1. Base Welfare5.2. Dimension-Specific Justice-Enhanced Welfare

$$W\left(t\right)=\sum _{i,l}{\varphi }_i^{\left(l\right)}{F}_i^{\left(l\right)}\left(t\right)$$

5.2. Dimension-Specific Justice-Enhanced Welfare

$$W^{*}\left(t\right)=W\left(t\right)+\sum _{i,l}\sum _d{\gamma }_d{J}_i^{d,\left(l\right)}\left(t\right)-\sum _{i,l}\sum _d{\delta }_d\max \left(0,J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d-J_i^{d,\left(l\right)}\left(t\right)\right)$$

The vectors $\gamma =\left({\gamma }_D,\dots ,{\gamma }_I\right)$and $\delta =\left({\delta }_D,\dots ,{\delta }_I\right)$encode value judgments about the relative moral importance of dimensions and their deficits. Setting ${\gamma }_d=\gamma \cdot w_d$and ${\delta }_d=\delta \cdot w_d$recovers the scalar form.

Default: ${\gamma }_d=0.75w_d$, ${\delta }_d=2.0w_d$.

5.3. Justice and Distributional Considerations

Following Rawls (1971), Sen (1999), Nussbaum (2011), and recent federalism scholarship (Sangiovanni, 2022; Miller, 2023), GSM-J recognizes that inequalities are permitted only if they benefit the least advantaged; fair equality of opportunity applies across jurisdictions; the difference principle extends to inter-jurisdictional relations; and compensation is a legitimate mechanism for inter-jurisdictional justice.

5.4. On the Multiplicity of Justice Roles

Justice enters in four roles:

Table 12. The four roles of justice in GSM-J.

Role	Where	Function
State variable	$J_i^{\left(l\right)}$in $\mathit{x}$	Co-evolves with capabilities
Direct welfare contribution	${\sum }_d{\gamma }_d{J}_i^d$	Constitutive of flourishing
Prioritarian penalty	$-{\sum }_d{\delta }_d{\left[J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d-J_i^d\right]}^{+}$	Deficits reduce welfare asymmetrically
Mediator of exploitation	$-\mu \mathrm{m}\mathrm{i}\mathrm{n}\left(J_i,J_j\right)E_{ij}$	Suppresses exploitative dynamics

Table 12. The four roles of justice in GSM-J.

Role	Where	Function
State variable	$J_i^{\left(l\right)}$in $\mathit{x}$	Co-evolves with capabilities
Direct welfare contribution	${\sum }_d{\gamma }_d{J}_i^d$	Constitutive of flourishing
Prioritarian penalty	$-{\sum }_d{\delta }_d{\left[J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d-J_i^d\right]}^{+}$	Deficits reduce welfare asymmetrically
Mediator of exploitation	$-\mu \mathrm{m}\mathrm{i}\mathrm{n}\left(J_i,J_j\right)E_{ij}$	Suppresses exploitative dynamics

Each term operates on a distinct mechanism. Ablation scenarios S13–S15 decompose the total effect.

6. Simulation Protocol

6.1. Parameters

Table 13. Default parameter values for GSM-J simulations.

PARAMETER	SYMBOL	ROLE	DEFAULT
JUSTICE WEIGHTS	$w_d$	Aggregate dimension weights	Simplex
JUSTICE FLOORS	$J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d$	Per-dimension minima	0.10–0.30
AGGREGATE FLOOR	$J_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{agg}}$	Threshold for C3	0.30
PRIORITARIAN PENALTY	${\delta }_d$	Dimension-specific penalties	$2.0w_d$
WELFARE WEIGHT	${\gamma }_d$	Dimension-specific contributions	$0.75w_d$
SUBSIDIARITY	$\varphi$	Vertical non-regression	0.85
DIFFUSION	$\eta$	Horizontal diffusion	0.20
DECAY	${\kappa }_d$	Per-dimension decay	0.05
INTERNAL COUPLING	${\alpha }_d$	Capability-to-justice coupling	0.20–0.35
RESTORATIVE	${\alpha }_C^{\mathrm{rest}}$	Compensation-to-restoration	0.30
ACCOUNTABILITY COUPLING	${\lambda }_c$	Parent–child convergence	0.15
ACCOUNTABILITY PENALTY	${\lambda }_p^d$	Dimension-specific penalties	0.20–0.45
EXPLOITATION SUPPRESSION	$\mu$	Justice suppression of exploitation	0.25
JUSTICE COUPLING	$m_{de}$	Signed coefficients	$\pm 0.30$bound
INTERVENTION COST	${\kappa }^{\mathrm{int}}$	Per unit of correction	0.10
INTERVENTION HORIZON	${\tau }^{\mathrm{int}}$	Steps to full implementation	5
INTERVENTION CHANNEL WEIGHTS	${\omega }^k$	Cost distribution	$\left(0.50,0.25,0.15,0.10\right)$

Table 13. Default parameter values for GSM-J simulations.

PARAMETER	SYMBOL	ROLE	DEFAULT
JUSTICE WEIGHTS	$w_d$	Aggregate dimension weights	Simplex
JUSTICE FLOORS	$J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d$	Per-dimension minima	0.10–0.30
AGGREGATE FLOOR	$J_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{agg}}$	Threshold for C3	0.30
PRIORITARIAN PENALTY	${\delta }_d$	Dimension-specific penalties	$2.0w_d$
WELFARE WEIGHT	${\gamma }_d$	Dimension-specific contributions	$0.75w_d$
SUBSIDIARITY	$\varphi$	Vertical non-regression	0.85
DIFFUSION	$\eta$	Horizontal diffusion	0.20
DECAY	${\kappa }_d$	Per-dimension decay	0.05
INTERNAL COUPLING	${\alpha }_d$	Capability-to-justice coupling	0.20–0.35
RESTORATIVE	${\alpha }_C^{\mathrm{rest}}$	Compensation-to-restoration	0.30
ACCOUNTABILITY COUPLING	${\lambda }_c$	Parent–child convergence	0.15
ACCOUNTABILITY PENALTY	${\lambda }_p^d$	Dimension-specific penalties	0.20–0.45
EXPLOITATION SUPPRESSION	$\mu$	Justice suppression of exploitation	0.25
JUSTICE COUPLING	$m_{de}$	Signed coefficients	$\pm 0.30$bound
INTERVENTION COST	${\kappa }^{\mathrm{int}}$	Per unit of correction	0.10
INTERVENTION HORIZON	${\tau }^{\mathrm{int}}$	Steps to full implementation	5
INTERVENTION CHANNEL WEIGHTS	${\omega }^k$	Cost distribution	$\left(0.50,0.25,0.15,0.10\right)$

6.2. Simulation Scenarios

Table 14. Simulation scenarios S0–S27.

SCENARIO	DESCRIPTION
S0	GSM without justice cluster
S1	GSM-J default
S2–S5	Ablate C2, C4, diffusion, correction
S6–S7	Utilitarian and strict prioritarian baselines
S8	Weight sweep
S9–S10	Shock; historical injustice
S11–S12	No $M_J;$recognition-only coupling
S13–S15	Isolate $\gamma ,\delta ,\mu$terms
S16–S17	Isolate accountability coupling, penalty
S18–S19	Soft-only, hard-only constraints
S20	Aggregate C4 mode
S21	Negative $M_J$disabled
S22	Dimension-specific welfare sweep
S23	High intervention cost
S24	Symmetric vs. asymmetric $M_J$
S25	Uniform vs. differentiated ${\lambda }_p^d$
S26–S27	Single-channel vs. multi-channel intervention cost

Table 14. Simulation scenarios S0–S27.

SCENARIO	DESCRIPTION
S0	GSM without justice cluster
S1	GSM-J default
S2–S5	Ablate C2, C4, diffusion, correction
S6–S7	Utilitarian and strict prioritarian baselines
S8	Weight sweep
S9–S10	Shock; historical injustice
S11–S12	No $M_J;$recognition-only coupling
S13–S15	Isolate $\gamma ,\delta ,\mu$terms
S16–S17	Isolate accountability coupling, penalty
S18–S19	Soft-only, hard-only constraints
S20	Aggregate C4 mode
S21	Negative $M_J$disabled
S22	Dimension-specific welfare sweep
S23	High intervention cost
S24	Symmetric vs. asymmetric $M_J$
S25	Uniform vs. differentiated ${\lambda }_p^d$
S26–S27	Single-channel vs. multi-channel intervention cost

6.3. Metrics

Aggregate flourishing $W^{*}$; flourishing variance; justice floor violations per dimension; exploitation persistence; convergence time; regime shifts; path dependence; intervention frequency and cumulative cost.

6.4. Constraint Enforcement Modes

Mode A — Constitutional projection via policy intervention (§6.5–6.6).

Mode B — Penalty dynamics.

Hybrid (default) — Per-constraint choice.

6.5. Policy Intervention: Cost, Delay, Feasibility

Projection $\mathsf{\Pi }$is not an autonomous state update. It represents the collective effect of institutional decisions—legislation, constitutional amendment, court order, administrative reform, international agreement. Every projection carries:

• A designated authority (C2: jurisdiction or parent; C3: exploiting jurisdiction; C4: parent).
• An implementation cost ${\kappa }^{\mathrm{int}}$ per unit of correction.
• A finite horizon ${\tau }^{\mathrm{int}}$ (steps to full implementation).
• A feasibility condition — projection is attempted only when the authority has sufficient capability.

6.6. Multi-Channel Capability Effects

Intervention cost ${\kappa }^{\mathrm{int}}\cdot \mid \mathsf{\Delta }\mid$is distributed across four capability channels:

$$\omega =\left({\omega }^C,{\omega }^S,{\omega }^T,{\omega }^A\right),\sum _k{\omega }^k=1,\mid {\omega }^k\ge 0$$

Capability update during intervention:

$$\mathsf{\Delta }{C}_i=-{\omega }^C{\displaystyle \frac{{\kappa }^{\mathrm{int}}\mid \mathsf{\Delta }\mid }{{\tau }^{\mathrm{int}}}},\mathsf{\Delta }{S}_i=-{\omega }^S{\displaystyle \frac{{\kappa }^{\mathrm{int}}\mid \mathsf{\Delta }\mid }{{\tau }^{\mathrm{int}}}},\mathrm{etc}.$$

Default weights:

Table 15. Multi-channel intervention cost weights (${\omega }^k$).

Channel	Weight	Rationale
${\omega }^C$	0.50	Administrative capacity is the primary constraint
${\omega }^S$	0.25	Interventions frequently produce short-term polarization
${\omega }^T$	0.15	Overturning prior commitments weakens continuity
${\omega }^A$	0.10	Override of local decision-making has modest accountability cost

Table 15. Multi-channel intervention cost weights (${\omega }^k$).

Channel	Weight	Rationale
${\omega }^C$	0.50	Administrative capacity is the primary constraint
${\omega }^S$	0.25	Interventions frequently produce short-term polarization
${\omega }^T$	0.15	Overturning prior commitments weakens continuity
${\omega }^A$	0.10	Override of local decision-making has modest accountability cost

Passive recovery. Once intervention horizons elapse, capability losses are gradually restored:

$${\displaystyle \frac{d{C}_i}{dt}}+={\rho }_C\left(C_i^{\mathrm{baseline}}-C_i\right)$$

with ${\rho }_k=0.05$default for each channel.

Consequences.

• Interventions are not free even when technically feasible.
• Recovery is slow relative to political cycles, so repeated interventions cumulatively depress capability.
• Intervention frequency ceiling. Aggressive justice-improvement programs are self-limiting unless balanced with capability-restoration periods.

7. Hypotheses

Table 16. Hypotheses H1–H14.

#	Hypothesis
H1	Stronger vertical accountability → stronger cross-level coordination
H2	Polycentric structures outperform monocentric on adaptive learning
H3	Well-calibrated information fidelity → better cross-level coordination
H4	Recursive learning at lower levels strengthens higher-level learning
H5	Bounded non-exploitation improves long-run flourishing
H6	Compensation reduces exploitation persistence
H7	Higher procedural justice → stronger adaptive learning
H8	Recognition justice moderates cohesion–exploitation relationship
H9	Intergenerational justice negatively correlated with short-term welfare maximization
H10	Justice diffusion reduces cross-level exploitation
H11	Justice floors reduce variance of flourishing outcomes
H12	Dimension-specific accountability penalties reduce recognition deficits more effectively than aggregate penalties
H13	Multi-channel intervention costs produce a frequency ceiling on justice-improving interventions
H14	Asymmetric $M_J$estimation improves fit when directional hypotheses hold

Table 16. Hypotheses H1–H14.

#	Hypothesis
H1	Stronger vertical accountability → stronger cross-level coordination
H2	Polycentric structures outperform monocentric on adaptive learning
H3	Well-calibrated information fidelity → better cross-level coordination
H4	Recursive learning at lower levels strengthens higher-level learning
H5	Bounded non-exploitation improves long-run flourishing
H6	Compensation reduces exploitation persistence
H7	Higher procedural justice → stronger adaptive learning
H8	Recognition justice moderates cohesion–exploitation relationship
H9	Intergenerational justice negatively correlated with short-term welfare maximization
H10	Justice diffusion reduces cross-level exploitation
H11	Justice floors reduce variance of flourishing outcomes
H12	Dimension-specific accountability penalties reduce recognition deficits more effectively than aggregate penalties
H13	Multi-channel intervention costs produce a frequency ceiling on justice-improving interventions
H14	Asymmetric $M_J$estimation improves fit when directional hypotheses hold

8. Python Implementation: gsm-governance

Open-source library, six modules: gsm.core, gsm.justice, gsm.enforcement, gsm.welfare, gsm.simulation, gsm.reporting. Core class signatures:

# python

@dataclass

class NormativeParams:

justice_weights: Dict[str, float]

justice_floors: Dict[str, float]

aggregate_floor: float

gamma_dim: Dict[str, float]

delta_dim: Dict[str, float]

lambda_p_dim: Dict[str, float]

phi: float

@dataclass

class StructuralParams:

eta, kappa, alpha, alpha_corrective_restorative: ...

beta_erosion, beta_compensation: float

lam_c, mu: float

intervention_cost: float

intervention_horizon: int

intervention_weights: Dict[str, float]

recovery: Dict[str, float]

class JusticeInteractionMatrix:

m: Dict[Tuple[str, str], float]

m_max: float

regime: MJRegime

def coupling(self, J: Dict[str, float], d: str) -> float: ...

def symmetrize(self) -> None: ...

class JusticeCapability:

d: Dict[str, float]

def aggregate(self, weights) -> float: ...

def satisfies_floors(self, floors) -> bool: ...

def step(self, ...) -> None: ...

class PolicyInterventionEnforcer:

def check_and_schedule(self, jurisdictions, exploitation) -> None: ...

def apply_step(self, jurisdictions, exploitation) -> None: ...

def apply_recovery(self, jurisdictions) -> None: ...

def enforce(self, jurisdictions, exploitation) -> None: ...

def welfare_dimension_specific(base_welfare, jurisdictions, n) -> float: ...

def update_accountability_dimension_specific(parent, jurisdictions, n, s) -> None: ...

Full source, tests, and worked examples are in the repository.

9. Stylized Demonstration Scenario

A six-level governance system with 98 stylized municipalities, 5 regions, one national level, and one EU-level jurisdiction. Initial capability profiles reflect a plausible high-capability system. No claim is made that these values correspond to actual data.

9.1. Qualitative Results

Under default parameters, the model converges to high distributive and procedural justice, moderate recognition, moderate corrective, and moderate intergenerational justice. Aggregate welfare rises modestly when justice is added (S1 vs. S0).

Four findings distinguish the current version:

1. Dimension-specific accountability (S25). Under uniform ${\lambda }_p^d$, recognition justice converges more slowly. Differentiated penalties produce measurably faster recognition improvement because aggregate penalties would permit masking.

2. Multi-channel intervention costs (S26 vs. S27). Under single-channel costs, aggressive intervention can be sustained at high frequency. Under multi-channel costs, cohesion and continuity deplete materially, producing an endogenous frequency ceiling after roughly 15–20 interventions in quick succession.

3. Symmetric vs. asymmetric ${\mathit{M}}_{\mathit{J}}$ (S24). When the data-generating process is asymmetric, forcing symmetry biases welfare trajectories by up to 22% in the stylized run.

4. Negative $M_J$ entries (S21). Disabling tension entries produces higher aggregate justice but lower long-run welfare, because tension entries prevent over-investment in single dimensions.

9.2. Justice–Flourishing Trade-Offs

Under strict prioritarianism (S7), present welfare falls slightly but long-run welfare rises substantially. Under utilitarianism (S6), present welfare is maximized but intergenerational justice falls below the floor.

9.3. From Stylized Demonstration to Empirical Calibration

Full empirical calibration would require indicator data per dimension per level, estimation of $M_J$under §3.3.2, estimation of exploitation from trade/fiscal/regulatory/ecological data, and validation against held-out data. None is performed here.

10. Discussion

10.1. What the Model Shows

Justice is not reducible to non-exploitation. A jurisdiction may satisfy bounded non-exploitation while violating the justice floor, exploiting a vulnerable neighbor, or eroding child justice.

Convergence conditions. Justice and flourishing converge when justice is treated as a capability, exploitation is justice-decomposed, corrective dynamics are active, subsidiarity is enforced dimension-wise, and cross-level accountability is dimension-specific.

Where they conflict. Intergenerational justice constrains present optimization; corrective justice reduces present consumption; recognition justice may reduce short-run cohesion; multi-channel intervention costs imply that aggressive justice improvement is self-limiting.

10.2. Normative Commitments

Table 17. Normative commitments exposed by GSM-J parameters.

Parameter	What it encodes
$w_d$	Dimension importance in aggregate
$J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d,J_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{agg}}$	Moral minimum per dimension
${\gamma }_d,{\delta }_d$	Dimension-specific welfare weights
${\lambda }_p^d$	Dimension-specific accountability penalties
$\varphi$	Tolerated vertical regression
${\tau }_j$	Tolerance for exploitation
$M_J,m_{\mathrm{m}\mathrm{a}\mathrm{x}},{\sigma }_{de}$	Interaction matrix, bounds, sign priors
${\omega }^k,{\kappa }^{\mathrm{int}},{\tau }^{\mathrm{int}}$	Intervention cost structure

Table 17. Normative commitments exposed by GSM-J parameters.

Parameter	What it encodes
$w_d$	Dimension importance in aggregate
$J_{\mathrm{m}\mathrm{i}\mathrm{n}}^d,J_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{agg}}$	Moral minimum per dimension
${\gamma }_d,{\delta }_d$	Dimension-specific welfare weights
${\lambda }_p^d$	Dimension-specific accountability penalties
$\varphi$	Tolerated vertical regression
${\tau }_j$	Tolerance for exploitation
$M_J,m_{\mathrm{m}\mathrm{a}\mathrm{x}},{\sigma }_{de}$	Interaction matrix, bounds, sign priors
${\omega }^k,{\kappa }^{\mathrm{int}},{\tau }^{\mathrm{int}}$	Intervention cost structure

10.3. Policy Implications

• Institutional design should target justice as a capability.
• Justice floors should be dimension-specific.
• Vulnerability-sensitive non-exploitation is stronger than bounded non-exploitation.
• Corrective mechanisms must build capability.
• Subsidiarity should be enforced dimension-wise.
• Constraint enforcement modes should be explicit.
• Justice dimensions interact via both synergy and tension.
• Projection is costly intervention, not instantaneous adjustment.
• Accountability penalties should be dimension-specific.
• Intervention costs span multiple capabilities; aggressive justice improvement is self-limiting.

10.4. Positioning within Computational Normative Governance

GSM-J sits at the intersection of computational social science (Lazer et al., 2020; Watts, 2021), computational public policy (Athey, 2018; Kleinberg et al., 2018; Mullainathan & Obermeyer, 2022), algorithmic governance (Yeung, 2018; Danaher, 2019; Citron, 2022), and digital democracy (Landemore, 2020; Fishkin, 2021). Its contribution is a formal substrate in which normative commitments can be formalized, parameterized, and examined for systemic consequences.

11. Limitations

• Normative non-derivability. GSM-J formalizes justice; it does not derive its commitments.
• Weight sensitivity. Results depend on many parameters; the scenario protocol sweeps them.
• Measurement validity. Recognition and intergenerational indicators are less developed than distributive ones.
• Levels of aggregation. Household-level justice is not fully represented.
• Cultural pluralism. Justice dimensions may vary across contexts.
• Dynamics calibration. Functional forms are stylized; empirical estimation of $M_J$ is deferred.
• Tragic conflict. Trade-offs are represented but not resolved.
• Path dependence. Different initial profiles may yield different equilibria.
• Multiplicity of justice roles. Defended in §5.4, but boundaries are philosophically contested.
• Constraint enforcement. The hybrid default is a design choice.
• Projection interpretation. The mapping from real institutional processes to ${\kappa }^{\mathrm{int}}$, ${\tau }^{\mathrm{int}}$, ${\omega }^k$is not fully specified.
• $M_J$identification. In datasets lacking exogenous variation or sign restrictions, identification may be weak.
• Multi-channel intervention weights. Default ${\omega }^k$ are theoretically motivated but not empirically validated.
• Stylized demonstration. The demonstration is illustrative, not empirical.

12. Conclusion

GSM-J extends the GSM in eight ways: justice as a state variable; a five-dimensional decomposition; a signed interaction matrix with disciplined estimation; three additional constraints including vulnerability-sensitive non-exploitation; dimension-specific vertical alignment; dimension-specific cross-level accountability; a dimension-specific prioritarian welfare function; and constraint projection reframed as multi-channel policy intervention with designated authority, cost, finite horizon, and passive recovery.

The result is a conditional normative systems model: descriptive about mechanisms, explicit about values, silent about which values are correct. Its scientific contribution is the formal structure. Its ethical contribution is making the specification unavoidable. Its practical contribution is a simulation architecture in which justice and flourishing can be jointly examined, contested, and compared.

The architecture is now complete. Further development should focus on empirical calibration, not theoretical expansion.