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A Hexagonal Algorithm for convening Cross-Sector Partnerships in the ANDES (Aug, 2026)

Roberto F. Salazar-Córdova

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Hexagon Toolkit®

Objective

To identify, organize and converge heterogeneous actors toward a legitimate, investable and household-centered partnership by minimizing transaction costs through the Hexagon Toolkit® and a Single-Crossing convergence process.

Inputs

• Set of actors \(A={a_1,\dots,a_n}\)

• Set of economic nuclei (vertices)

• Initial transaction-cost matrix \(C\)

• Institutional constraints

• Available resources

• Governance rules

• Time horizon

Step 1. Leadership Mapping (L1)

Identify the actor(s) capable of initiating convergence.

Evaluate:

• convening capacity;

• credibility;

• technical competence;

• commitment;

• execution capacity.

Output:

Leadership vector

\[ L=(l_1,l_2,\ldots,l_n) \]

Step 2. Hexagonal Topology

Represent the system as a weighted graph.

• Vertices = economic nuclei.

• Edges = transaction and transfer costs.

• Weight =

\[ w_{ij}=c_{ij} \]

Communities become interconnected hexagons.

Step 3. Open Interest Collection

Every participant independently declares:

• objectives;

• constraints;

• risks;

• opportunities;

• desired investments.

No negotiation occurs at this stage.

Step 4. Interest Clustering

The Hexagon Toolkit groups compatible interests.

Outputs:

• common interests;

• conflicting interests;

• complementary interests;

• isolated interests.

Step 5. Single-Crossing Ordering

Preferences are ordered until a monotonic convergence emerges.

The algorithm searches for an ordering in which agreement increases while transaction costs decrease.

Output:

Priority agenda.

Step 6. Priority Ranking

Projects are ranked according to:

• expected impact;

• feasibility;

• urgency;

• scalability;

• household impact.

Step 7. Legal Feasibility (L2)

Each priority is tested against:

• legislation;

• regulations;

• institutional mandates;

• contractual compatibility.

Non-compliant initiatives return to redesign.

Step 8. Legitimacy Assessment (L3)

Evaluate acceptance by:

• communities;

• governments;

• investors;

• private sector;

• academia;

• civil society.

Only socially legitimate initiatives advance.

Step 9. Legalizing Actors

Identify who can formally authorize implementation:

• governments;

• ministries;

• municipalities;

• boards;

• indigenous authorities;

• regulators;

• investors;

• international organizations.

Step 10. Convergence Dynamics

Estimate, for every actor:

• decision time;

• negotiation time;

• implementation time.

The Toolkit identifies the critical path.

Step 11. Investment Capacity (L4)

Estimate available capital:

• financial capital;

• human capital;

• technological capital;

• institutional capital;

• natural capital;

• social capital;

• time.

Construct the investment matrix.

Step 12. Household Convergence

This is the defining optimization criterion.

The solution is accepted only if it simultaneously:

• reduces transaction costs;

• increases cooperation;

• attracts investment;

• improves household welfare.

Households constitute the global attractor of the network.

Step 13. Dynamic Hexagonal Reconfiguration

Communities may reorganize continuously.

Hexagons merge, divide or connect without altering the convergence objective.

The network evolves toward a stable configuration of minimum transaction costs.

Hexagon Toolkit® Decision Rule

A proposal advances only if all four dimensions are satisfied simultaneously:

• L1 – Leadership: someone can mobilize the process.

• L2 – Legality: the proposal is legally executable.

• L3 – Legitimacy: stakeholders accept and support it.

• L4 – Leverage: sufficient investment capacity exists to implement it.

If any dimension fails, the process iterates until convergence is restored.

Optimization Objective

The Hexagonal Algorithm seeks to:

\[ \min \sum_{i,j} c_{ij} \]

subject to:

• legal feasibility;

• institutional legitimacy;

• investment viability;

• stable cross-sector cooperation;

• maximization of household welfare.

Under this framework, the Hexagon Toolkit® functions as a decision-support and governance engine for Single Cross-Sector Partnerships, transforming dispersed stakeholder preferences into an investable, legitimate and scalable agenda centered on households as the ultimate beneficiaries.

SALAZAR-CÓRDOVA, R.F., 2026

HEXAGON GROUP LAT-AM|UK-GLOBAL