Dec 28, 2024 3 min read

Dividing the Whole: More than the Sum of its Parts

The Great Power of Mjölnir: Wielded with Balance and Alignment of Cosmic Forces.

At the heart of SagaHalla's cooperative design is a fundamental question: how do we divide the whole into parts that balance fairness, sustainability, and efficiency? In SagaHalla, the whole—represented by 100% of contributions—is divided into three key components: members, investors, and the community. This division reflects deep natural principles while accommodating the practical realities of governance and system dynamics.

The Design Constraint: Dividing 100 into Three Parts

To build a sustainable system, SagaHalla divides the total contributions (100%) as follows:

Members’ Contributions: Representing labor and financial capital, members contribute the majority share to reflect their active participation in the system.
Investors’ Contributions: External capital supports growth, but its share is constrained to maintain cooperative control by members.
Community Contributions: Allocated to non-capital contributions, this ensures inclusivity and engagement from a broader network without an ownership interest in distributions.

The sum of these parts must equal the whole:

$C_{\text{total}} = C_{\text{members}} + C_{\text{investors}} + C_{\text{community}}$

Where:

$C_{\text{total}} = 100$
$C_{\text{members}}$ : Members' contributions (financial and labor).
$C_{\text{investors}}$ : Investors' financial contributions.
$C_{\text{community}}$ : Community's share for non-capital contributions.

The Significance of Ratios in Nature

Closest Integer Approximation

Golden Ratio and Proportionality

The ratio 53, 33, 14 is the division of a whole with integers that mostly closely approximates the mathematical harmony inspired by natural systems.

The 53:33 ratio closely mirrors the golden ratio ( $\phi$ ), which appears in natural systems, art, and architecture. It reflects the inherent balance and efficiency found in ecosystems, where contributions scale proportionally without overwhelming one component.:

$\frac{53}{33} \approx 1.606 \quad \text{vs.} \quad \phi \approx 1.618$

Fractal Scaling and Community Contributions

14% Community Share: Reflects fractal scaling laws often observed in nature, where smaller components (e.g., $1/7$ ) sustain larger systems. This ensures that even minor contributions play a vital role in sustaining the broader ecosystem.

$R_{\text{fractal}} = \frac{1}{7} \approx 0.14$

These proportions balance labor (members), capital (investors), and distributed contributions (community) with remarkable mathematical precision at the whole integer level. However, these odd ratios introduce complexity in governance and understanding of the system.

The Practicality of 51, 34, 15

SagaHalla has adopted 51, 34, 15 for its practical benefits:

51% Members’ Share: The smallest integer majority ensures cooperative control while simplifying governance.
34% Investors’ Share: A near-equivalent balance to members’ financial contributions, ensuring equity without over-reliance on external capital.
15% Community Share: A rounded value for inclusivity, slightly exceeding the fractal $1/7$ principle to incentivize broader participation.

This ratio simplifies implementation while maintaining alignment with natural principles and cooperative values.

Financial and Governance Constraints

SagaHalla’s design enforces strict constraints to balance contributions:

Members’ Majority Control:

$Contrib_{\text{members}} \geq 51\% \quad \text{and} \quad Capital_{\text{members}} : Capital_{\text{investors}} = 60:40$

Members maintain majority ownership while ensuring equitable capital balance.
Investors’ Capital Limits:

$Contrib_{\text{investors}} \leq 34\% \quad \text{and} \quad C_{\text{individual}} \leq 40\%$

No single investor can dominate, preserving decentralization.
Community Contribution and Reward Cap:

$Contrib_{\text{community}} \leq 15\%$

Community contributions remain impactful yet bounded.
Labor and Financial Capital: Members contribute both labor and financial capital, constrained by system-wide resource dynamics:

$Capital_{\text{total}} = Capital_{\text{members}} + Capital_{\text{investors}}$

Balancing Practicality and Elegance

SagaHalla’s choice of 51, 34, 15 represents a thoughtful compromise:

Governance Simplicity: The ratio is operationally efficient, ensuring seamless decision-making and communication.
Natural Principles: It retains an approximate alignment with $\phi$ and fractal scaling, balancing practicality with elegance.
Financial Equity: The split between members and investors ensures proportional contributions without compromising cooperative control.

Conclusion

The division of contributions in SagaHalla reflects a delicate interplay between natural harmony and practical governance. The 51, 34, 15 ratio simplifies implementation, fostering inclusivity and balance while maintaining the cooperative ethos at the heart of SagaHalla.

Through these carefully chosen ratios, SagaHalla creates a system that is not only resilient and adaptive but also grounded in principles of equity and sustainability. The practical and philosophical underpinnings of these ratios ensure that SagaHalla remains a benchmark for sustainable cooperative design.