Mycelith Voting System

The Mycelith Voting System is an advanced, multi-layered voting mechanism designed to achieve fair and adaptive decision-making within the Seigr ecosystem. Inspired by the branching and adaptive qualities of mycelium, the Mycelith system ensures that community decisions are representative, resilient, and aligned with Seigr’s ethical framework.

Mycelith incorporates a unique senary (base-6) structure, dividing the voting process into six layers that progressively refine consensus, encourage observation, and reward consistent voting commitment. This system is designed to align with Seigr’s goals of decentralized governance, promoting fairness and adaptability in community-driven decisions.

Introduction to Mycelith

The Mycelith Voting System operates in multiple rounds, or senary layers, which structure the voting process over six distinct stages. Voters in the Seigr ecosystem are encouraged to participate gradually, observing early results and aligning their commitment level with the depth of their conviction. Each layer has a unique influence weight, giving greater weight to those who remain consistent in their stance across rounds.

Mathematical Foundations

Let:

$W_{j}^{(i)}$ denote the influence weight of participant $i$ in layer $j$ .
$W_{i}$ be the base influence of participant $i$ determined by their WCAS.
$S_{j}$ be the senary scaling factor for each layer.

The scaling factor $S_{j}$ is derived based on senary principles: $S_{j}=1.2^{j}$ where $j=1,2,...,6$ represents each layer.

Calculation of the Voting Outcome

The final outcome $O$ of the proposal is determined by aggregating all influence-weighted votes across layers. Let $V_{i}^{(j)}$ represent participant $i$ 's vote in layer $j$ , where $V_{i}^{(j)}\in \{+1,-1\}$ for a binary decision.

The final outcome $O$ is given by: $O={\text{sign}}\left(\sum _{j=1}^{6}\sum _{i=1}^{n}W_{j}^{(i)}\cdot V_{i}^{(j)}\right)$ where $O=+1$ represents a pass (yes) and $O=-1$ represents a fail (no).

Example Scenario

Consider three participants (A, B, and C) with WCAS-derived influence scores of:

"A": $W=0.7$ , consistent "yes."
"B": $W=0.5$ , switches from "no" to "yes."
"C": $W=0.4$ , consistent "no."

The influence scaling factors for each layer $S_{j}$ are:

- $S_{1}=1.0$ - $S_{2}=1.2$ - $S_{3}=1.44$ - $S_{4}=1.728$ - $S_{5}=2.0736$ - $S_{6}=2.48832$

Influence Calculations

1. **Participant A (consistent "yes")**:

${\text{Total Influence}}_{A}=0.7\times (1.0+1.2+1.44+1.728+2.0736+2.48832)=7.236$

2. **Participant B (switches from "no" to "yes")**:

  - Layers 1-3: "no" votes.
  - Layers 4-6: "yes" votes, reduced by  $\gamma =0.5$ .

${\text{Total Influence}}_{B}=0.5\times (1.0+1.2+1.44)+0.5\times (1.728+2.0736+2.48832)\times 0.5=2.73$

3. **Participant C (consistent "no")**:

${\text{Total Influence}}_{C}=0.4\times (1.0+1.2+1.44+1.728+2.0736+2.48832)=4.136$

Thus, the aggregated outcome is: $O={\text{sign}}(7.236\cdot (+1)+2.73\cdot (+1)+4.136\cdot (-1))=+1$ indicating a "yes" outcome.