Mycelith Voting System

The Mycelith Voting System is a decentralized voting mechanism created for the Seigr ecosystem. Inspired by the interconnected and resilient nature of mycelium, the system aims to empower participants to vote on proposals fairly and transparently, while providing an adaptive, multi-layered approach to voting.

Introduction to Mycelith

In the Mycelith Voting System, proposals go through a series of voting rounds called layers. This multi-layered structure encourages participants to engage in decision-making gradually, with each layer adding additional influence based on participants' consistency and commitment to their initial vote.

Key Features

1. Senary-Based Voting Layers: The voting process is divided into six sequential layers, each increasing in influence weight. This means early voters who are consistent across layers gain more influence, while those who switch their votes have their influence moderated.

2. Weighted Voting: Each participant’s influence in voting is weighted by their commitment, experience, and consistency within the ecosystem, forming a dynamic influence score known as the WCAS.

3. Adaptive Scaling: The system incorporates a senary (base-6) scaling approach that reflects Seigr’s alignment with efficiency and sustainability. This senary structure shapes how influence is calculated across the six layers.

This layered approach results in a more nuanced decision-making process, allowing participants to reflect and adjust their votes based on evolving insights, while incentivizing early, consistent voting behavior.

Structure of the Mycelith Voting System

The voting process in Mycelith is broken down into six layers, each representing a phase in the decision-making process. Each layer offers a chance for participants to either maintain their original vote or adjust it based on the previous results.

The Six Voting Layers

The six layers, represented as $L_{1}$ through $L_{6}$ , function as follows:

Layer 1 (Initial): Participants cast an initial vote with minimal influence weight.
Layer 2 (Observation): Influence slightly increases for participants who either maintain their stance or join the vote based on the results of Layer 1.
Layers 3-6 (Commitment Phases): Influence weights increase for participants who reinforce their commitment to their initial choice, with the highest influence weight reached in Layer 6.

This progression allows voters to observe early trends before deepening their commitment, creating a system that values both initial opinions and refined decisions.

Mathematical Foundations

Mycelith’s influence is calculated using a senary-based scaling system, where influence is increased in each layer according to senary principles. This scaling ensures that consistent voting has a higher influence over time, while participants who switch their votes incur influence adjustments.

Let:

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

The scaling factor $S_{j}$ is calculated as: $S_{j}=1.2^{j}$ where $j=1,2,\ldots ,6$ represents each layer. This exponential factor ensures influence grows gradually, providing a solid base for consistent participants.

Influence Weight Calculation

The influence of a participant in each layer is determined as follows: $W_{j}^{(i)}=W_{i}\cdot S_{j}$

This calculation ensures that participants with a higher WCAS start with more influence, which is then amplified or moderated across the layers.

Consistency Reward and Weighted Voting

Participants who maintain consistency in their voting stance across layers are rewarded with increasing influence, while those who switch votes have their influence moderated. This is achieved through an adjustment factor $\gamma$ applied to participants who switch their vote.

If a participant maintains the same vote in all layers, their influence is maximized.
If a participant switches, their influence in layers where they changed is reduced by a factor $\gamma$ , where $0<\gamma <1$ .

This consistency mechanism rewards participants who commit to their original stance while allowing flexibility for others to change their decision with adjusted influence.

Calculation of the Voting Outcome

The final outcome $O$ of a 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 calculated as: $O={\text{sign}}\left(\sum _{j=1}^{6}\sum _{i=1}^{n}W_{j}^{(i)}\cdot V_{i}^{(j)}\right)$ where:

$O=+1$ indicates a "yes" outcome.
$O=-1$ indicates a "no" outcome.

Example Scenario

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

Participant A: $W=0.7$ , votes "yes" consistently.
Participant B: $W=0.5$ , changes vote from "no" to "yes" mid-process.
Participant C: $W=0.4$ , votes "no" consistently.

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

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

The total influence for each participant is calculated as follows:

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"):

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

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

Senary Influence Summary

By applying a senary scaling system, Mycelith provides an adaptive, fair voting process that rewards consistency while allowing participants flexibility. The senary influence structure gives balanced weight across each phase, aligning with Seigr’s commitment to transparency and ethical governance.