Editing Weighted Consistency and Alignment Score (WCAS)

= Weighted Consistency and Alignment Score (WCAS) =

The '''Weighted Consistency and Alignment Score (WCAS)''' is a core metric in the Seigr ecosystem that measures the reliability, engagement, and alignment of a participant’s voting behavior over time. Designed specifically for the [[Special:MyLanguage/Mycelith Voting System|Mycelith Voting System]], WCAS influences each participant's voting weight, rewarding consistent and aligned participation while moderating influence for inconsistent or erratic voting patterns.

== Introduction to WCAS ==

The WCAS system encourages participants in Seigr's governance model to vote thoughtfully and consistently. Participants who frequently change their stance on issues without reasonable justification may see a reduction in their WCAS, which affects their influence in votes. Conversely, participants who maintain a consistent alignment with ethical, well-founded decisions are rewarded with higher WCAS scores, increasing their voting influence.

=== Key Objectives ===
1. '''Encourage Thoughtful Voting''': WCAS incentivizes participants to carefully consider their voting decisions by providing increased influence for consistent, well-aligned behavior.

2. '''Moderate Influence for Inconsistency''': Participants with erratic voting patterns have a reduced WCAS, which limits their voting weight until their behavior becomes more stable.

3. '''Promote Ethical Alignment''': WCAS values votes that align with Seigr’s principles of sustainability, transparency, and community focus, thereby promoting decisions that are in the best interest of the ecosystem.

== Structure of WCAS ==

The WCAS is calculated based on a combination of the following factors:
* '''Consistency Score (CS)''': Measures how consistent a participant’s votes are over time, especially across multiple layers in the Mycelith Voting System.
* '''Alignment Score (AS)''': Evaluates how well the participant’s voting behavior aligns with Seigr’s ethical principles and community goals.
* '''Weight Adjustment Factor (WAF)''': A scaling factor that adjusts influence based on a participant’s overall WCAS, which is recalculated periodically.

Each of these components is weighted to produce a participant’s final WCAS, which in turn influences their voting power in the Mycelith Voting System.

== Mathematical Calculation of WCAS ==

The WCAS for a participant \( i \), denoted as \( WCAS_i \), is defined as:
<math> WCAS_i = \alpha \cdot CS_i + \beta \cdot AS_i </math>
where:
* \( \alpha \) and \( \beta \) are weighting coefficients, with \( \alpha + \beta = 1 \).
* \( CS_i \) is the Consistency Score of participant \( i \).
* \( AS_i \) is the Alignment Score of participant \( i \).

The coefficients \( \alpha \) and \( \beta \) control the emphasis on consistency versus alignment, allowing the system to adjust the balance based on current governance needs.

=== Consistency Score (CS) ===

The Consistency Score \( CS_i \) measures the stability of a participant’s voting behavior across the six layers in the Mycelith Voting System. A high CS indicates that the participant’s stance remains consistent across rounds, while a low CS reflects frequent switching.

1. Let:
   * \( V^{(j)}_i \) be the vote of participant \( i \) in layer \( j \) where \( V^{(j)}_i \in \{+1, -1\} \).
   * \( \gamma_j \) be a consistency factor for each layer \( j \) (with values between 0 and 1), which rewards consistency more in later layers.

2. The CS is calculated as:
<math> CS_i = \frac{1}{6} \sum_{j=1}^{6} \gamma_j \cdot V^{(j)}_i </math>
where higher values of \( CS_i \) indicate greater consistency. 

For example, if a participant maintains a consistent "yes" vote (represented by +1) across all layers, their \( CS_i \) will approach the maximum value.

=== Alignment Score (AS) ===

The Alignment Score \( AS_i \) reflects how closely a participant’s voting pattern aligns with Seigr’s values. AS is computed based on the participant’s voting history and ethical alignment with past decisions. 

1. Let:
   * \( E_k \) denote an ethical score for decision \( k \), based on a community consensus on Seigr’s ethical principles.
   * \( V_i^{(k)} \) be participant \( i \)’s vote on decision \( k \).

2. The AS is calculated as:
<math> AS_i = \frac{1}{K} \sum_{k=1}^{K} E_k \cdot V_i^{(k)} </math>
where:
* \( K \) is the total number of decisions evaluated for alignment.
* \( E_k \) ranges between -1 and +1, representing how ethically aligned a decision is based on community evaluation.

A participant who votes in alignment with high-ethics decisions will achieve a higher \( AS_i \), enhancing their overall WCAS.

=== Weight Adjustment Factor (WAF) ===

The Weight Adjustment Factor (WAF) moderates a participant’s influence by scaling WCAS relative to the highest WCAS in the current voting period. This normalization ensures that influence remains fair across participants.

<math> WAF_i = \frac{WCAS_i}{\max(WCAS)} </math>

Each participant’s final voting influence in the Mycelith Voting System is then calculated as:
<math> W_i = WAF_i \cdot W_{\text{base}} </math>
where \( W_{\text{base}} \) is a standard base influence assigned to all participants.

== Example Calculation ==

Consider three participants (A, B, and C) with the following characteristics:
* '''Participant A''': Consistent "yes" voter with high ethical alignment.
* '''Participant B''': Occasional switching, moderate ethical alignment.
* '''Participant C''': Frequent switching, low ethical alignment.

For simplicity, let:
* \( \alpha = 0.6 \) and \( \beta = 0.4 \).
* Ethical scores for recent decisions \( E_k = [0.9, 0.7, 0.85, 0.95] \).

Assuming consistency and alignment scores:
* \( CS_A = 0.9 \), \( AS_A = 0.85 \).
* \( CS_B = 0.6 \), \( AS_B = 0.65 \).
* \( CS_C = 0.4 \), \( AS_C = 0.3 \).

We calculate WCAS as:
<math> WCAS_A = 0.6 \cdot 0.9 + 0.4 \cdot 0.85 = 0.87 </math>
<math> WCAS_B = 0.6 \cdot 0.6 + 0.4 \cdot 0.65 = 0.63 </math>
<math> WCAS_C = 0.6 \cdot 0.4 + 0.4 \cdot 0.3 = 0.36 </math>

With these WCAS values, we apply WAF to normalize influence:
* '''Max WCAS''': \( WCAS_A = 0.87 \)
* '''Weight Adjustment Factor''':
<math> WAF_A = \frac{0.87}{0.87} = 1.0 </math>
<math> WAF_B = \frac{0.63}{0.87} \approx 0.72 </math>
<math> WAF_C = \frac{0.36}{0.87} \approx 0.41 </math>

Thus, each participant's final influence weight in a vote is:
<math> W_A = W_{\text{base}} \cdot 1.0 </math>
<math> W_B = W_{\text{base}} \cdot 0.72 </math>
<math> W_C = W_{\text{base}} \cdot 0.41 </math>

== Significance of WCAS in the Mycelith Voting System ==

WCAS plays a crucial role in ensuring fair, thoughtful, and ethical decision-making by:
* '''Rewarding Consistency''': Participants who demonstrate consistent engagement are rewarded with increased voting influence, promoting stable, reliable voting behavior.
* '''Encouraging Ethical Alignment''': By aligning voting influence with Seigr’s ethical values, WCAS incentivizes participants to vote in the best interest of the community.
* '''Maintaining Fairness''': Through the Weight Adjustment Factor, WCAS normalizes influence across participants, ensuring that no single participant can dominate votes solely based on their WCAS score.

== Future Enhancements ==

Potential improvements for WCAS include:
* '''Dynamic Weighting''': Adjusting \( \alpha \) and \( \beta \) dynamically to reflect community priorities over time.
* '''Real-Time Alignment Feedback''': Providing participants with real-time feedback on how their voting behavior impacts their WCAS.
* '''Community-Based Calibration''': Allowing the community to help calibrate ethical scores \( E_k \) to reflect evolving values.

== Conclusion ==

The Weighted Consistency and Alignment Score (WCAS) is an innovative metric in the Seigr ecosystem, integral to the [[Special:MyLanguage/Mycelith Voting System|Mycelith Voting System]]. By combining consistency, alignment, and adaptive influence adjustment, WCAS fosters an ethical, fair, and community-aligned governance model. It embodies Seigr’s commitment to sustainable, transparent, and values-driven decision-making.

For more technical insights, explore:
* [[Special:MyLanguage/Mycelith Voting System|Mycelith Voting System]]
* [[Special:MyLanguage/HyphaCrypt|HyphaCrypt]]
* [[Special:MyLanguage/Temporal Layering|Temporal Layering]]
* [[Special:MyLanguage/Seigr Protocol|Seigr Protocol]]