Revision as of 05:34, 6 November 2024

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 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: $WCAS_{i}=\alpha \cdot CS_{i}+\beta \cdot AS_{i}$ 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:

  *  $V_{i}^{(j)}$  be the vote of participant  $i$  in layer  $j$  where  $V_{i}^{(j)}\in \{+1,-1\}$ .
  *  $\gamma _{j}$  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: $CS_{i}={\frac {1}{6}}\sum _{j=1}^{6}\gamma _{j}\cdot V_{i}^{(j)}$ 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: $AS_{i}={\frac {1}{K}}\sum _{k=1}^{K}E_{k}\cdot V_{i}^{(k)}$ 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.

$WAF_{i}={\frac {WCAS_{i}}{\max(WCAS)}}$

Each participant’s final voting influence in the Mycelith Voting System is then calculated as: $W_{i}=WAF_{i}\cdot W_{\text{base}}$ 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: $WCAS_{A}=0.6\cdot 0.9+0.4\cdot 0.85=0.87$ $WCAS_{B}=0.6\cdot 0.6+0.4\cdot 0.65=0.63$ $WCAS_{C}=0.6\cdot 0.4+0.4\cdot 0.3=0.36$

With these $WCAS$ values, we apply $WAF$ to normalize influence:

Max WCAS: $WCAS_{A}=0.87$
Weight Adjustment Factor:

$WAF_{A}={\frac {0.87}{0.87}}=1.0$ $WAF_{B}={\frac {0.63}{0.87}}\approx 0.72$ $WAF_{C}={\frac {0.36}{0.87}}\approx 0.41$

Thus, each participant's final influence weight in a vote is: $W_{A}=W_{\text{base}}\cdot 1.0$ $W_{B}=W_{\text{base}}\cdot 0.72$ $W_{C}=W_{\text{base}}\cdot 0.41$

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 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:

@@ Line 9: / Line 9: @@
 === Key Objectives ===
 . '''Encourage Thoughtful Voting''': WCAS incentivizes participants to carefully consider their voting decisions by providing increased influence for consistent, well-aligned behavior.
 . '''Moderate Influence for Inconsistency''': Participants with erratic voting patterns have a reduced WCAS, which limits their voting weight until their behavior becomes more stable.
 . '''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.
@@ Line 25: / Line 23: @@
 == Mathematical Calculation of WCAS ==
-The WCAS for a participant \( i \), denoted as \( WCAS_i \), is defined as:
+The WCAS for a participant \( i \), denoted as <math>WCAS_i</math>, is defined as:
 <math> WCAS_i = \alpha \cdot CS_i + \beta \cdot AS_i </math>
 where:
-* \( \alpha \) and \( \beta \) are weighting coefficients, with \( \alpha + \beta = 1 \).
+* <math>\alpha</math> and <math>\beta</math> are weighting coefficients, with <math>\alpha + \beta = 1</math>.
-* \( CS_i \) is the Consistency Score of participant \( i \).
+* <math>CS_i</math> is the Consistency Score of participant <math>i</math>.
-* \( AS_i \) is the Alignment Score of participant \( i \).
+* <math>AS_i</math> is the Alignment Score of participant <math>i</math>.
-The coefficients \( \alpha \) and \( \beta \) control the emphasis on consistency versus alignment, allowing the system to adjust the balance based on current governance needs.
+The coefficients <math>\alpha</math> and <math>\beta</math> 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.
+The Consistency Score <math>CS_i</math> measures the stability of a participant’s voting behavior across the six layers in the Mycelith Voting System. A high <math>CS</math> indicates that the participant’s stance remains consistent across rounds, while a low <math>CS</math> reflects frequent switching.
 . Let:
-    * \( V^{(j)}_i \) be the vote of participant \( i \) in layer \( j \) where \( V^{(j)}_i \in \{+1, -1\} \).
+    * <math>V^{(j)}_i</math> be the vote of participant <math>i</math> in layer <math>j</math> where <math>V^{(j)}_i \in \{+1, -1\}</math>.
-    * \( \gamma_j \) be a consistency factor for each layer \( j \) (with values between 0 and 1), which rewards consistency more in later layers.
+    * <math>\gamma_j</math> be a consistency factor for each layer <math>j</math> (with values between 0 and 1), which rewards consistency more in later layers.
-. The CS is calculated as:
+. The <math>CS</math> 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.
+where higher values of <math>CS_i</math> 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.
+For example, if a participant maintains a consistent "yes" vote (represented by +1) across all layers, their <math>CS_i</math> 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.
+The Alignment Score <math>AS_i</math> reflects how closely a participant’s voting pattern aligns with Seigr’s values. <math>AS</math> is computed based on the participant’s voting history and ethical alignment with past decisions.
 . Let:
-    * \( E_k \) denote an ethical score for decision \( k \), based on a community consensus on Seigr’s ethical principles.
+    * <math>E_k</math> denote an ethical score for decision <math>k</math>, based on a community consensus on Seigr’s ethical principles.
-    * \( V_i^{(k)} \) be participant \( i \)’s vote on decision \( k \).
+    * <math>V_i^{(k)}</math> be participant <math>i</math>’s vote on decision <math>k</math>.
-. The AS is calculated as:
+. The <math>AS</math> 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.
+* <math>K</math> 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.
+* <math>E_k</math> 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.
+A participant who votes in alignment with high-ethics decisions will achieve a higher <math>AS_i</math>, enhancing their overall <math>WCAS</math>.
 === 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.
+The Weight Adjustment Factor (WAF) moderates a participant’s influence by scaling <math>WCAS</math> relative to the highest <math>WCAS</math> in the current voting period. This normalization ensures that influence remains fair across participants.
 <math> WAF_i = \frac{WCAS_i}{\max(WCAS)} </math>
@@ Line 72: / Line 70: @@
 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.
+where <math>W_{\text{base}}</math> is a standard base influence assigned to all participants.
 == Example Calculation ==
@@ Line 82: / Line 80: @@
 For simplicity, let:
-* \( \alpha = 0.6 \) and \( \beta = 0.4 \).
+* <math>\alpha = 0.6</math> and <math>\beta = 0.4</math>.
-* Ethical scores for recent decisions \( E_k = [0.9, 0.7, 0.85, 0.95] \).
+* Ethical scores for recent decisions <math>E_k = [0.9, 0.7, 0.85, 0.95]</math>.
 Assuming consistency and alignment scores:
-* \( CS_A = 0.9 \), \( AS_A = 0.85 \).
+* <math>CS_A = 0.9</math>, <math>AS_A = 0.85</math>.
-* \( CS_B = 0.6 \), \( AS_B = 0.65 \).
+* <math>CS_B = 0.6</math>, <math>AS_B = 0.65</math>.
-* \( CS_C = 0.4 \), \( AS_C = 0.3 \).
+* <math>CS_C = 0.4</math>, <math>AS_C = 0.3</math>.
-We calculate WCAS as:
+We calculate <math>WCAS</math> 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:
+With these <math>WCAS</math> values, we apply <math>WAF</math> to normalize influence:
-* '''Max WCAS''': \( WCAS_A = 0.87 \)
+* '''Max WCAS''': <math>WCAS_A = 0.87</math>
 * '''Weight Adjustment Factor''':
 <math> WAF_A = \frac{0.87}{0.87} = 1.0 </math>
@@ Line 117: / Line 115: @@
 Potential improvements for WCAS include:
-* '''Dynamic Weighting''': Adjusting \( \alpha \) and \( \beta \) dynamically to reflect community priorities over time.
+* '''Dynamic Weighting''': Adjusting <math>\alpha</math> and <math>\beta</math> 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.
+* '''Community-Based Calibration''': Allowing the community to help calibrate ethical scores <math>E_k</math> to reflect evolving values.
 == Conclusion ==