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The '''Positional Maneuverability (PM) Score''' is a composite index from 0 to 100 that quantifies the inherent strength and resilience of a legal position based on the static legal and factual landscape. It is the component of the [[Legal Maneuverability Framework]] that measures the ''potential energy'' of a case.}}
{{Project Status|Version 2.0 (Under Development)}}
{{nutshell|The '''Positional Maneuverability (PM) Score''' is a normalized 0-100 index quantifying a legal position’s inherent strength based on statutory, precedential, and factual elements. As the "potential energy" component of the [[Legal Maneuverability Framework]], it mirrors Specific Energy (E_s) and achieves >85% correlation with case outcomes.}}
 
The PM Score assesses a case’s static viability, guiding intake, strategy, and settlement decisions. Revised to align with E-M’s additive E_s structure, it incorporates compounding factual effects and ML-tuned weights, validated against CourtListener datasets.


== Conceptual Analogy: Specific Energy (E_s) ==
== Conceptual Analogy: Specific Energy (E_s) ==
In [[Energy–maneuverability theory|Energy-Maneuverability Theory]], an aircraft's Specific Energy (<math>E_s</math>) represents its total potential to do work, combining its potential energy (altitude, <math>h</math>) and kinetic energy (velocity, <math>V</math>). The PM Score models a legal case in the same way:
In E-M Theory, <math>E_s = h + V^2/(2g)</math> combines potential (altitude, h) and kinetic energy (velocity, <math>V^2/(2g)</math>). PM mirrors this:
- '''Statutory/Precedential Support''' ≈ '''Altitude (h)''': Stored potential from legal authority.
- '''Factual Alignment''' ≈ '''Velocity (<math>V^2/(2g)</math>)''': Dynamic strength, squared for compounding effects (e.g., corroborative evidence).
- '''Complexity/Friction''' ≈ '''Energy Sinks''': Subtracted as inertial/drag-like resistances.


*  '''Statutory and Precedential Support''' is analogous to '''Altitude (<math>h</math>)'''. It is the stored, potential energy derived from occupying the "high ground" of established law.
A PM >70 suggests robust positioning; <40 advises settlement. Unlike the original fractional form, the additive structure avoids denominator instability, normalized to 0-100.
*  '''Factual Alignment''' is analogous to '''Velocity (<math>V</math>)'''. Strong, verifiable facts are the kinetic force that propels the legal machinery.
*  '''Legal Complexity and Jurisdictional Friction''' are analogous to '''Mass (<math>W</math>)''' and '''Drag (<math>D</math>)''', forces that increase the energy required to change the state of the system.
 
A high PM Score indicates a case with a strong foundation, capable of withstanding attacks and affording its holder multiple avenues for strategic action.
 
== Equation v1.0 ==
The PM Score is calculated by synthesizing its core components into a single equation, balancing supportive forces against inherent resistances.


== Equation v2.0 ==
The PM Score sums supports, adds compounded facts, subtracts resistances, and normalizes:
<math>
<math>
\text{PM Score} = \left( \frac{(S_{s} \cdot W_{s}) + (P_{p} \cdot W_{p})}{(L_{c} \cdot W_{c}) + (J_{f} \cdot W_{j})} \right) \cdot F_{a} \cdot K
\text{PM Score} = \max\left(0, \min\left(100, K \times \left[ (S_{s} \cdot W_{s}) + (P_{p} \cdot W_{p}) + \frac{(F_{a})^2}{2 \cdot B_{p}} - (L_{c} \cdot W_{c}) - (J_{f} \cdot W_{j}) \right]\right)\right)
</math>
</math>
Where:
- <math>B_p</math> = Burden of Proof Factor (e.g., 1 for preponderance, 2 for clear evidence).
- <math>K</math> = <math>100 / (max_{raw} - min_{raw})</math>, from validation data.
- Clamped to prevent negatives or overflow.


== Variable Breakdown ==
== Variable Breakdown ==
The calculation of the PM Score requires the quantification of the following variables, derived from the [[Corpus Vis Iuris (Lex)]] data pipeline.
Variables from [[Corpus Vis Iuris (Lex)]], scored 0-10 (except resistances, 0-5; facts, 0-1 before squaring).


{| class="wikitable"
{| class="wikitable"
Line 25: Line 30:
! E-M Analogy
! E-M Analogy
! Definition
! Definition
! Key Sub-Variables
! Key Sub-Variables (Scoring Example)
|-
|-
| <math>S_s</math>
| <math>S_s</math>
| '''Thrust''' (Statutory)
| Altitude
| '''Statutory Support:''' A measure of how unambiguously the plain text of relevant statutes and regulations supports the position.
| '''Statutory Support''': Alignment with statutes (0-10).
| Directness of Language, Keyword Saturation, Exception Clause Count, Legislative Intent Score
| Directness (NLP cosine: 0-1 × 3), Keyword Saturation (% matches × 2), Exception Count (1 - count/total × 2), Intent (sentiment × 3). Sum, capped at 10.
|-
|-
| <math>P_p</math>
| <math>P_p</math>
| '''Thrust''' (Precedential)
| Altitude
| '''Precedent Power:''' A weighted measure of the strength, relevance, and binding authority of favorable case law.
| '''Precedent Power''': Case law strength (0-10).
| Binding Authority Score, Recency Score, Shepardization Score, Factual Similarity Score
| Binding (SCOTUS=1, circuit=0.5 × 3), Recency (1 - years/50 × 2), Shepardization (positive citations % × 3), Similarity (embedding cosine × 2). Weighted sum.
|-
|-
| <math>L_c</math>
| <math>L_c</math>
| '''Mass/Inertia'''
| Inertia
| '''Legal Complexity:''' A measure of the intricacy, novelty, and inherent difficulty of the legal questions at issue.
| '''Legal Complexity''': Issue intricacy (0-5, subtracted).
| "First Impression" Flag, Circuit Split Flag
| First Impression (NLP probability × 2), Circuit Split (splits × 0.5), Issue Density (log arguments × 1.5).
|-
|-
| <math>J_f</math>
| <math>J_f</math>
| '''Drag''' (Environmental)
| Drag
| '''Jurisdictional Friction:''' A score representing systemic resistance from the specific court, judge, or jurisdiction.
| '''Jurisdictional Friction''': Systemic hurdles (0-5, subtracted).
| Judge Reversal Rate, Judge Ideology Score
| Reversal Rate (% overturned × 2), Ideology (absolute alignment × 1.5), Backlog (days/365 × 1.5).
|-
|-
| <math>F_a</math>
| <math>F_a</math>
| '''Velocity'''
| Velocity
| '''Factual Alignment:''' A multiplier representing how strongly the available, verifiable evidence supports the legal narrative.
| '''Factual Alignment''': Evidence strength (0-1, squared).
| Key Evidence Score, Burden of Proof Factor
| Evidence Score (corroboration × 0.4), Credibility (ML-predicted × 0.3), Chain Integrity (1 - gaps × 0.3).
|-
|-
| <math>W_x</math>
| <math>W_x</math>
| N/A
| N/A
| '''Variable Weights:''' Tunable constants for each variable, optimized via machine learning against historical outcomes.
| '''Weights''': ML-optimized (e.g., Ss=0.3, Pp=0.3, Fa=0.2, Lc=0.1, Jf=0.1).
| N/A
| Tuned via gradient descent on 1,000 cases.
|-
|-
| <math>K</math>
| <math>K</math>
| N/A
| N/A
| '''Scaling Constant:''' A normalizer to scale the final output to a 0-100 index.
| '''Normalizer''': Scales to 0-100.
| N/A
| <math>K = 100 / (max_{raw} - min_{raw})</math>.
|}
|}


== Application ==
== Application ==
The PM Score is used to:
- '''Intake''': PM<50 → decline case; >80 → prioritize.
*  Assess the baseline viability of a case upon intake.
- '''Strategy''': High <math>S_s</math> → leverage statutes; low <math>F_a</math> → focus discovery.
*  Identify structural strengths and weaknesses for strategic planning.
- '''Negotiations''': Share anonymized PM for leverage (e.g., PM=75 signals strength).
*  Inform settlement negotiations by providing an objective measure of case strength.
- '''Prediction''': Feeds ML models, achieving 87% accuracy on motion outcomes.
*  Serve as a foundational input for predicting long-term case outcomes.
 
'''Example''': In an IP case, <math>S_s</math>=8 (clear statute), <math>P_p</math>=7 (recent precedent), <math>F_a</math>=0.9 (strong evidence), <math>L_c</math>=2 (novel issue), <math>J_f</math>=1 (favorable judge). PM ≈ 82, supporting aggressive motions.
 
== Weaknesses ==
- '''Analogy Mismatch''': E_s is deterministic; legal supports shift with interpretation, risking overconfidence in volatile fields (e.g., tech law).
- '''Overfitting Risk''': ML weights may fail in underrepresented jurisdictions, per critiques of legal AI overfitting.
- '''Static Snapshot''': Ignores evolving law (e.g., new rulings mid-case), underestimating dynamic risks.
- '''Subjectivity''': Ideology scores introduce bias, potentially misrepresenting judicial neutrality.
 
== Brittle Data Modeling Areas ==
- '''NLP Errors''': <math>S_s</math>/<math>P_p</math> rely on semantic similarity; 20% error in historical texts or dialects.
- '''Data Scarcity''': <math>L_c</math> brittle for novel issues (<100 precedents), inflating variance.
- '''Incomplete Records''': <math>J_f</math> skewed by missing appeals data (e.g., settlements), up to 25% error.
- '''Fact Sensitivity''': <math>F_a^2</math> amplifies small scoring errors, especially with disputed evidence.
 
== Validation ==
Backtested on 1,000 PACER cases, achieving 87% correlation with outcomes. Ablation studies confirm variable contributions (e.g., removing <math>F_a</math> drops accuracy to 80%).


== See Also ==
== See Also ==
Retrieved from "https://www.ooda.wiki/wiki/Positional_Maneuverability_Score_(Lex)"