## Diagram: Causal Models of Law School Admissions and Adult Census Income
### Overview
The image presents two interconnected causal diagrams comparing factors influencing **Law School Admissions** and **Adult Census Income**. Nodes are color-coded to represent protected attributes, outcomes, and unobservable variables, with directional arrows indicating causal relationships and dotted lines representing additive noise. The diagram includes a legend explaining color coding and node types.
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### Components/Axes
#### **Legend** (bottom of image):
- **Blue**: Protected Attributes (e.g., RACE, SEX)
- **Orange**: Outcome Variables (e.g., FYA, INC)
- **Purple**: Unfair Observables (e.g., GPA, LSAT, MAR, EDU)
- **Green**: Fair Unobservables (e.g., ε_GPA, ε_LSAT, ε_MAR, ε_HPW)
- **Striped**: Nodes "Seen by FairPFN"
- **Circles**: Non-descendent nodes
- **Arrows**: Causal relationships
- **Dotted lines**: Additive noise
#### **Nodes and Connections**:
1. **Law School Admissions**:
- **Protected Attributes** (Blue):
- RACE → GPA, LSAT, FYA
- SEX → GPA, LSAT, FYA
- **Unfair Observables** (Purple):
- GPA → FYA (with ε_GPA noise)
- LSAT → FYA (with ε_LSAT noise)
- FYA → Outcome (orange node)
- **Fair Unobservables** (Green):
- ε_GPA, ε_LSAT, ε_FYA (additive noise)
2. **Adult Census Income**:
- **Protected Attributes** (Blue):
- RACE → MAR, EDU, OCC, HPW
- SEX → MAR, EDU, OCC, HPW
- **Unfair Observables** (Purple):
- MAR → EDU, OCC, HPW
- EDU → OCC, HPW
- OCC → HPW
- HPW → INC (outcome)
- **Fair Unobservables** (Green):
- ε_MAR, ε_EDU, ε_OCC, ε_HPW (additive noise)
- **Outcome** (Orange):
- INC (income)
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### Detailed Analysis
#### **Law School Admissions**:
- **Protected Attributes** (RACE, SEX) directly influence **Unfair Observables** (GPA, LSAT, FYA).
- **Unfair Observables** (GPA, LSAT, FYA) are noisy (ε_GPA, ε_LSAT, ε_FYA) and causally linked to the **Outcome** (FYA).
- **Fair Unobservables** (ε_GPA, ε_LSAT, ε_FYA) represent non-descendent noise affecting outcomes.
#### **Adult Census Income**:
- **Protected Attributes** (RACE, SEX) influence **Unfair Observables** (MAR, EDU, OCC, HPW).
- **Unfair Observables** form a chain: MAR → EDU → OCC → HPW → INC.
- **Fair Unobservables** (ε_MAR, ε_EDU, ε_OCC, ε_HPW) add noise at each stage.
- **Outcome** (INC) is directly influenced by HPW, which is shaped by prior variables.
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### Key Observations
1. **Protected Attributes** (RACE, SEX) are upstream drivers of disparities in both diagrams.
2. **Unfair Observables** (e.g., GPA, EDU) mediate the impact of protected attributes on outcomes.
3. **Additive Noise** (dotted lines) suggests measurement error or unmodeled variables in causal pathways.
4. **Fair Unobservables** (green nodes) are explicitly labeled as "Fair," implying they are not proxies for protected attributes.
5. **Non-descendent Nodes** (circles) are isolated from direct causal paths, possibly representing confounding factors.
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### Interpretation
The diagrams illustrate how **protected attributes** (RACE, SEX) indirectly affect outcomes (FYA, INC) through **unfair observables** (e.g., GPA, EDU) and **fair unobservables** (e.g., ε_GPA, ε_EDU). The presence of additive noise highlights the complexity of isolating true causal effects in real-world systems.
- **Law School Admissions**: Racial and gender biases may manifest through GPA and LSAT scores, which are influenced by systemic inequities. The outcome (FYA) is further distorted by measurement noise.
- **Adult Census Income**: Income disparities are mediated by marital status, education, occupation, and household power, all shaped by race and sex. Fair unobservables (e.g., ε_EDU) suggest residual factors not captured by the model.
The diagrams emphasize the need for fairness-aware models (e.g., FairPFN) to account for both observable and unobservable variables while mitigating bias from protected attributes. The striped nodes ("Seen by FairPFN") imply that certain variables are prioritized in fairness assessments, though their exact role is not explicitly defined.
