Assessing Electricity Service Unfairness with Transfer Counterfactual Learning

TL;DR

This paper tackles the challenge of identifying counterfactual unfairness in electricity service by framing it through the Average Causal Effect within Rubin's Potential Outcome framework. It introduces Counterfactual Unfairness under the Potential Outcome (CUPO) concept and develops a novel Transfer Counterfactual Learning ($\ell_1$-TCL) approach that combines inverse probability weighting, subgroup analysis, and sparse-transfer learning to address confounding, heterogeneity, and data scarcity. The authors provide non-asymptotic guarantees for the estimator, propose hyperparameter selection via covariate balance (MMD) and nuisance-model criteria, and apply the method to a large city-level outage dataset from Massachusetts. The empirical findings show that low-income and elderly-populated areas experience longer outages, with effects amplified under severe weather, underscoring energy justice concerns and the need for targeted policy interventions.

Abstract

Energy justice is a growing area of interest in interdisciplinary energy research. However, identifying systematic biases in the energy sector remains challenging due to confounding variables, intricate heterogeneity in counterfactual effects, and limited data availability. First, this paper demonstrates how one can evaluate counterfactual unfairness in a power system by analyzing the average causal effect of a specific protected attribute. Subsequently, we use subgroup analysis to handle model heterogeneity and introduce a novel method for estimating counterfactual unfairness based on transfer learning, which helps to alleviate the data scarcity in each subgroup. In our numerical analysis, we apply our method to a unique large-scale customer-level power outage data set and investigate the counterfactual effect of demographic factors, such as income and age of the population, on power outage durations. Our results indicate that low-income and elderly-populated areas consistently experience longer power outages under both daily and post-disaster operations, and such discrimination is exacerbated under severe conditions. These findings suggest a widespread, systematic issue of injustice in the power service systems and emphasize the necessity for focused interventions in disadvantaged communities.

Figures (7)

• Figure 1: Evidence and illustration of the selection bias caused by confounders. Sub-figure (a) shows the scatter plot of raw median income---with the lower $80\%$-percentile shaded in gray and the upper $20\%$-percentile in black---and SAIDI, with each panel's trend captured by a red fitted regression line. Although the data visualization on the Massachusetts map in sub-figure (b) indicates lower SAIDI in wealthier areas (especially the Boston Harbor) under severe conditions, the statistical correlation in sub-figure (a) says otherwise. Sub-figure (c) illustrates the selection bias due to potential confounders in $\boldsymbol{X}$: Commonly in practice (top), the allocation of "treatment" is influenced by $\boldsymbol{X}$, making the selected (or observed) "treatment" cohort NOT independent of the outcome variable. As a result, this selected cohort fails to reflect the entire population accurately, leading to potentially biased inferences. In our study, as exhibited in sub-figures (a) and (b), we postulate the presence of selection bias, which could account for the discrepancies between the naïve correlation outcomes and the findings of prior studies roman2019satelliteDVORKIN2021bhattacharyya2023dataganz2023socioeconomicshah2023inequitablecoleman2023energy, necessitating the counterfactual approach here.
• Figure 2: Comparison of different hyperparameter selection criteria: We use "$\star$" to denote the selected hyperparameter in the first four rows; The corresponding $\ell_1$-TCL estimation errors are highlighted with "$\bullet$" in the last row. We can observe that in-sample MMD and all cross-validation nuisance model performance metrics can select $\lambda$'s that output similar and accurate causal effect estimates.
• Figure 3: Box plots of the absolute values in the difference of the estimated nuisance parameters, (i.e., $\widehat{\beta}_\texttt{T} - \widehat{\beta}_\texttt{S}$), and their ratios (i.e., the difference divided by $(\widehat{\beta}_\texttt{T} + \widehat{\beta}_\texttt{S})/2$), where $\widehat{\beta}_\texttt{T}$ and $\widehat{\beta}_\texttt{S}$ are estimated using $\ell_1$ regularized logistic regression (where wealthiness indicator is the response variable and other attributes are the predictors). Although most of the raw estimated differences are close to zero (as shown in sub-figure (a)), the estimated nuisance parameters themselves could also be close to zero. Therefore, we also report the ratios in sub-figure (b), which shows that the estimated differences are mostly close to zero relative to their raw estimates, which supports Assumption \ref{['assumption']}.
• Figure 4: Bootstrap UQ visualization for unfairness assessment w.r.t. protected attributes (as detailed in the sub-captions on the left). In each violin plot, the median is highlighted: For the naïve approach, blue signifies a positive effect, while red denotes a negative effect; For counterfactual approaches, blue (median ACE $>-100$) represents a positive causal effect, red (median ACE $<-100$) indicates a negative effect, and black ($-100 \leq$ median ACE $\leq 100$) suggests a neutral effect. Notably, naïve methods oftentimes output results lacking statistical significance; Both naïve methods and vanilla IPW (i.e., w/o TL) are prone to produce outcomes that contradict both established literature and intuitive reasoning; In contrast, our proposed $\ell_1$-TCL constantly (irrespective of the protected attribute or hyperparameter selection criterion) delivers findings that align with prevailing research.
• Figure 5: Data visualization on the Massachusetts map: The background color gradient, ranging from light to dark grey, illustrates the magnitude of the protected attributes; The size of the red bubbles corresponds to the magnitude of SAIDI, with larger bubbles indicating higher SAIDI values. Sub-figure (b) presents a standardized customer number, scaled between 0 and 1, to maintain data sensitivity, contrasting with the real data range shown in sub-figure (a).

Theorems & Definitions (15)

• Definition 1: Group-level counterfactual fairness under PO
• Definition 2: SCM-counterfactual fairness for the DGP tang2023and
• Definition 3: Individual-level counterfactual fairness under PO
• Proposition 1
• Remark 1: Further clarification on the TL set-up
• Remark 2: Selection criterion for hyperparameter $\lambda$
• Remark 3: Theoretical guarantee
• Definition 4: $\ell_2$ err.
• Definition 5: CE err.
• Definition 6: Cohen's d