Blind Judgement: Agent-Based Supreme Court Modelling With GPT
Abstract
We present a novel Transformer-based multi-agent system for simulating the judicial rulings of the 2010-2016 Supreme
Court of the United States.
We train nine separate models with the respective authored opinions of each supreme justice active ca. 2015 and test the resulting system on 96 real-world cases.
We find our system predicts the decisions of the realworld Supreme Court with better-than-random accuracy.
We further find a correlation between model accuracy with respect to individual justices and their alignment between legal conservatism & liberalism.
Our methods and results hold significance for researchers interested in using language mod- els to simulate politically-charged discourse between multiple agents.
Introduction
Recent and ongoing political turmoil in the United States has magnified the actions of the federal Supreme Court in the public eye.
The Court has taken to overturning judicial precedent in recent years, with the number of such decisions in the last six years reaching over twice the number of overturns between 2010 to 2015 1 .
The weakening rule of stare decisis has encouraged judicial researchers to develop holistic models of Supreme Court behaviour to better predict and account for future trends (Blake 2019; Allcorn and
Stein 2021).
Accurate models of Supreme Court behaviour are rare despite this focus.
The best performing models only reach accuracy levels of ≈ 70% on out-of-distribution cases (Katz,
Bommarito, and Blackman 2017).
Models achieving even this middling accuracy are complex in their architecture, generally consisting of a mix of SVM and logistic regression models.
This complexity is necessitated by the variables involved.
Confounding variables discussed in the literature include little agreed-upon theories regarding the legal doctrines practiced by individual justices (Jr, Curry, and Marshall 2011) and their rarely-documented social realities (Kromphardt 2017; Peterson, Giallouri, and Menounou 2021).
While the in-court behaviour of the justices is well documented, exogenous factors have an equal impact on
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case decision-making.
A model capable of both cognitive and social reasoning would therefore benefit justice behaviour modelling.
To this end, we investigate whether recent advances in social simulation with language models can promote simple and effective models of Supreme Court behaviour.
Background
In this section we describe the rationale behind our project.
Judicial Modelling
Three major theories of judicial behaviour generally inform the design of Supreme Court models: the legal theory, the attitudinal theory, and the strategic theory (Jr, Curry, and Marshall 2011).
The legal theory suggests justices are bound by constitutional precedent.
The attitudinal theory instead argues justices account for policy preference first, precedent second.
Between the two lies the strategic theory , which says justices vote according to a mix of precedent and preference.
As we show in Figure 1, decision correlations between justices active between 2010 and 2016 (hereafter referred to as the Roberts IV court) indicate the strategic theory is most accurate to reality.
While justices will invoke precedent when writing their rationales, evidence suggests justices remain somewhat beholden to the political alignment of their nominator.
We note, however, that the correlations are only medium in their strength.
This indicates accurate models should account for precedent, but not exclusively.
Integrating one of these three theories into a Supreme
Court model requires choosing how to best cast the influence of precedence and preference as variables.
Given this conversion can itself result in significant drawbacks via unforeseen factors, we instead choose a simulative tool which allows to us to make fewer assumptions as to the most correct theory of judicial behaviour: language models.
Simulation
Large Language Models (LLMs) are adept at simulating complex social phenomena.
Recent research has demonstrated their ability to predict populated social media platforms (Park et al.
the distribution of votes for presidential candidates in the 2012-2020 American elections (Argyle et al. 2022), and the general sentiment of news articles reporting COVID-19 in the early stages of the pandemic (Hamilton and Piper 2022).
These developments show model bias is valuable for those in the social sciences given bias is derived from the underlying distributions of their training material.
Prior simulation research benefits from new techniques for eliciting cognitive activity from LLMs nominally designed for next-token prediction.
These include chain of thought reasoning (Wei et al. 2022), discretely-structured prompts (Liu et al. 2021), and fine-tuning (Drori et al. 2022).
These techniques have the model draw on internal biases to make predictions, allowing researchers to embed fewer assumptions into their simulative models.
LLMs are alluring given judicial modelling necessitates a system capable of both social and cognitive reasoning.
Agent-Based Modelling
The process by which the Court arrives at a decision is nominally rational (Jr, Curry, and Marshall 2011).
While predilections are known to influence vote outcomes, justices are expected to justify dissenting decisions in written documents called opinions .
Opinions are typically one to five pages in length within which the justice (or their aid) lays out their argument in a manner similar to an essay.
For our simulation task, we assume justices record their rationale honestly and so treat the opinions as our primary target of prediction, meaning any model we train will be predicting opinions.
Because opinions are long documents (i.e. longer than the 1024 token-long context window GPT-2 is trained for), having one model produce multiple opinions in the same run is untenable.
We turn to agent-based modelling for a solution.
Whether consolidating multiple generative LLMs into a single architecture is beneficial has been heretofore understudied, with the only significant prior experiment with
LLMs showing promise (Betz 2022).
However, given the
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Judge n
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Vote
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success of the Mixture of Experts (MoE) method in machine translation (NLLB Team 2022), we argue further exploration of similar techniques for simulation tasks is warranted.
While social simulation experiments suggest a single language model is capable of producing a wide range of opinions, training multiple models separately prevents cross-contamination when studying multiple data sources
Method
We present the general design of our architecture in three parts: data collection, system architecture, and measures.
Dataset
We source data from two datasets for this experiment.
The first corpus is the Supreme Court Database (SCDB) released by researchers at Washington University in St. Louis, which provides variables for 9,095 cases decided betweenand 2021 (Spaeth et al. 2014).
We supplement the SCDB with all written opinions from all slips provided on the Supreme Court website.
2 Extracting the opinions from the PDF documents with an optical character recognition (OCR) utility leaves us with 145MiB of text written between 2003 and 2022.
We then associate each opinion with the justice and case from which it originated.
System Architecture
We choose to simulate the Roberts IV court (2010-2016) given this period outlasts all other Supreme Court iterations in recent history
Design Our multi-agent system is composed of nine fullsized GPT-2 models (Radford et al. 2019).
We present the system architecture in Figure 2.
At a high level, our system receives the topic of a case being brought before the court and passes it along to nine justice models.
The system then receives back nine opinions and corresponding decisions of whether to approve the appellant.
The system totals the results and returns the majority vote.
Prompt We train each justice model with a discrete prompt structured like a Python dictionary: { ’issue’: ’Lorem ipsum...’, ’topic’: ’Lorem ipsum...’, ’opinion’: ’Lorem ipsum...’ ’decision’: ’Lorem ipsum...’ }
The issue value corresponds to the issueArea variable provided by SCDB.
The topic value is a short description of what the appellant is bringing before the court.
We extract this information from the syllabus of each opinion slip and summarize it with GPT-3 Davinci (Brown et al. 2020).
The opinion value is the corresponding rationale the justice produces when formulating their decision value, here a categorical variable signalling (dis)approval.
We provide an example in the appendix.
Training All models are trained for a total 30 epochs at a learning rate of 2 e − 4 with the Adam optimizer (Kingma and
Ba 2014).
This training process is conducted in two steps:
Construct ≤ 1000 token prompts of the above style for all cases
in
which the Roberts IV
court came to a unanimous decision.
This model serves as the base for all further trained models
Collect all prompts generated in step 1 for each of the opinions (2003-2016) written by each justice active during Roberts IV.
We thereby collect nine training sets and further train the model generated in step 1 with each separately.
Average model loss after both steps is 1 . 5 , indicating there remains significant room for improvement.
Measures
We assess the performance of our multi-agent system ontest cases withheld from the training set with two measures: accuracy and a novel measure for judicial ideological alignment.
Accuracy We measure accuracy with a receiver’s operating characteristic curve (ROC) together with Cohen’s κ to account for a slight distribution bias in our test set.
Alignment Justices are understood as being more or less in favour of overturning precedent.
We capture this alignment by taking the Pearson coefficient ( r ) between model accuracy and the frequency with which the respective justice
Justice
Accuracy κ
Samuel Alito
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Ruth Bader
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Clarence Thomas
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Stephen Breyer
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John Roberts
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Elena Kagan
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Anthony Kennedy
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Sonia Sotomayor
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Antonin
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voted against precedent-altering decisions betweenand 2016.
Our measure is intended to capture where a justice is aligned between conservative (e.g. textualism, formalism, originalism) or liberal (e.g. legal realism) frameworks of judicial decision making (Post and Siegel 2006).
Results
All results are reported with a minimum confidence rate of 80% and are controlled for training material size and topic.
Generations are run with a temperature of 0 .
5 and a maximum length of 1000 tokens.
Accuracy
Our system achieves an aggregate accuracy of 60% ( κ ≈ 0 . 18 ) on 96 test cases.
While less predictive than the state of the art, our model nonetheless achieves better-than-random performance despite having been trained solely on opinions.
We find a wide variation in the accuracy of each simulated justice when examining system performance more closely.
As shown in Table 1, model accuracy varies between 65% and 50% despite having controlled for training data volume and case outcome.
Alignment
We measure a moderate correlation ( r ≈ [-
 .between-]0 . 56 ) between simulated justice accuracy and the frequency with which each respective justice did not agree with the Court overruling or re-interpreting precedent.
This result suggests our system achieves better accuracy with justices who are less likely to overturn precedent.
We discuss the implications of this result below.
Validation
We train a single agent model to ensure having many agents provides non-negligible benefits.
We fine-tune this single agent with the majority opinions of all cases decided on by the Roberts IV court.
Testing this single agent on the test set results in an overall accuracy of 54% ( κ = 0 . 08 ).
The predicted decisions differs from the original test set with a Cohen’s d of ≈ − 0 .
86 versus d ≈ 0 .
19 for our multiagent model, increasing the population overlap from 68.5% to 92.4%.
We implement software controls to ensure program output validity given training to a low loss does not guarantee the model produces both the opinion and decision variables.
We therefore rerun each case until all models have returned a valid result.
Once having processed all 96 cases, we sample agent-produced opinions belonging to half to ensure coherency.
Discussion
In this section we discuss two major consequences of our research.
Precedent Hallucination GPT-2 is not an expert on legal precedent, nor should one expect it to be when the only formal source of legal information ingested by the model during pre-training were some seven thousand pages from FindLaw , a website principally known for tort law (Clark 2022).
This becomes evident when surveying model output.
While the model will occasionally reference real laws, these citations prove to be happenstance as GPT-2 will confuse details and thus render the references meaningless.
That the model generates its own precedent when arguing over a case is an example of hallucination , a well known property of language models (Rohrbach et al. 2018).
Because causal language models are only tasked with predicting the next most likely token given some prior sequence, they are not given incentive to withhold factually incorrect statements—the model will say whatever is necessary to return the number of tokens requested in a cogent manner.
Our justice models will hallucinate precedence when producing opinions.
They produce this pretend precedence implicitly by citing it throughout the argumentation process.
That our models achieve greater-than-random decision accuracy in voting outcomes despite not producing legally valid arguments suggests Supreme Court decisions may not always rest on legally coherent rationales.
Alignment Correlation
The correlation between model accuracy and judicial alignment indicates conservative justices are more predictable given their general unwillingness to overturn precedent.
Considering the model hallucinates precedent, this correlation suggests conservative justices are conservative for ideological rather than rational reasons.
We find this result surprising given conservative justices often make it a point to rationalize their unwillingness to overturn precedent with legal justifications.
Common formalist theories of this sort include both originalism and textualism, doctrines practiced by conservative members of the current court (Esbeck 2011).
Our results suggest these decision-making patterns are less grounded in rational logic than anticipated given they are partially captured in a model not familiar with common law.
Conclusion
The aim of our project was to produce a multi-agent system capable of predicting Supreme Court decision-making with little to no prior theory-based assumptions of judicial behaviour.
Given our resulting model achieves better-thanrandom accuracy despite having been trained only on opinion matter, we argue our process serves as an example for researchers seeking to develop simulative experiments with language models.
Limitations
As should be expected of any project promoting the creative output of AI, we make note of the biased material used in the production of large language models like GPT-2.
While we contend this culturally-derived bias is beneficial for researchers using foundation models in the the social sciences, we nonetheless ensure our model does not cause unwanted harm.
As such, we clearly mark all samples as having been generated and refrain from releasing large collections of generated material to the public.
Next Steps
We propose the following next steps after having demonstrated the basic viability of our architecture.
Larger Model Can we improve system accuracy with larger language models?
Recent research suggests language models develop emergent cognitive features when scaled above 6.7 billion parameters, narrowing future possible candidates to the likes of GPT-NeoX-20B and T5X
(Dettmers et al. 2022;
Black et al. 2022; Roberts et al. 2022).
Larger Training Corpus Another avenue for increasing system accuracy involves fine-training GPT-2 with the whole corpus of American law as captured by proceedings and opinions written in lower courts.
The principle of stare decisis means the practice of common law is a social venture, suggesting language models would do well in predicting precedent-dependent cases if prepared.
Improved Prompting Research indicates language models can avoid the long tail of token probabilities by repetitively querying the model (Portelli et al. 2022;
Kim et al.
Integrating repetitive prompting strategies into the opinion-generating schema is a promising avenue for improvement.
Another avenue would be to assess how reinforcement learning from human feedback (RLHF) models like InstructGPT simulate court proceedings (Ouyang et al.
Investigating Future Cases How would the Roberts IV court fare with cases brought before the court after 2016?
Would their court overturn precedent at the rate the post2016 Supreme Court has?
Questions of this caliber would be made approachable with a more accurate Roberts IV system.
Appendix
We demonstrate our system with a real-world case fed to the
Ruth Bader Ginsburg model.
We first provide our prompt followed by the model’s response.
Note the model correctly predicts Ginsburg’s real-world decision (to deny the appellant) despite the ”California Childhood Video Game Act” not existing.
Prompt
Issue: ‘First Amendment’,
Topic: ‘The California law restricting the sale or rental of violent video games to minors was challenged by the videogame and software industries.
The Federal District Court concluded that the Act violated the First Amendment and permanently enjoined its enforcement.
The Ninth Circuit affirmed.’,
Appellant is seeking a: ‘certiorari’,
Model Response
Opinion: ‘The California Childhood Video Game Act is on its face both overbroad and vague.
It prohibits the sale or rental of “any device or medium designed for or capable of reproducing visual images of decapitation, blood, or dismemberment of a human body,” in the presence of a child under the age of 13.
It also prohibits the importation into the State of California of “any video game system, computer game software, or computer program that contains a killing or violent content.”
The Act specifically identifies video games that have been determined by the State to be “violent,” and any person who “possesses, or has under his control,” one of those video games is subject to the Act’s restrictions.
The Act falls outside the First Amendment because it interferes with the creative expression and acquisitive impulse that go to make up the quintessential activity of a child’s life.
The majority points out that the Act does not regulate the mere possession of these games, but seeks to regulate the medium in which they are played.
It reasons that
the
State may regulate what the child sees and does not see by preventing the child from becoming engrossed in the game world and thereby “sustaining or supporting the action or activity.”
But the majority does not ask whether the regulation of what the child sees and does not see is content-based.
It neither considers nor concludes whether the regulation is narrowly tailored to the interests it seeks to protect.
And it does not consider the adverse impact that its rule may have on legitimate play.
The majority says that the regulation is content-neutral because it does not regulate “the medium in which the [killing or violent content] is embodied,” or the “context in which the [killing or violent content] is presented.”
But to the extent that the regulation of medium and context are related, the majority’s rule will be unworkable.
The child who might otherwise play The Last of Us might otherwise play The Path, instead, because the former game has fewer graphic content and the latter is rated M for Mature.
And the child who might otherwise enjoy the violent video game The Walking Dead might otherwise have played might instead have played The Secret of Monkey Island, which has no violence or blood and is rated A.
The child who might otherwise have played Grand Theft Auto might instead have played The Legend of Zelda, which has no violence or blood and is rated E.
And so on.
The variety of content that the child may choose from makes it virtually impossible to determine with any precision what the regulation of what the child sees and does not see will look like.
The only thing that the majority seems to be able to say with any precision is that the regulation will likely contain some content-based exceptions.
But as the San Francisco ordinance demonstrates, those exceptions are exceedingly rare.
And when they do appear, they almost always involve content the State has determined is not suitable for children.
Ifearthat the majority’s rule will produce a generation of
Americans—white, middle-class, suburban—who have no interest in, and no capacity to, engage in the kinds of play the First Amendment protects.
And I fear that this Court, which prides itself on its willingness to protect the most vulnerable members of our society from harm, will be complicit in that generation’s continued marginalization.
I respectfully dissent.’,
Decision: ‘deny’