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    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>At the Boundary of Law and Software: Toward Regulatory Design with Agent-Based Modeling</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Sebastian Benthall</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Michael Carl Tschantz</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Erez Hatna</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Joshua M. Epstein</string-name>
          <email>joshua.epstein@nyu.edu</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Katherine J. Strandburg</string-name>
          <email>katherine.strandburg@nyu.edu</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>International Computer Science Institute</institution>
          ,
          <addr-line>2150 Shattuck Avenue, 94704, Berkeley</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>New York University, School of Global Public Health</institution>
          ,
          <addr-line>708 Broadway, New York, NY 10003</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>New York University, School of Law</institution>
          ,
          <addr-line>40 Washington Sq So, 10012, New York</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
      </contrib-group>
      <fpage>0000</fpage>
      <lpage>0003</lpage>
      <abstract>
        <p>Computer systems that automate the making of decisions about people must be accountable to regulators. Such accountability requires looking at the operation of the software within an environment populated with people. We propose to use agent-based modeling (ABM) to model such environments for auditing and testing purposes. We explore our proposal by considering the use of ABM for the regulation of ad targeting to prevent housing discrimination.</p>
      </abstract>
      <kwd-group>
        <kwd>Modeling</kwd>
        <kwd>agent-based modeling</kwd>
        <kwd>accountability</kwd>
        <kwd>regulation</kwd>
        <kwd>automated decision making</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>The use of agent-based models (ABMs) can improve software accountability by representing
populations of actors (e.g., house buyers, job seekers, college and insurance applicants) afected
by software. Unaccountable software can embed and exacerbate societal biases or have other
pernicious efects. ABMs can be used to explore the societal efects of software systems to aid the
design and enforcement of regulations. Currently, software accountability measures are largely
defined very narrowly, as mechanical compliance with regulations, written without a systematic
way of predicting societal impact. ABMs are a way to model the societal impact of software
and to correct or design regulations accordingly. We argue, in essence, that agent-based models
(ABMs) of the interactions between software systems, those systems’ social environments,
and applicable regulations can help to improve software accountability. We focus on software
systems that employ personal data, have significant impacts on individuals, and are subject to
regulation or used within regulatory agencies.</p>
      <p>For example, anti-discrimination regulations in the housing context focus on societal goals
such as fairness in housing or the reduction of residential segregation. Some of these regulations
nEvelop-O
LGOBE
https://sbenthall.net (S. Benthall); https://www.icsi.berkeley.edu/~mct/ (M. C. Tschantz)
are applicable to the software systems that target online housing ads. These systems, typically,
are written not by regulators but by private sector software designers. The resulting deployed
advertising systems may produce efects that are inconsistent with – even subverting – the
regulatory intent. One possible reason for such an outcome is that the social environment in
which the software is deployed is absent from the analysis of software impact. We want to
include it and make it accessible to the regulators. If the social environment were represented,
auditors could better anticipate whether the software is likely have the intended social efect.
We propose to use ABMs to fill this gap, making software more accountable in this sense.</p>
      <p>This sort of transformation has occurred in other fields. Infectious disease modeling is one.
Faced with a novel pathogen, like Swine Flu or SARS-CoV-2, it is crucial to have some way to
estimate how fast it may spread, how much vaccine to produce, whether to ban international
travel or close schools and workplaces. Before the advent of infectious disease transmission
models, doctors and public health oficial were operating in the dark. Now, we have disease
simulation models at scales from the local to planetary for forecasting and mitigation. They are
part of the fabric of public health decision making, and are used to inform policy at the CDC,
NIH, WHO, and many national governments. They are not crystal balls and do not always
agree, as in weather forecasting. But collectively, they can bound our uncertainties, estimate
sensitivities, explore tradeofs, and ofer headlights in uncertain settings. Agent-Based Models
specifically, which can include social networks and cognitive factors, are increasingly used.
ABMs have the enormous advantage that they are also visual and rule-based (not
equationbased) allowing non-technical audiences and domain experts to understand their results and,
indeed, to participate in their construction. At the same time, they can be calibrated to epidemic
data. The net efect of all this is that ABMs can have higher impact than complex diferential
equation models. We are proposing to do this for software accountability.</p>
      <p>We see potential in this method because ABMs are legible to software engineers, social
scientists, and regulators. We have also identified key challenges to this approach, which are
the potential politicization of model choice, the selection of appropriate robustness metrics, and
the design of the interface between the ABM and audited software.</p>
    </sec>
    <sec id="sec-2">
      <title>2. The urgent challenge of software accountability</title>
      <p>
        Software’s importance as an object of regulation is increasing as ever more individually and
socially significant private sector activities are automated. Controversial examples include the
use of automated decision tools in employment [
        <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
        ], lending [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], targeted advertising [
        <xref ref-type="bibr" rid="ref4 ref5">4, 5</xref>
        ]
and higher education [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Increasingly, the use of personal data by information services is
being regulated by expansive data protection laws such as the E.U. General Data Protection
Regulation (GDPR) and California’s combined Privacy Rights Act (CPRA) and Consumer Privacy
Act (CCPA), whose interpretations are largely unsettled.
      </p>
      <p>
        Applying regulatory standards created for human actors to automated systems may fail to
further the policy goals of the regulatory regime. Software poses critical challenges to traditional
policy and regulatory approaches to accountability, both as an object and as a tool of regulation
[
        <xref ref-type="bibr" rid="ref7 ref8">7, 8</xref>
        ]. Most proposals for meeting these challenges have focused on increasing transparency
regarding when and how software is used, its provenance and verification, relationships
between inputs and outputs, or the software code itself. These eforts are complicated by the
dificulty of adequately explaining software, even to domain expert regulators who are not
trained in computer science [
        <xref ref-type="bibr" rid="ref10 ref9">9, 10</xref>
        ]. Suggested approaches to this problem include “algorithmic
impact assessments,” which systematize consideration of the potential efects of automation on
regulatory outcomes [
        <xref ref-type="bibr" rid="ref11 ref12 ref13">11, 12, 13</xref>
        ], summaries modeled on nutrition labels [
        <xref ref-type="bibr" rid="ref14 ref15 ref16 ref17">14, 15, 16, 17</xref>
        ] and
various forms of black box testing [
        <xref ref-type="bibr" rid="ref18">18, 19</xref>
        ]. While these approaches often require regulators to
gather input from afected individuals, communities and institutions, they lack a systematic
mechanism for using such input to explore the complex interactions between the software,
other aspects of the regulatory system and the afected social systems.
      </p>
      <p>We posit that there are three elements to the design of accountable software systems. The
ifrst two are the software system itself and the regulatory environment, including regulations,
regulators, and their enforcement mechanisms. Our key insight is that the third, the social
environment in which the system operates, is neglected in current software accountability
techniques. The appropriateness of the software given a regulation, and in light of regulatory
goals, depends not just upon the software’s behavior but upon its impacts on people in the
social environment. Accountable software regulation thus requires expertise relating to all
three elements and collaboration between software engineers, regulators, and domain scientists,
as well as mechanisms for oversight by the legislature and ultimately the public.</p>
    </sec>
    <sec id="sec-3">
      <title>3. ABMs as an answer to software accountability’s challenges</title>
      <p>ABM is already part of the policy-making toolkit [20]. ABMs may have additional advantages
when software is a regulatory object or tool. Coglianese and Lehr [ 21] argue that as “regulation
by robot”, or regulations designed and implemented using machine learning, become more
common, other analytic techniques will need to be used to test them. In particular, they
recommend the use of ABMs or multi-agent systems (MAS) to test the impact of regulations on
the complex social environment.</p>
      <p>By modeling the social environment, ABMs can capture regulatory concepts dificult to
express in terms of software alone, such as people’s beliefs and purposes, and how regulations
are often designed to be open to ongoing reinterpretation as new circumstances arise. We
suggest that this method of testing the social impact of a software system can be more intuitive
to regulators and domain experts than other means for projecting likely impact. ABMs can
also more accurately account for social complexity and feedback loops, including unintended
ones not readily apparent from the behaviors of individuals or the software acting in isolation.
Furthermore, ABMs are implemented as explicit programs, making them intelligible to software
engineers, thereby facilitating dialogue between them and regulators about policy goals and
the interpretation and meaning of regulations. The dificulty of expressing the accountability
goals of software in the traditional language of software testing, test suites expressed as the
approved outputs for a given input, inspires the turn to ABMs.</p>
      <p>As a concrete example, the goal of contact tracing is to slow the spread of a disease by
identifying people who have likely been exposed to it and notifying them for testing, treatment,
and/or isolation. Contact tracing may also be subject to policy making by public health
departments, various privacy regulations, and protections of confidentiality. In the COVID-19
pandemic, many countries controversially turned to smartphone based contact tracing, despite
public outcry in places about inappropriate surveillance. To understand whether an app is
compliant with this regulatory environment requires information about the social environment.
Policymakers may also seek to encourage or mandate the use of contact tracing. Software
designed to be responsive to privacy concerns might increase the public adoption of the apps.
ABMs can model this complex social environment, calibrated to empirical data to predict social
outcomes, and provide information necessary to assess compliance. Because ABMs are software
objects, they may be coupled directly with regulated software systems or model their social and
behavior impact.</p>
      <p>We picture, for example, a regulator that has been entrusted by the public and legislature (the
“agenda setters”) with social goals in a particular domain. The regulator works with domain
scientists, who provide a descriptive ABM that includes the entities important to regulations,
such as actors and social outcomes. The regulator introduces normative elements into the
model, which may be hard rules on agent behavior or objective functions to be tracked and
optimized. This model can be used to analyze the intended and unexpected consequences of
the regulation.</p>
      <p>We propose a regulatory design process that uses ABMs to enhance accountability by spanning
the boundaries between law, software, domain expertise, and ultimately, the public (Fig. 1 &amp;
2). ABMs can be developed to simulate the social efects of such a private software system and
thus evaluate its implications for regulatory goals. Regular reports to government agencies
on the social impact of software systems (“Impact Assessments”), and reports responding to
investigations, are an unsettled requirement of many laws governing software systems including
the CCPA/CPRA, the GDPR, and the E.U.’s more recently proposed technology regulations such
as the Digital Services Act, Digital Markets Act and Artificial Intelligence Act. There remain
many open questions about the legal and technical feasibility of software that allows regulatory
users to interact with and visualize results from the model. A key aspect of this workflow
are methods for testing the robustness of the system’s compliance to social changes, modeled
as both endogenous change within an ABM and as variation of the ABM’s performance over
variations in its parameter space. These will be truly new capabilities.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Example: Housing advertising</title>
      <p>
        The Fair Housing Act and related regulations prohibit certain discriminatory housing practices,
including ad targeting that would “deny particular segments of the housing market information
about housing opportunities” based on “race, color, religion, sex, handicap, familial status,
or national origin.”1 Prior to 2019, Facebook’s ad targeting options included targeting based
on Facebook-constructed attributes, including “ethnic afinity” (later renamed “multicultural
afinity”). Though based on users’ activities on the platform, “ethnic afinity” could obviously
have the efect of targeting ads unevenly across racial groups. In fact, Speicher et al. [ 22]
demonstrated that, even without using an attribute such as “ethnic afinity,” it was not dificult
to obtain biased targeting, intentionally or unintentionally, using Facebook’s targeting tools.
Related work has shown similar issues with Google’s advertising platform for race [23] and
gender [
        <xref ref-type="bibr" rid="ref4">24, 4</xref>
        ]. Facebook later changed its practices in response to a charge of discrimination
from the Department of Housing and Urban Development (HUD v. Facebook, 2019) and in
settlement of related class action litigation. Thus, there has been no judicial ruling on whether
its past or current automated ad targeting violates the FHA [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
      </p>
      <p>One well-studied area of AI accountability is machine learning fairness, which has been
developed in part to support the accountability of software to nondiscrimination laws. A result is
that diferent fairness metrics are appropriate under diferent assumptions about bias in the data
generation process [25, 26, 27]. There are also concerns about the “ripple efects” of automated
decision-making, such that an automated decision becomes involved in a feedback loop with
the social environment it’s acting upon [28]. With just access to the inputs and outputs of an
ad targeting program, an auditor can merely detect bias in the presentation of advertisements
(e.g., [23, 24]). Adding a calibrated ABM of housing choice, lets the auditor additionally predict
how such biases play out in society, including feedback loops, as represented in the ABM. For
example, the ABM could show how the biased ads increase segregation. We are not aware of
any auditors combining software and ABMs in this way.</p>
      <p>ABMs have, however, long been used to study housing segregation, beginning with models
based on ethnic homophily and over time introducing models of market dynamics [29, 30, 31].
The Schelling Segregation Model [29] uses a square grid of residences, most of which house an
agent. The main counterintuitive result of this model is that the relationship between the level
of in-group preference and the amount of segregation in aggregate is non-linear. Even a weak
preference for in-group neighbors can generate strong segregation. For example, with 2 groups
and a 30% preference for in-group neighbors, the model will converge to near 75% of all
neighboring pairs being of he same group. There are many variations on the Schelling segregation
model, including more groups, variable preference rates, more realistic land topologies, and
market dynamics [32].</p>
      <p>We will develop a modified Schelling segregation model that includes the efects of advertising
which may influence of the residential behavior of agents and the socioeconomic characteristics
of neighborhoods.</p>
      <p>The new modified model can be designed to include parameters representing the degree to
which advertising is targeted based on (a) race and ethnicity, (b) location, and (c) socio-economic
status. Measurements of interest will include metrics for segregation along similar axes. A
contribution of the model will be that it can reveal the extent to which targeting based on, for
example, socio-economic status contributes to segregation based on race and ethnicity. Rather
than rely on point estimates to predict these efects, through multiple simulations the model can
be tested over its entire parameter space. The results of this simulation can then be analyzed to
determine efects and phase transitions on the dependent variables of interest (such as positive
and negative rates on groups; positive and negative error rates; and so on).</p>
    </sec>
    <sec id="sec-5">
      <title>5. New challenges</title>
      <p>We have identified several key challenges to the proposed approach. These pain points are each
opportunities for future technical and policy research.</p>
      <p>One challenge is designing and selecting the ABM for testing. Modeling the full complexity
of the agents interacting with or afected by software may be beyond an auditor’s capabilities
and knowledge. The auditor will have to make simplifying assumptions to produce an ABM. If
the ABM is consequential for regulation, its details will entail diferent outcomes for diferent
stakeholders. What process can improve the scientific accuracy and objectivity of the simulation
results?</p>
      <p>A related challenge is identifying the key metrics for translating ABM output into
policyrelevant information. The output of an ABM can be very sensitive to the calibration of its input
parameters, choices about its rules, as well as its own endogenous dynamics. Policy decisions
should be based on robust outcomes of the model, rather than on brittle point estimates or
single examples. The use of ABMs for software accountability requires well chosen metrics
(e.g.,statistical indices of spatial segregation) for outcome robustness.</p>
      <p>Lastly, we have identified a challenge at the technical interface between the audited software
and the ABM. This part of the accountability process is likely to be least transparent to regulators,
as it will be informed by the technical expertise of both the domain scientists and the audited
system engineers. The choice of which system outputs are entered into the ABM is a sensitive
one for which there is little preexisting guidance. For example, in our housing advertising
example, the auditing mechanism requires measurements of the degree to which the advertising
system discriminates with respect to race, location, and socioeconomic status. While it is
possible to take these measurements using black box testing techniques with synthetic web
user profiles, the resulting measurements are likely to vary with the technical specifics of the
measurement technique. It would be better to have general guidelines and standards for how to
design these interfaces between the audited software and the ABM.</p>
      <p>Beyond these scientific and technical challenges is the fact that, in an area as politically
fraught as fair housing, the politicization of model design (e.g., behavioral assumptions regarding
diferent social groups) is a distinct possibility. The fact that all assumptions are explicit and all
runs are replicable will help minimize this risk.</p>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusions</title>
      <p>Agent-based models are a promising solution to one significant obstacle to software
accountability: the modeling of the social environment of the software system. We envision a regulatory
process that embeds ABMs to bridge the expertise of software engineers, regulators, and domain
social scientists. In this article, we have developed one scenario for the use of ABMs for software
accountability: the testing of advertising system’s efects on housing segregation. By developing
this example, we have identified several key challenges to our proposed approach. We will
address these challenges in future research.</p>
    </sec>
    <sec id="sec-7">
      <title>Acknowledgments</title>
      <p>This material is based upon work supported by the National Science Foundation under Grant Nos.
2131532, 2131533, and 2105301. Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the author(s) and do not necessarily reflect the views of
the National Science Foundation. One of the authors of this article is supported by the NYU
Information Law Institute’s Fellows program, which is funded in part by Microsoft Corporation.
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