AA Bayesian Model of Cash Bail Decisions
Joshua Williams
Computer Science Department,Carnegie Mellon University [email protected]
J. Zico Kolter
Computer Science Department,Carnegie Mellon UniversityBosch Center for AI [email protected]
ABSTRACT
The use of cash bail as a mechanism for detaining defendants pre-trial is an often-criticized system that many have argued violates thepresumption of “innocent until proven guilty.” Many studies havesought to understand both the long-term effects of cash bail’s useand the disparate rate of cash bail assignments along demographiclines (race, gender, etc). However, such work is often susceptibleto problems of infra-marginality – that the data we observe canonly describe average outcomes, and not the outcomes associatedwith the marginal decision. In this work, we address this problemby creating a hierarchical Bayesian model of cash bail assignments.Specifically, our approach models cash bail decisions as a probabilis-tic process whereby judges balance the relative costs of assigningcash bail with the cost of defendants potentially skipping courtdates, and where these skip probabilities are estimated based uponfeatures of the individual case. We then use Monte Carlo inferenceto sample the distribution over these costs for different magistratesand across different races. We fit this model to a data set we havecollected of over 50,000 court cases in the Allegheny and Philadel-phia counties in Pennsylvania. Our analysis of 50 separate judgesshows that they are uniformly more likely to assign cash bail toblack defendants than to white defendants, even given identical like-lihood of skipping a court appearance. This analysis raises furtherquestions about the equity of the practice of cash bail, irrespectiveof its underlying legal justification.
KEYWORDS
Infra-marginality; Hierarchical Bayesian Model; Cash Bail
ACM Reference Format:
Joshua Williams and J. Zico Kolter. 2021. A Bayesian Model of Cash BailDecisions. In
ACM Conference on Fairness, Accountability, and Transparency(FAccT ’21), March 3–10, 2021, Virtual Event, Canada.
ACM, New York, NY,USA, 11 pages. https://doi.org/10.1145/3442188.3445908
In the criminal justice system, cash bail is the often-used practiceof requiring that defendants pay a monetary fee in order to bereleased pretrial, which is returned upon making all necessarycourt appearances. The inability to pay the set bail amount resultsin defendants being detained in jail for no reason other than their
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FAccT ’21, March 3–10, 2021, Virtual Event, Canada © 2021 Copyright held by the owner/author(s).ACM ISBN 978-1-4503-8309-7/21/03.https://doi.org/10.1145/3442188.3445908 inability to pay an often arbitrarily large fee. The practice has comeunder a great deal of criticism, with many experts arguing thatit violates the underlying notion of “innocent until proven guilty.”Indeed, such pretrial detention, for those unable to afford bail, orfor those who need to seek commercial bail bonds in order to securetheir bail, is one of the main drivers of the United States’ growingincarceration rate [21].The effects of pretrial detention are larger than just ensuringa defendant appears at their trial; there are lasting, devastatingconsequences on individual, family, and job security [19]. Pretrialdetention has been found to coerce defendants to plead guilty, re-gardless of reality, for the opportunity to return home, rebuild theirlives and prepare for trial [31]. Moreover, several other studies havefound that pretrial detention increases the likelihood of conviction,increases the chance that a defendant will receive a mandatoryminimum sentence if charged, and increases the defendant’s ulti-mate sentence [13, 37]. The use of cash bail alone has also beensuggested to make defendants more likely to recidivate [18], i.e. itacts counter to the belief that our justice systems are rehabilitative.Many jurisdictions have taken steps to address the concerns of cashbail decisions, including changes in the necessary requirementsfor a magistrate to issue cash bail, the use of pretrial risk assess-ments with the intent to curb human biases in the decision-makingprocess, or altogether stopping cash bail practices [20].In addition to the studied effects of cash bail, a further issuearises in considering the disparate rates of its use across groups(ie. race, gender, sexual identity, etc). Many prior studies describethis disparity by demonstrating the different rates of cash bailassignments with respect to race, gender, wealth, etc. However,as has been recently highlighted by the statistics community inmany other settings, such benchmark tests are susceptible to theproblem of infra-marginality. Due to differences in the unobservedmarginal distributions, observing average outcomes does not yieldenough information in order to determine whether a particulardecision-making process is biased [10, 24, 34]. The outcomes thatwe observe may or may not be a necessary result of the currentreality.In this paper, we propose a stylized model of bail decisions, whichdirectly estimates how cash bail assignments result from different(abstract) decision-making costs associated with defendants appear-ing in court – i.e., we assume that cash bail is assigned if the “ex-pected cost” of assigning cash bail is lower than the “expected cost”of the defendant potentially failing to appear for a court date (FTA).This captures a loose categorization of the National Association ofpretrial Services Agencies (NAPSA) 2020 guiding principles [27]for pretrial decision making in that: 1) the goal of bail setting isto find a bail amount and bail type that maximizes a defendant’slikelihood of pretrial release, while ensuring a defendant’s court a r X i v : . [ s t a t . A P ] J a n AccT ’21, March 3–10, 2021, Virtual Event, Canada 1 and 1 appearance; 2) these bail decisions and amounts should not im-pose a disparate or discriminatory outcome based on race, gender,sexual identity and other legally protected attributes; 3) pretrialdetention should be limited only to those defendants who pose anunmanageable risk to public safety. Under the proposed model, weinfer a latent variable which captures the cost that each magistratebelieves that society bears by a defendant being unable to pay theset cash bail versus the cost of this defendant failing to appear fora court date (itself based upon a linear model of probability of anFTA as a function of the covariates describing the particular casein question). Because we specifically allow these probabilities to depend upon group characteristics such as the race of the defendant,the model separates out the relative decision-making costs of bailfrom the actual probabilities involved. This enables the model todeal with the infra-marginality problem to some degree, and we es-timate the mechanism behind a magistrate’s cash bail decisions evenaccounting for potential differences in FTA rates amongst differentgroups.
We estimate these costs by creating a dataset of 89 ,
751 courtdockets from Philadelphia and Allegheny counties in Pennsylvaniafrom the years 2016 to 2019. We then fit the model parametersfor the 50 most active magistrates within our dataset. Here, wefound that nearly every one of the 50 most active magistrates showsa greater willingness to assign cash bail to Black defendants than toWhite defendants, even given equal probabilities of skipping trial . Inother words, for two defendants with the same relative probabilityof skipping their court appearance, judges were uniformly morelikely to assign cash bail to a Black defendant. This is particularlystriking given the fact that some of the simpler baseline analyses(such as simply comparing bail assignment rates for black andwhite defendants) show more similar treatment for each group.From a more algorithmic perspective, we believe our methodologyalso presents a valuable contribution to work on addressing infra-marginality problems via Bayesian modeling. While past work hasaddressed similar questions, to the best of our knowledge ours is thefirst to simultaneously estimate a full parametric predictive modelof relevant outcomes that includes group identifying components,while simultaneously attempting to estimate the relative costs ofdecisions based upon these groups. Thus, we believe that the currentwork presents both an important study from a societal perspective,and a methodological advance of interest to the broader algorithmiccommunity.
In this section, we introduce the pretrial process, as it relates to baildecision-making in Allegheny County and Philadelphia County,and address prior analysis for this aspect of the judicial process.
In Philadelphia County, after an arrest, typically a video confer-ence is set up between a magistrate and a defendant, where themagistrate will assign a bail type and bail amount in a hearing thatgenerally lasts one to three minutes [25, 26]. Each shift of bail hear-ings takes place for approximately four hours every day, with oneof Philadelphia’s six arraignment court magistrates presiding overeach shift [17]. Pretrial processes work much the same in Allegheny county, where one of 46 magisterial district judges will preside overa preliminary arraignment in which a defendant’s bail is set. Bailneed not be set only at the preliminary arraignment, it may also beset during a preliminary hearing or bail hearing. However, in mostcriminal cases, it is set at this preliminary arraignment.Of the bail types assigned, a magistrate has the option under thelaw [2] to choose one of the following:(1) Release on recognizance (ROR) – a written agreement froma defendant to appear on their court date. This agreementmay come with additional stipulations, but does not requireany monetary commitment.(2) Release on nonmonetary conditions – a magistrate may re-lease a defendant on nonmonetary bail if they believe thatset conditions such as restricting travel or requiring the de-fendant to report in are sufficient for their court appearance.(3) Release on nominal bail – a magistrate may release a defen-dant on nominal bail by requiring a small amount of money(eg. one dollar) and another entity (a person or organization)to act as surety.(4) Release on unsecured bail – a magistrate may release a defen-dant on unsecured bail by requiring a written agreement thatthe defendant becomes liable for the set amount of moneyin the event of non-appearance. This does not require anymoney or other form of security in order to be released.(5) Release on monetary bail – a magistrate may release a de-fendant on cash bail if they believe that a defendant willbe unlikely to comply with the conditions of release with-out an immediate guarantee. In Allegheny County, the bailauthority may require that individual to pay no more than10% of the full bail amount in order to secure their release.If a defendant is unable to pay, they will be detained untiltrial [4]. In Allegheny County, cash bail should not be setunless a magistrate investigates the defendant’s financialbackground and finds that the set amount is reasonable [3].
If a defendant is detained pretrial because the set bail was not rea-sonable then there can be serious consequences, both inside andoutside of the case. In a qualitative assessment of 23 interviewsamong defendants who pled guilty, Euvrard and Leclerc [16] found,among other effects, that pretrial detention acts as a coercive mech-anism in which by pleading guilty, the defendant can avoid jail time,whereas by pursuing a trial, the defendant will have to wait in jailfor an undetermined amount of time. Similarly, some intervieweesacknowledged that the jail-time offered by accepting a plea dealmay be equivalent to their time spent in jail by waiting for trial.Pleading guilty often leads to the minimum amount of time spentin jail, regardless of innocence or guilt.Further quantitative studies have confirmed similar effects. In astudy of New York’s pretrial outcomes, by regressing convictionand pretrial detainment on defendants’ relevant features, Leslie andPope [22] found a positive correlation between pretrial detainmentand conviction. In other words, the authors find that the morelikely a judge is to detain an individual pretrial, the more likely thatthis individual pleads guilty or is convicted of a crime. In a similaranalysis, Dobbie et al. [14] use a measure of judge leniency, based Bayesian Model of Cash Bail Decisions FAccT ’21, March 3–10, 2021, Virtual Event, Canada on the residuals of release decisions in a probit model, in order toestimate the influence of the assigned magistrate on pretrial releaseand its subsequent effects on future crime, court appearances, andemployment. They find that while pretrial release increases thelikelihood of failing to appear, release both decreases the likelihoodof rearrest over the next two years and increases the likelihood ofhaving any income over the next two years.In particular, such models generally follow the rationale that theimpact that the presiding authority has on a case can be isolatedand that we can estimate regression coefficients for outcomes inways that glean new insights, as in the example below. For example,Gupta et al. [18] propose a regression model 𝑍 𝑖𝑐𝑡 𝑗𝑜 = 𝑛 𝑐𝑡 𝑗𝑜 − ∑︁ 𝑘 ≠ 𝑖 (cid:16) Bail 𝑘𝑐𝑡 𝑗𝑜 (cid:17) − 𝑛 𝑐𝑡 − ∑︁ 𝑘 ≠ 𝑖 (cid:16) Bail 𝑘𝑐𝑡 (cid:17) (1)Outcome 𝑖𝑐𝑡 𝑗𝑜 = 𝛼 + 𝛽 Bail 𝑖𝑐𝑡𝑜 + 𝛿𝑋 ′ 𝑖𝑐𝑡𝑜 + 𝜖 𝑖𝑐𝑡 𝑗𝑜 (2)Bail 𝑖𝑐𝑡 𝑗𝑜 = 𝛼 + 𝛾𝑍 𝑖𝑐𝑡 𝑗𝑜 + 𝑋 ′ 𝜁 + 𝜈 𝑖𝑐𝑡 𝑗𝑜 (3)where Bail 𝑖𝑐𝑡 𝑗𝑜 is an indicator for whether or not cash bail wasset for defendant 𝑖 with offense 𝑜 in court 𝑐 for year 𝑡 by judge 𝑗 and 𝑋 ′ are defendant controls, such as age, race, gender, charges,priors, etc. 𝑍 𝑖𝑐𝑡 𝑗 is a measure of judge leniency, calculated as thedifference in leave-one-out means of a judge’s rate of cash bailassignments compared to the rate of cash bail assignments for court 𝑐 . A litany of prior literature [7, 15, 18, 19, 36] uses such methodsbased on probit/logistic regression models with or without residualmeasures of judge leniency/severity in order to model how ourobserved pretrial data influences defendant outcomes after theirpreliminary arraignments/bail hearings, with most work comingto similar conclusions. Due to the harmful long-term impact of cash bail use, further workhas sought to verify whether or not magistrates assign cash bailuniformly among demographic groups. For cases in which a judgeassigned cash bail, prior work [6, 12, 32, 35, 38] has reviewed pretrialdecisions for instances of judge bias and found that across thestate of Pennsylvania, the proportion of Black defendants who areassigned cash bail is significantly greater than the proportion oftheir non-Black counterparts who were assigned cash bail, withadditional work [33] finding that even after controlling for thetypes of crimes, judges still assign cash bail to Black and Whitedefendants differently for the same crime in 20% of cases.Furthermore, a 2019 investigation by the American Civil LibertiesUnion (ACLU) [6] found that cash bail was assigned in as many as25% of cases, with some magistrates setting cash bail in up to 57%of cases. In Philadelphia, a 2018 review by the ACLU found thatupwards of 43% of defendants were assigned cash bail [30]. Otherstudies [28, 33] have also found cash bail assignment rates rangingfrom 40% to 70% over all magistrates.Beyond biases along racial lines, a 2017 class action suit broughtagainst Harris County, Texas [1] argued that the county had beenusing money bail on misdemeanor defendants who could not pay.The district court, who’s ruling was later affirmed by the FifthCircuit Court of Appeals, “concluded [that] Hearing Officers wereaware that, by imposing a secured bail on indigent arrestees, theywere ensuring that those arrestees would remain detained.” [1]. In essence, from jurisdiction to jurisdiction, we see trends that showthat cash bail has been used as a barrier to justice for individuals ofa certain race or financial status.
Among the studies on both the disparate rate of cash bail assign-ment and the downstream effects of cash bail, there has been agrowing emphasis that the methods employed in these studies maynot be able to show the entire story [24]. Specifically, such meth-ods are susceptible to the problem of infra-marginality. As coinedin [10], the infra-marginality problem notes that our observed datais only able to provide average outcomes and not the outcomesassociated with the marginal decisions. This problem has the po-tential to undermine analyses that are based solely on the observedinformation, causing such work to be unable to provide a completepicture of the underlying reasons for observed disparities. Beyondthe infra-marginality problem, studies of bail decisions are alsosusceptible to Simpson’s paradox, where the marginal associationbetween categorical variables changes after controlling for one ormore other variables.As an illustrative example, suppose that there exist two groupswith different probabilities of missing their court dates, and thatthere exists some threshold where a judge assigns cash bail to alldefendants whose court failure to appear (FTA) probability exceedsthis threshold. We may observe that one group is assigned cash bailat a higher rate than a second and we may observe that under ajudge’s cash bail assignments, one group is less likely to miss a courtappearance than another, we may reasonably conclude that thereis bias in a judge’s decisions. However, without prior knowledge ofthe underlying distributions and the marginal decision threshold,there exist cases in which these seemingly biased outcomes occurwithout an bias on the part of the judge. For example, figure 1shows two hypothetical cases in which both the rate of cash bailassignment for the red and blue groups (0.55, 0.35) and the expectedFTA rate for those who were assigned cash bail for each group(0.311, 0.335) does not change.These observed statistics tell us that a judge is assigning cashbail to the red group at a higher rate, and that the expected FTA ratefor defendants in the red group who are assigned cash bail is alsolower than the expected FTA rate for those members in the bluegroup who receive cash bail. This may be indicative of some biason the part of the judge. However, if we consider the judge’s bailassignment thresholds, the first case shows that the judge is usinga consistent decision threshold, irrespective of group membership.The disparate rates of cash bail assignment are not based on bias onthe part of the judge, but a result of each group’s marginal FTA rate.In the second case, the rate of cash bail assignments and expectedFTA rates under cash bail assignments remain the same as in thefirst case, however, the decision threshold shows that the judgeis assigning cash bail to members of the red group who have alower probability of failing to appear than the blue group. Here,the differences in cash bail assignment rates and FTA rates areactually a result of bias on the part of the judge. The problem ofinfra-marginality lies in such cases, where, due to the fact that wecannot observe the marginal distribution of FTA probabilities, the AccT ’21, March 3–10, 2021, Virtual Event, Canada 1 and 1
Figure 1: How the infra-marginality problem may manifestin bail analyses. (Left) Example Beta Distributions of FTAprobabilities: red=Beta(6,18), blue=Beta(2,8). (Right) Exam-ple Beta Distributions of FTA probabilities: red=Beta(1,4),blue=Beta(2,8); In both cases, thresholds are set so that theproportion above the threshold are . and . for red andblue groups respectively. Additionally thresholds are set sothat expectation above the threshold are . and . re-spectively. Outcome statistics remain unchanged despite thethreshold’s reflecting different policies by a judge. observed data is unable to differentiate between the regime wherea judge favors one group and one where judges are unbiased withrespect to group membership. For a more detailed example, see [34].Ayres [10] explicitly argues that the bail-bond setting avoids theinfra-marginality problem. The author argues that that the problemin cash bail assignment is non-dichotomous, as judges also assigna continuous variable, bail amount. By assigning bail amounts ina way that changes individual FTA probabilities, we effectivelymarginalize the distribution over all covariates, so that the observedoutcomes are outcomes on the true marginal distribution. However,while the assigned bail amount is continuous, the decision to assigncash bail in the first place is dichotomous; judges choose to usecash bail in lieu of four other options. Before cash bail amounts areconsidered, we are already in the setting in which Ayres arguesthat the problem of infra-marginality undermines outcome tests.Even considering the setting where we condition on defendantswho were assigned cash bail, the notion that bail amounts allowus to avoid this problem requires the assumption that a judge actson full knowledge of a defendant’s ability to pay, which is unlikelygiven the short (1-3 minute) nature of preliminary hearings. If ajudge assigns cash bail at an amount that a defendant cannot pay,then we are still effectively marginalizing over two distinct sub-groups, those defendants detained pretrial and those defendantsreleased on cash bail. Such observations are then subject to Simp-son’s paradox, in which the trends change after again conditioningon those who are released pretrial on cash bail.Moreover, such models as equation (3), that emphasize a residualmeasure of judge leniency, are also susceptible to infra-marginalityeffects. For instance, the model above can be simplified to Outcome 𝑖𝑐𝑡 𝑗𝑜 = 𝛼 + 𝛽𝛾𝑍 𝑖𝑐𝑡 𝑗𝑜 + ( 𝛿 + 𝜁 ) 𝑋 ′ 𝑖𝑐𝑡𝑜 + 𝜖 𝑖𝑐𝑡 𝑗𝑜 + 𝜈 𝑖𝑐𝑡 𝑗𝑜 (4) As judge leniency measures themselves are the difference of suc-cessive benchmark tests, emphasizing measures of judge leniencyintroduces a new component that suffers from the problem of infra-marginality. While such analyses provide valuable insight, finding ways to address this shortcoming is valuable for a full understand-ing of such processes.This issue of infra-marginality has been directly addressed in adifferent setting [29, 34] in an analysis of nationwide traffic stops,with a hierarchical Bayesian model that fits a threshold to themarginal probability distribution of contraband possession amonggroups. Officers are not expected to search a vehicle unless thelikelihood of contraband possession is above this fit threshold. Thissetup avoids the issue of infra-marginality, by not directly basingindicators of bias on the observed outcomes, but on the latentvariables that describe these outcomes.We follow a similar problem setup in this work, in which weposit a hierarchical Bayesian model of cash bail assignments basedon the a group’s FTA (failure to appear) rate and their pretrial re-lease rate. The FTA and release probabilities are then used to fita latent variable, based on a magistrate’s perceived societal costof members of a group failing to appear for their court dates orbeing unable to post their bail. In our approach, the latent variablesdescribing economic costs and the parameters of the predictivemodel are simultaneously estimated via MCMC sampling. Thus,the model presented here makes contributions on both the algorith-mic and societal levels, in two ways: 1) providing a new examplein which Bayesian modeling may be able to address problems ofinfra-marginality in complex decision-making systems 2) adding toexisting evidence within the conversation regarding group-basedbiases within the United States judicial system.
In order to mitigate the infra-marginality effect, we take a similarapproach as Simoiu et al. [34] in creating a generative model thatcompares the probability distributions of different groups, and findsoutcomes which are dependent on both the probability distribu-tions and a latent variable that describes the underlying beliefs foreach magistrate. Here, we assume a simple process bail assignment.We base this analysis on two major assumptions for the behaviorof judges: 1) That cash bail should be a means of decreasing thelikelihood that a defendant will fail to appear for a court appearance2) Judges act rationally, using cash bail to minimize the balance incosts between assigning cash bail and defendants missing a courtdate. In other words, we disregard the possibility that cash bail isused in a punitive manner by any judge, and assuming that judgesassign cash bail in order to minimize some (abstract) cost. Whilethese assumptions may not always be satisfied in practice [1], weare effectively assuming the commonly understood purpose of bail,that bail is simply meant to ensure defendants will appear for trialand all pretrial hearings for which they must be present [9] andthat (as per law) judges apply the least restrictive conditions thatwill reasonable ensure a defendant’s attendance at future courtproceedings and enhance public safety [8].Our model then follows the rationale that whenever a case comesbefore the presiding authority, all available information, 𝑥 ∈ R 𝑑 ,such as severity of the charged crime and number of prior crimes,dictates the probability of this defendant not appearing on theirtrial date. We model this probability of failing to appear as a logistic Bayesian Model of Cash Bail Decisions FAccT ’21, March 3–10, 2021, Virtual Event, Canada model with a Normal prior on the weights, 𝜃 fta ∼ N ( , 𝐼 ) . (5)To model the effect of cash bail on FTA rates, we introduce anadditional coefficient with prior 𝜃 𝑏 ∼ N + ( 𝜎 𝑏 ) , where N + is thehalf-normal distribution (making the reasonable assumption thatadding cash bail should not increase the probability of failing toappear for a court date). Thus, the probability of missing a courtdate is given as, Pr [ fta | 𝑏 ] = 𝜎 ( 𝜃 𝑇 fta 𝑥 − 𝜃 𝑏 𝑏 + 𝜃 ) , (6)where 𝜎 is the sigmoid function, 𝑏 is the indicator for whether ornot cash bail was assigned and 𝜃 ∼ N ( , ) is a bias term, againwith a Normal prior.Secondly, we consider the case where the presiding authoritymay be assigning the bail amount in excess of what the defendantis able to reasonably pay. We model the probability of a defendant’srelease for any type of bail by a second logistic model with a Normalprior 𝜃 release ∼ N ( , 𝐼 ) (7)and the probability of being released pretrial given by Pr [ release | 𝑏 ] = 𝜎 ( 𝜃 𝑇 release 𝑥 − 𝜃 𝑏 𝑏 + 𝜃 ) , (8)where, 𝜎 is the sigmoid, 𝜃 𝑏 ∼ N + ( 𝜎 𝑏 ) , and 𝜃 ∼ N ( , ) is biasterm.After estimating these probabilities, each magistrate determineswhether to set cash bail based on a tradeoff between the probabilityof the defendant appearing if released pretrial with/without cashbail, and the probability of them being able to post their bail if cashbail is assigned. Each magistrate has a measure of societal harminduced by a defendant not coming to their trial. We represent thiscost of not appearing, as the latent variable 𝜏 ∼ N + ( 𝜎 ) .Should the presiding authority believe that cash bail is an appro-priate assignment for a defendant, they legally must still ensure thatthe bail amount is reasonable. While reasonable may mean differentthings to different magistrates, we represent the cost of the defen-dant facing pretrial incarceration (i.e., having cash bail imposedand being unable to pay) via the latent variable 𝜏 ∼ N + ( 𝜎 ) . In the model here, these underlying beliefs, 𝜏 , 𝜏 , determine whethercash bail is an effective tool for bringing a specific defendant totheir trial date. If a defendant is likely to not appear for a courtappearance, regardless of the type of bail set, instead of setting cashbail, a magistrate will opt to deny bail to the defendant. However, ifcash bail acts as a deterrent for a missed court appearance and thedefendant can afford it, then the magistrate will instead choose toset cash bail. Alternatively, if the defendant cannot afford bail, andthey are still unlikely to miss their court date under non-monetaryrelease, the magistrate will choose not to use cash bail.We represent this dilemma as choosing the option that minimizesthe cost of setting cash bail, 𝜏 Pr [ fta | cash bail = ] + 𝜏 ( − Pr [ post | cash bail = ]) (9)or the cost of not using cash bail, 𝜏 Pr [ fta | cash bail = ] + 𝜏 ( − Pr [ post | cash bail = ]) (10) 𝑓 𝑡𝑎 𝜇𝑥𝑏 𝜎 𝑏 𝜃 𝑟 𝜃𝜃 𝑏 𝜆 𝜎 𝑟 𝜎𝐼𝜏 𝑟 𝜇 𝑟 Race
Magistrate
Person
Figure 2: Generative model describing how magistrates setcash bail and how these decisions influence probabilities offailing to appear. Not pictured here is the analogous modelfor individual probabilities of pretrial release; both genera-tive models use the same 𝜏 𝑟 parameter from the magistrateplate. (Note if cash bail is not used, then the defendant posts bail with prob-ability 1). For convenience in notation, let 𝑝 𝑏 [ 𝑌 ] = Pr [ 𝑌 | cash bail = 𝑏 ] . In this model cash bail is assigned if, 𝜏 𝑝 [ fta ] + 𝜏 ( − 𝑝 [ release ]) ≤ 𝜏 𝑝 [ fta ] (11)Rather than estimating both 𝜏 , 𝜏 , we simplify this equation tohave a single latent variable, 𝜏 = 𝜏 𝜏 , 𝜏 ∼ 𝐶 + ( , ) , where 𝐶 + is theHalf-Cauchy distribution. This distribution is chosen by consideringthe case where 𝜏 , 𝜏 are both Half-Normal random variables withthe same variance. The ratio distribution, 𝜏 𝜏 is itself a randomHalf-Cauchy variable with location 0 and scale 1.Simplifying equation (11), cash bail is set if, 𝜏 ( 𝑝 [ fta ] − 𝑝 [ fta ]) − ( − 𝑝 [ release ]) ≥ . (12)We would like to enforce this constraint by modeling the observedcash bail as a Bernoulli random variable, with probability,ˆ 𝑝 ( cash bail ) = 𝜎 (cid:16) 𝜏 ( 𝑝 [ fta ] − 𝑝 [ fta ]) − ( − 𝑝 [ release ]) (cid:17) , (13)where 𝜎 is the inverse logit function. In doing so, we capture thenotion that as the cost of setting cash bail increases, the probabilityof setting cash bail falls.While ideally it captures our constraint, in its current form, theinverse logit alone cannot model the probability of bail decisionsdue to the bias being governed by ( − 𝑝 [ cash bail ] . This bias islimited to the range [ , ] , which in turn would cause the outputprobabilities to range from [ + 𝑒 , ] , instead of [ , ] . In order toaddress this, we rescale the sigmoid outputs in order to force theprobability of assigning cash bail back into the [ , ] range. Themarginal probability of being assigned cash bail is just given by, 𝑝 ( cashbail ) = ˆ 𝑝 ( cashbail ) − + 𝑒 − + 𝑒 (14)Our final hierarchical Bayesian model is shown in Figure 2. AccT ’21, March 3–10, 2021, Virtual Event, Canada 1 and 1
Figure 3: A histogram and the fitted normal distribution oflog bail amounts for defendants accused of felony drug of-fenses and who saw any of the five most common magis-trates in our dataset. The variance of the bail assignmentsin these cases is too wide for meaningful inference, so wedo not include it in our analysis. The stochasticity of a mag-istrate’s assigned cash bail amounts may be instructive in itsown right as a metric for understanding judicial treatment.
Finally, it is worth noting that while the set cash bail amount isavailable in our data, we do not include it in this model. In order toestimate the cost of setting/not setting cash bail, we need counter-factual information on bail assignments. The probability of failingto appear for a court appearance is designed so that the counterfac-tual cash bail assignment is easily computable, however, due to theinherent stochasticity of the bail amounts that judges choose, wefound that a counterfactual assignment of cash bail will not providea reasonable estimate of what a defendant’s bail amount would behad the judge set cash/non-monetary bail.If we consider the defendants who were assigned cash bail by oneof the magistrates in our dataset and accused of similar crimes/crimeseverity, after normalizing their feature vectors and selecting a sub-set of these defendants whose euclidean distance is less than 0 . Our dataset of cash bail decisions makes use of the publicly avail-able Unified Judicial System of Pennsylvania’s Web Portal, whichrecords all court dockets for cases in the state of Pennsylvania. Thewebsite provides a pdf for each docket and pdf summary file foreach defendant’s criminal history. The Pennsylvania judiciary alsoincludes a separate API, in which users can retrieve json formattedfiles of case information. We use text-extraction tools in order toretrieve an individual’s history from the summary pdf and combinethis with the json docket information.We performed this process on 33 ,
566 records from the Court ofCommon Pleas in Philadelphia, 66 ,
982 from the court of CommonPleas in Allegheny county, with a total set of 89 ,
751 cases fromJanuary 1, 2016 to December 31, 2019 over these two counties.From each docket-summary pair, we extract a feature vector foreach case that consists of:(1)
Magistrate
Categorical identifier for which magistrate setthe defendant’s bail.(2)
Race : Binary variable, White/Black.(3)
Sex : Binary variable, Male/Female.(4)
Age : Defendant’s age when the case was filed(5)
Lead Offense Type : Categorical identifier of the defen-dant’s lead offense (eg. First/Second/Third Degree Felony orMisdemeanor).(6)
Lead Offense Description : Categorical identifier for thelead offense based on the lead offense’s statute number: Of-fenses against Public Administration, Offenses against Prop-erty, Offenses Involving Danger to the Person, Drug Offenses,Inchoate Crimes, Vehicle Offenses, Driving after ImbibingAlcohol or Utilizing Drugs, Miscellaneous Offenses(7)
Number of charges : Number of charges brought againstthe defendant in the current case(8)
Attorney Type : Categorical variable, Public Defense Attor-ney, Private Defense Attorney, Attorney Waived.(9)
Number of Prior Felonies : Categorical variable of priorfelony convictions; zero prior convictions, one to two priorconvictions, three to five prior convictions, six to nine priorconvictions, ten or more convictions.(10)
Number of Prior Misdemeanors : Categorical variable ofprior misdemeanors; zero prior convictions, one to two priorconvictions, three to five prior convictions, six to nine priorconvictions, ten or more convictions.(11)
Bail Status : Categorical variable of the status of the defen-dant’s bail; Bail Set, Bail Posted, Bail Forfeited, Bail Revoked.Anyone who has not had their bail status changed from "BailSet" is treated as being detained pretrial. Individuals whosestatus is, "Bail Posted", "Bail Forfeited", and "Bail Revoked"are all treated as having posted bail and been released pre-trial.(12)
Bail Type : Categorical variable of the defendant’s bail type;Monetary Bail, Unsecured Bail, Non-monetary Bail, NominalBail. We only consider the bail set at an initial hearing andnot subsequent changes to bail types and amounts(13)
Fail to Appear : Binary variable describing whether or notthe defendant did not appear on their court date. Bayesian Model of Cash Bail Decisions FAccT ’21, March 3–10, 2021, Virtual Event, Canada (14)
Census Based Confounders : Each docket contains the de-fendant’s zip code or city of residence. We try to minimizeconfounders such as socioeconomic status or education levelby including the following for each defendant based on theUS Census 2018 American Community Survey 5-Year censusestimate for their zip code of residence: • Median Income • High School Graduation Rate • College Graduation Rate • Poverty Rate • Employment Rate • Median Age
Signed in 2018, Pennsylvania has implemented the first-of-its-kind“Clean Slate” law, which begun to seal millions of criminal records inan effort to allow Pennsylvania residents who have not been foundguilty of serious crimes (eg. violence, sexual assault, homicide, etc.)to more easily continue with their lives. This law seals records sothat they do not show up in employer background searches norin Pennsylvania’s online docket database. It allows persons whosecases have been sealed to act as if their offense had never occurred.As a result of this law, we base our analysis on cases stemmingfrom the Court of Common Pleas, rather than Municipal Courts,as the Court of Common Pleas sees more serious crimes and hasfewer cases which are not sealed under the “Clean Slate” law. Thisallows a more consistent measurement among court decisions andwill hopefully minimize the effects of covariate shift from before toafter the "Clean Slate" law.
Again, the data used in this analysis consists of court filings fromAllegheny County, Pennsylvania and Philadelphia County, Penn-sylvania from 2016 to 2019 in the Court of Common Pleas andMagisterial District Courts. The Court of Common Pleas hears ma-jor civil and criminal cases, as opposed to the Municipal Courts.After removing cases with either missing or ignored features, ourdataset’s descriptive statistics are given below.Descriptive StatisticsAllegheny PhiladelphiaN 35345 20072Black 0 .
412 0 . .
587 0 . .
738 0 . .
262 0 . .
509 0 . .
361 0 . .
128 0 . .
323 0 . .
603 0 . .
338 0 . .
562 0 . .
047 0 . .
003 0 . In the dataset used here, the number of cases in which defendantsmiss their court dates (0 . − . . .
179 (Philadelphia andMiami Dade County; Released pretrial) [14], 0 .
121 (Philadelphia andMiami Dade County; Detained pretrial) [14], 0 .
17 (Philadelphia only;eligible under Philadelphia DA’s No-Cash-Bail policy) [28], 0 . , , .
043 [23]. From our review, there is no clear andconsistent notice that a defendant did not appear at their court datewithin the publicly available dockets. We flag a defendant as havingfailed to appear at their court date if one of two cases is satisfiedwithin the docket: 1) if the related docket both lists their bail ashaving been revoked/forfeited and the reason for being revokedexplicitly lists that either the defendant did not appear or that abench warrant was put out 2) if a bench warrant was authorizedand if the comments within the case registry entry explictly statesthat the defendant did not appear.Failure to appear rates are only a single aspect of pretrial fail-ure. Defendants may fail their pretrial release conditions by beingarrested for a new crime while waiting for their trials. Again, thedockets do not provide a clear and consistent notice that an individ-ual was arrested while awaiting trial. While the court summariesdo provide a view of all arrests for an individual, in many cases, thesame incident was recorded multiple times, and it may also be pos-sible that an individual was arrested in other jurisdictions, althoughthis case is likely an uncommon occurrence over all cases. Withoutthe ability to cross-reference our dataset with prison records, we areunable to confidently determine if an individual was arrested againpretrial. As a result, we focus on a more limited view of pretrialfailure by only considering whether individuals missed their courtdate.
There were several other features that we would have liked to in-clude, yet ultimately decided to remove from our dataset. In futurebail analyses, it may be worth considering how some of these fea-tures play into the cost model. Such features include a) whetheror not a defendant had violated their probation when they werearrested; and b) the time since a defendant’s most recent arrest.For the former, the dockets are unclear on whether probation wasviolated when the defendant was arrested. Some cases referencea violation of probation hearing, yet we are not confident that theoccurrence of this hearing should be the sole indicator of whethera defendant was in violation of their probation. Concerning thelatter, we are unable to retrieve prison data for each defendant, sothere are likely cases where arrest dates would not differentiatebetween someone who was released 20 years ago and only recentlyrearrested, and someone who was imprisoned for 20 years and im-mediately rearrested. While both of these are highly consequentialin determining bail, including this information would at best giveus an extremely noisy estimate of the true features. AccT ’21, March 3–10, 2021, Virtual Event, Canada 1 and 1
The data used in this analysis has been released under the followinggithub repository: https://github.com/jnwilliams/padockets .In releasing the full data, we have consulted with members of thePennsylvania ACLU on the necessary protections for the individu-als represented within. Following their recommendations, we haveanonymized the data by a) removing any reference to the referreddocket identifiers; b) replacing magistrate names with a numericalidentifier; c) replacing exact docket filing/arrest dates with onlythe month and year; d) removing specific ages of defendants andinstead providing an age range over 5 years, beginning from 18years of age; e) replacing the median income for the defendant’s zipcode with an income range of $5,000; f) replacing the statistics foran individuals zip code (ie. high school and college graduation rate,poverty rate, unemployment rate) with a range of 5% (eg. povertyrate of 7% is presented as 5-10%).We feel that releasing the full dataset may be beneficial for futureanalyses, however in making this data public, our goal was to makeretrieving information for any particular case within this datasetno easier to obtain here, than by searching through the UnifiedJudicial System of Pennsylvania’s online portal.
We estimate the posterior of our random variables using PyMC4 Pre-Release, a probabilistic modeling language built on top of Tensor-Flow Probability [5]. PyMC4 uses the No-U-Turn sampler (NUTS),a variant of Hamiltonian Monte Carlo in order to sample from theposterior.
In high-dimensional spaces, commonly used techniques for sam-pling from the posterior distribution, such as the Metropolis-HastingsAlgorithm or Gibbs Sampling, are susceptible to getting stuck inpathological regions of high curvature. In these spaces, the volumeof the neighborhood around the mode of a distribution vanishes asthe dimensionality increases, while the neighborhood away fromthe mode has an increasingly large volume, yet vanishing proba-bilities. As a result, both of these neighborhoods have a negligibleeffect on the expectation. In such high-dimensional spaces, explo-ration of the typical set can lead to the discovery of small regionsof high curvature. As Monte Carlo Integration recovers a distri-bution’s expectation asymptotically, sampling procedures tend tocompensate for being unable to explore such pathological regionsby spending large amounts of time exploring them when they getthe opportunity. This long period of exploration causes MCMC tofail, as the sampled mean approaches the expectation within thisregion of high curvature rather than the expectation of the fulldistribution.Hamiltonian Monte Carlo Sampling avoids this issue via a moreeffective sampling procedure that numerically integrates alongthe gradient of the log-posterior in order to oscillate around thetypical set, rather than perform a random walk. See [11], for afull introduction to Hamiltonian Monte Carlo sampling. Followingstandard practice, our sampling procedure consists of 2 phases, aburn-in phase, in which we sample from a random starting pointuntil the posterior samples move toward the typical set. After this
Figure 4: Comparison of computed 𝜏 values compared to thebail assignment rate for the most common magistrates.(Top Left) 𝜏 𝐵𝑙𝑎𝑐𝑘 vs 𝜏 𝑊 ℎ𝑖𝑡𝑒 for each magistrate. (Top Right)Proportion of Black defendants assigned cash bail vs propor-tion of White defendants assigned cash bail for each mag-istrate. (Middle Left) 𝜏 𝑀𝑎𝑙𝑒 vs 𝜏 𝐹𝑒𝑚𝑎𝑙𝑒 for each magistrate.(Middle Right) Proportion of Male defendants assigned cashbail vs proportion of Female defendants assigned cash bailfor each magistrate. (Bottom Left) 𝜏 𝐹𝑒𝑙𝑜𝑛𝑦 vs 𝜏 𝑀𝑖𝑠𝑑𝑒𝑚𝑒𝑎𝑛𝑜𝑟 foreach magistrate. (Bottom Right) Proportion of Felony defen-dants assigned cash bail vs proportion of Misdemeanor de-fendants assigned cash bail for each magistrate. pre-set number of burn-in steps, the final posterior sampling processbegins so as to give us our final parameters. In order to ensure thatthe posterior is not multimodal, it is common to perform this processover multiple Markov chains. In this study, we found that 5 chains,500 burn in steps and 1 ,
500 sampling steps were sufficient for allchains to converge.
Based on the average estimated 𝜏 produced when estimating theparameters of our model, Figure 4 shows that nearly every magis-trate has a striking difference in the costs of missing a court datefor Black defendants as opposed to White defendants. Recall that Bayesian Model of Cash Bail Decisions FAccT ’21, March 3–10, 2021, Virtual Event, Canada
Figure 5: Difference in 𝜏 among seasons our model defines 𝜏 as the ratio of the cost of missing a court dateto the cost of being unable to post cash bail, so a greater 𝜏 impliesthat a judge is more willing to assign cash bail to a group in a waythat minimizes the risk of missing their court date, regardless of anindividual’s ability to post bail. While a few magistrates have 𝜏 lessthen 1 for white defendants (implying that they want to make surethat these defendants are released pretrial) no magistrate has 𝜏 lessthan 1 for black defendants. Most magistrates place an outstand-ingly high emphasis on a defendant missing their court date for alldefendants, but this trend is exacerbated based on racial differences,which is in line with the higher rate at which these magistratesassign cash bail to Black defendants.Over these magistrates, the cash bail assignment rate sits at anaverage 75% decrease in the likelihood of being assigned cash bailwhen comparing their treatment of black defendants as opposed towhite defendants. While such an change is indicative of a directionof bias, the results based on 𝜏 give a more actionable response tothis behavior. The majority of judges have high 𝜏 values for Blackdefendants, with the median value being 19 .
51, whereas Whitedefendants have a median 𝜏 .
82. In this case, it is much moreclear that the action for improving pretrial release rates requiresaddressing magistrate bail assignments or assigned bail amountsfor Black defendants.Similarly when comparing 𝜏 for men and women, we see a simi-lar trend in which most judges assign cash bail with less regard formale defendant’s ability to pay. In this case, there may be confound-ing reasons why a magistrate may be more willing to ensure thatwomen are able to be released pretrial, such as child care. We see asimilar trend in the greater proportion in which male defendantsare assigned cash bail, however, as in the case or racial differences,we are able to better pinpoint the specific judges who place lowercost on some individuals being unable to pay their bail than others.This again can be a more targeted mechanism for addressing thethe cash bail assignment habits of the magistrates.We also consider two additional settings in which we want todetermine the disparate treatment of those defendants accused offelonies compared misdemeanors and the treatment of defendantswith respect to the season (ie. Spring, Summer, Fall, Winter). Both Figure 6: Average difference of the bail assignment rate viathe posterior draws compared to the true bail assignmentrate with respect to each subgroup. of these act as validation for the simple model here. As conven-tional wisdom would suggest that those defendants accused offelonies are significantly more likely to be assigned cash bail thandefendants accused of misdemeanors, and that the treatment of de-fendants should remain relatively constant regardless of the season,we expect that this analysis would show similar effects.For those defendants accused of felonies, magistrates are muchmore concerned with ensuring that these defendants appear at theirtrial date, hence they are significantly more likely to assign cashbail. Many magistrates assign cash bail so as to ensure that thosewho are accused of misdemeanors are able to be released pretrial.However, still we show that there are some who are relativelyunconcerned with defendants being able to post bail, regardless ofoffense severity.Figure 5 provides the comparison of 𝜏 based on seasons, whereSpring groups together all cases between March to May of any year,Summer groups together all cases between June to August, Falltakes place from September to November, and Winter is Decemberto January. In this additional validation step, comparisons over 𝜏 should not be susceptible to groupings in which we expect cashbail assignments to be invariant, such as seasonal differences. Here,we see this effect; there is little difference in 𝜏 among each season.Our model is able to capture conventional wisdom on how cashbail assignments are done regarding offense severity and groupingsin which these cash bail assignments should be invariant. As a final robustness step of our model, we perform posterior predic-tive checks on our observed variables. Such checks use the sampledjoint posterior distribution to generate new outcome variables forevery case, telling us, under our posterior, whether or not a specificdefendant will be assigned cash bail. We present these results in Fig-ure 6. Our model shows that among the groups (gender, race, offenseseverity),we are able to match the expected cash bail assignmentrates of each magistrate, giving credence that the approximated 𝜏 is able to act as a descriptor of magistrate behavior. AccT ’21, March 3–10, 2021, Virtual Event, Canada 1 and 1
We do see a significant drop-off in accuracy for magistrateswho assign cash bail in less than 20% of cases. This is likely dueto a limitation in our model. Based on the cost model shown inequation (12), the co-domain of the difference in magisterial cost ofassigning cash bail is limited to the range [− , inf ) . The re-scalingdone in equation (14) is able to successfully make this a probabilitydistribution, however, we still have significantly less flexibility incases in which magistrates are unlikely to assign cash bail. Thislikely results in our model being unable to create a strong descriptoramong these magistrates.While our model’s efficacy drops off for magistrates who havelow rates of cash bail assignment, in most circumstances, it is un-likely that magistrates who assign cash bail in less than 20% of casesare abusing the cash bail system to the extent that magistrates withhigher cash bail assignment rate may. As such, this model maybe useful to understand the behavior of problematic magistrates,whereas other methods may be beneficial for less problematic mag-istrates. In this paper we have revisited the infra-marginality problem forcash bail assignments in pretrial decisions. There has been a signifi-cant amount of work in understanding why judges assign cash bailat disparate rates among groups, and when such analyses comparethe rate of observable outcomes such as bail assignment, recidi-vism, or pretrial failure, these outcomes may in turn be influencedby the unobserved features that cause an incomplete view of thesystem. Much work attempts to mitigate these effects by includ-ing measures of judge leniency in analyses on the influence cashbail decisions, however, these measures may also be influenced byexogenous variables.We address this problem via Bayesian modeling, so as to focuson understanding how well judge decision making matches boththe believed purposes and the legal requirements for setting cashbail. This method may be useful in providing a more nuanced viewof why judges assign cash bail to certain groups at a higher ratethan others. In this work, we show not only that in the Court ofCommon Pleas, magistrates universally assign a lower cost to Blackdefendants being unable to be released pretrial as opposed to Whitedefendants, but that these estimated costs are able to avoid the infra-marginality problem. Hence, these costs are more representative ofreal world effects. By presenting this view in which we can directlyinfer how judges value an individuals ability to pay cash bail, we canbetter address disparities in the cash bail system, and more closelytarget the exact mechanisms by which these disparate treatmentsoccur.While the results presented here suggest specific values for theunderlying beliefs for each magistrate, due to the limitations here,it would be beneficial to repeat this analysis with a dataset thatincludes more information on pretrial failure, such as arrests forother crimes while released pretrial. This is especially important,because pretrial release decisions are based on more than missing acourt date alone. For example, by replacing Pr [ fta | cash bail ] with Pr [ pretrial failure | cash bail ] alone may provide a fuller view ofmagistrate decision-making than we present here. Despite this,we believe that the results presented here are an important study that should be built on further, and that an additional method foraddressing the problem of infra-marginality in cash bail decisionsis a useful contribution for the broader algorithmic community. ACKNOWLEDGEMENTS
We thank Jessica Li and Nyssa Taylor from the American CivilLiberties Union of Pennsylvania for useful discussions regarding ourdata collection efforts and in helping us gain a better understandingof the cash bail system.
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