What Exactly Is the Bargain? The Sensitivity of Plea Discount Estimates

Abstract

Defendants who plead guilty receive less harsh sentences than those convicted at trial. Theories suggest that the magnitude of the plea discount reflects local courtroom norms, and also guides the behavior of defendants. The testing of theories on plea bargaining relies on credible estimates of the size of the plea discount. This study found that plea discount estimates were sensitive to the dependent variable used. The data used included the full sample of felony defendants in New York State who pled guilty, in which nearly half were not incarcerated. When a severity score that encompassed the severity of probation was used instead of the length of incarceration, the plea discount estimate decreased by 26 percentage points for the full sample. This pattern was found in all subsamples as well.

Keywords:

• Plea bargaining
• severity scale
• alternative sanctions
• counterfactual

Acknowledgements

I thank Shawn Bushway, Hank Fradella, Cassia Spohn, Gary Sweeten, and the three anonymous reviewers for their comments. I also thank Jason Walker for the copyediting.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 For simplicity, the term “alternative sanctions” refers to non-incarceration sentences throughout the paper. As presented later in the paper, the use of this term does not necessarily designate incarceration as the default sentencing option.

2 For a thorough review and test of the shadow model, see Bushway, Redlich, and Norris (2014). This study has no intention to validate the theory, but only utilizes the framework to depict why large plea discounts are problematic. For details on challenges to the shadow model, see Bibas (2004), Redlich, Bibas, et al. (2017), and Yan and Bushway (2018).

3 There was no special coding for life sentences without parole since only 1% among those sentenced to life sentences (and less than 0.05% of the total sample) had the “without parole” clause.

4 The data-granting agency, DCJS, advised that the coding of probation lengths in the CCH dataset was more reliable and accurate than some other types of alternative sanctions.

5 Logging both sides of Equation (3) gets $\mathit{lnS}=\mathit{\text{lnα}}+\mathrm{\beta }\mathit{lnQ}.$

6 Specifically, Abrams (2011) adopted an instrumental variable approach. He used the judges’ length of tenure as an instrument to estimate the effect of pleading on sentence length. While the method had its merits, it was also built on strong assumptions, and the instrument was relatively weak (p. 217). Another possible way to measure some of the unobserved variables (such as cognitive traits and risk preference) is through experimental design. A group of studies explored the role of psychological factors in guilty pleas (e.g. Dervan & Edkins, 2013; Redlich & Shteynberg, 2016; Tor, Gazal-Ayal, & Garcia, 2010). Yet the focus was mostly on the decision to plead guilty rather than the size of plea discounts. These studies also have known external validity issues.

7 Although both scales by Leclerc and Tremblay and Pina-Sánchez were more recent, they were developed outside of the United States (one in England and Wales and the other in Canada). Although Wodahl et al.’s scale was developed in the United States, it did not contain the exchange rates between prison and other types of sentences.

8 Specifically, when I developed May and Wood’s point estimates into scales following the procedure described above, the severity of long probation terms (3 years or longer) well exceeded the severity of prison terms of the same length. This issue is likely to be due to the parametric assumption in Equation (3). To the contrary, as shown in Table 1, the severity scores generated from Spelman’s study were more reasonable. In either case, I have no intention to challenge the measures of the original studies, since neither group of researchers appeared to intend to develop the point estimates into scales and to provide out-of-bound estimates.

9 Chauhan et al. (2017, p. 38) reported that for felony defendants in New York City, the median length of pretrial detention was around 10 days, and the average length was around 75 days. In the current sample, the average sentence for New York City defendants who pled was 12.44 months – nearly five times as long as the average length of pretrial detention. In the full plea sample, fewer than 5% of defendants received a term of time served.

10 The Penal Law of New York State prescribes very large range of discretion at the sentencing stage. For example, with no predicate records, a defendant convicted of a class B violent felony can be sentenced to a determinate term between 5 and 25 years in prison. A defendant convicted of a class B non-violent-non-drug felony can be sentenced to an indeterminate term with the upper bound ranging between 3 and 25 years. This stands in sheer contrast with jurisdictions that have presumptive sentencing guidelines and narrowly prescribed sentence intervals, such as the federal jurisdiction (Lynch, 2016).

11 Out of defendants who had a severity score of zero, 66.2% received conditional discharge, whereas 23.3% received time served. I was unable to model the severity of either sanction types due to the lack of comparable measures in the literature (conditional discharge) and missing information (time served, see Methodological Notes above).

12 Both estimates compare the plea sentence against the predicted counterfactual trial sentence. The common practice to estimate the individual-level plea discount is to use the predicted plea sentence (estimated from Equation 2, using the plea sentence as the dependent variable on the plea sample) rather than the actual plea sentence, as the former accounts for the systematic components in sentencing better (Johnson & Larroulet, 2019; Piehl & Bushway, 2007). The current study presents both because the estimates with the actual plea sentence better demonstrate the consequence of zero sentences (or “100% plea discounts”).

13 A negative plea discount occurs when the estimated trial sentence is positive but lower than the plea sentence, whereas a plea discount over 100% occurs when the estimated trial sentence is negative. These could either be merely random noise or bear a substantive meaning (for a theory on “the plea penalty,” see Abrams, 2011). It is also noteworthy that much fewer individuals had an unreasonable plea discount estimate when the severity score served as the dependent variable (Figure 1). Nevertheless, the present study simply leaves the values as they are since the interpretation of these unreasonable values is beyond the scope of the current study.

14 For example, for both robbery and burglary, the first degree was a class B felony, the second degree was a class C felony, and the third degree was a class D felony. For both criminal sale of a controlled substance and criminal possession of a controlled substance, the first to the fifth degree were distributed through classes A to D.

15 A key difference here is that when the researcher uses the Tobit model to conduct the counterfactual analysis, both plea and trial sentences need to be predicted values under the Tobit model (for details on the technique, see Piehl & Bushway, 2007, pp. 111–113). By definition, on a defendant sample who pled, the average predicted sentence at plea from an OLS model is equal to the observed average plea sentence. However, this is not the case for the Tobit model. Most defendants in Piehl and Bushway’s study were incarcerated, and their plea discount estimates were still reasonable despite the Tobit model shifted the distributions to the left as well (Piehl & Bushway, 2007; Tables 1 and 4). In the present study, the average plea sentences for all samples in Table 6 were all considerably lower than the corresponding actual average plea sentence because of the prevalence of the zeros.

Additional information

Notes on contributors

Shi Yan

Shi Yan is an assistant professor at the School of Criminology and Criminal Justice, Arizona State University. His research focuses on plea bargaining, sentencing, and measurement issues in crime and criminal justice research.