Abstract
Objectives
It is well established that defendants who plead guilty receive reduced sentences compared to the likely outcome if convicted at trial. Prominent theories of plea bargaining posit that the plea discount is determined by the strength of the evidence against the defendant. Research on this claim has produced mixed findings, however, and others have suggested that discounts may be influenced by extra-legal characteristics such as race, age, and sex. To date, there have been few attempts to directly compare the effects of these factors on plea discount estimates.
Methods
This study uses a penalized ridge regression to predict counterfactual trial sentences for a sample of defendants who pled guilty. Plea discounts are estimated using each defendant’s predicted trial sentence and observed plea sentence. Discount estimates are then regressed on variables related to case evidence and the demographic characteristics of the defendant.
Results
Results suggest that increases in the amount of evidence associated with a case lead to decreases in the size of the plea discount. Both main and interaction effects are observed for race/ethnicity and sex, with Hispanic and male defendants receiving significantly smaller discounts than White or female defendants. Calculation of standardized effect sizes further indicates that demographic characteristics exert larger effects on plea discount estimates than evidentiary variables.
Conclusions
Plea discounts appear to be influenced by both evidence and extra-legal factors. Legal participants may indeed consider the strength of the evidence when determining acceptable plea discounts, but this alone appears to be an insufficient explanation.
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Notes
While Ulmer et al. (2010) do not directly report this estimate, they do report a grand mean sentence of 62 months and suggest that the trial penalty would be approximately 28 months. This would correspond to a trial sentence of roughly 90 months and a plea discount of 31%. This discount decreased when Ulmer et al. controlled for various forms of guideline departures, though it remained statistically significant.
LaFree (1985) and Elder (1989) examined the impact of evidence on plea sentences but not plea discounts. While LaFree (1985) found physical evidence and number of witnesses to significantly increase plea sentences, confession evidence had no effect across all model specifications. Additionally, Elder (1989) found no significant effect of physical evidence, identification evidence, or confession evidence on plea sentence length. However, neither study directly examined the relationship between evidence and plea discounts.
It is also important to note that individual pieces of evidence can be of varying strength. For example, not all eyewitness evidence is equally strong; one witness may be a person with poor eyesight who witnessed the crime 100 yards away at night, whereas another witness may previously know the defendant and witnessed the crime up close and personal. To our knowledge, such indicators of the reliability of evidence are not available in archival datasets.
This two-year timeframe was chosen to match the data collection period for our target data set described below.
These data are available to download in bulk from https://virginiacourtdata.org/.
Two jurisdictions in Virginia do not make their case processing data publicly available. However, our data still represents over 98% of all jurisdictions in the state.
We acknowledge that this is an imperfect solution and that it is also possible for the severity and number of charges to be increased or decreased prior to trial. Given the parameters of our data, this approach provided the best adjustment for charge bargaining and is consistent with prior efforts of this kind (see Yan & Bushway 2018).
Only 214 (4%) of cases were censored at 600 across the full trial conviction sample. However, it is important to note here that we only included cases where a carceral sentence was imposed. While this approach improves the distribution of the outcome variable, it can create concerns regarding selection bias for any inferences aimed at the broader population of defendants (Bushway and Piehl, 2007; Elder 1989; Winship and Mare 1992). However, likely because we aggregated sentence lengths across all charges within a case, all cases in our trial conviction sample received some length of incarceration. Additionally, only 11% (n = 68) of eligible plea cases did not receive a carceral sentence. Thus, our estimation of trial sentences should not suffer from selection bias, though we note that our plea discount results are limited to defendants who pled guilty and received some term of incarceration.
More specifically, these factors would be explicitly modeled in both the dependent and independent variables, which may lead to correlations that are an “artifact of the model” (Bushway & Redlich 2012, p. 449). Because evidence and demographic factors are inherently included in the plea sentence but not in the trial sentence prediction, variation in the difference between these values may be attributed to these variables.
The inclusion of both a maximum potential sentence across all charges and a minimum potential sentence across all charges led to VIF values that were greater than 10 for these factors. To test the importance of including both variables, we ran an OLS regression including only the maximum potential sentence and its squared term and then added the minimum potential sentence and its squared term to the model. Results of an F-test indicated that the addition of these variables significantly improved model fit (F(2, 5635) = 365.02, p < 0.001).
We chose to use a ridge regression over similar methods such as the LASSO regression because, while the ridge regression shrinks parameters toward 0, it will never fully eliminate any coefficients from the model. In contrast, the penalty parameter in a LASSO regression is free to shrink coefficients to 0 and eliminate them from the model (Tibshirani 1996). While LASSO regressions may lead to more parsimonious models, we did not want any of our coefficients eliminated from the model, given that each variable has a theoretical connection to sentencing outcomes.
To do this we used the “glmnet.cv” function in the glmnet package (Hastie et al. 2016) in R statistical software. This function automatically generates a \(\lambda\) sequence between the minimum and maximum \(\lambda\) values.
For example, an OLS regression estimated using the non-logged dependent variable produced an R2 of 0.66 while the same model estimated with the logged dependent variable produced an R2 of 0.51. In this regard, it is important to reiterate that our dependent variable did not contain any 0 s and was top-coded, which reduced skew. Additionally, by including all charges associated with a case in cumulative fashion, our dependent variable may have better resembled an additive process.
Note that we also tested the number of pieces of evidence as a categorical variable using 0 pieces of evidence as the reference category. Results support the idea that this relationship resembled a linear one. Here, one piece of evidence decreased plea discounts by 28% (p = 0.05), two pieces of evidence decreased plea discounts by 29% (p = 0.04), three pieces of evidence decreased plea discounts by 42% (p < 0.01), and four pieces of evidence decreased plea discounts by 62% (p = 0.02), controlling for the presence of video/photo/audio evidence. However, operationalizing this measure as a categorical variable did not significantly improve model fit (F(2, 477) = 1.71, p = 0.18).
We had a limited sample with which to examine age. For example, 75% of White defendants, 75% of Black defendants, and 81% of Hispanic defendants were between the age of 18–39. Few defendants were in age groups where significantly decreasing punishment might be expected. Thus, our comparisons are predominately between young males in each racial category.
Note that only 12 Hispanic female defendants are represented in this sample, however.
The effect size for the number of pieces of evidence here represents a linear effect. If this effect size is calculated comparing defendants with four pieces of evidence to those with none, it becomes the largest effect (r = −.60, 95% CI [ −0.95, −0.26]). However, there are very few defendants with either zero or four pieces of evidence. A more realistic comparison of defendants with three pieces of evidence to those with one suggests an effect size of r = −0.15, 95% CI [ −0.27, −0.02], which remains smaller than both the interaction effect for being Hispanic and male, as well as the main effect for Hispanic alone.
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Acknowledgements
This research was in part supported by the National Science Foundation and the National Institute of Justice. We are particularly grateful to Shawn Bushway, Jodi Quas, Amy Dezember, Skye Woestehoff, Megan Stoltz, and Melissa Manley. We also are indebted to the county court for their cooperation.
Funding
This work was partially supported by the National Science Foundation (Grant #1603944) and the National Institute of Justice.
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Petersen, K., Redlich, A.D. & Wilson, D.B. Where is the Evidence? Comparing the Effects of Evidence Strength and Demographic Characteristics on Plea Discounts. J Quant Criminol 39, 919–949 (2023). https://doi.org/10.1007/s10940-022-09555-8
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DOI: https://doi.org/10.1007/s10940-022-09555-8