Skip to main content

Advertisement

Log in

Measuring Self-Reported Wrongful Convictions Among Prisoners

Journal of Quantitative Criminology Aims and scope Submit manuscript

Abstract

Objectives

Estimate the frequency of self-reported factual innocence in non-capital cases within a state population of prisoners.

Methods

We conducted a survey of a population sample of state prisoners who were asked to anonymously report their involvement in the crimes for which they were most recently convicted. To assess the validity of verifiable responses, prisoner self-report data were compared to aggregate conviction and demographic information derived from administrative records. To assess the validity of unverifiable responses, we developed a non-parametric test to estimate the probability of false innocence claims.

Results

We estimate that wrongful convictions occur in 6% of criminal convictions leading to imprisonment in an intake population of state prisoners. This estimate masks a considerable degree of conviction-specific variability ranging from a low of 2% in DUI convictions to a high of 40% in rape convictions. Implausible or false innocence claims are estimated to occur in 2% of cases.

Conclusions

The present investigation demonstrates that survey methods can provide bounded estimates of factual innocence claims within a discrete and known population. The resulting estimates, the first to formally separate claims of legal and factual innocence and to incorporate a formal measure of response plausibility, suggest that prisoners themselves are very often willing to self-report the correctness of their convictions. At the same time, a considerable minority indicate that procedural weaknesses with the administration of justice occurred in their cases. And, a distinct minority, with considerable offense variation, maintain that they are completely innocent of the charges against them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Notes

  1. Liebman et al. (1999) provides estimates of U.S. legal errors beyond factual innocence in capital cases.

  2. Assuming exonerations only occur in cases where the defendant was actually innocent (which may not be the case), prevalence estimates in this sub-literature are likely to be lower bounds on the actual rate of wrongful conviction in capital cases, since they are samples of surfaced wrongful conviction cases rather than samples of all wrongful convictions. The degree of bias in this estimator will be a function of the bias in the “surfacing” mechanism, which is a combination of post-adjudication legal effort and publicity as well as the discoverability of new information bearing on the guilt or innocence of the convicted person or his/her alternates.

  3. A parallel literature exists on measuring criminal victimization using surveys. See, generally (Biderman 1967; Biderman and Reiss 1967; Skogan 1981).

  4. A similar commitment of effort can be seen in the health literature on self-reporting on disease and treatment (U.S. National Center for Health Statistics 1965a, b, 1966, 1967; Hill and Ross 1982; Harlow and Linet 1989; Bergmann et al. 1998) as well as earnings and employment history (Borus 1966; Weiss 1968).

  5. Scholars of wrongful convictions have maintained the distinction between two forms of innocence—factual and legal. [For a non-binary typology based on the legal concept of burden of proof, see Laufer (1995).] Factual innocence, also referred to as actual innocence (Zalman et al. 2008), generally refers to the situation in which a defendant is convicted of a crime that he or she did not actually commit. In the simplest and most extreme case, the factually innocent and wrongfully convicted person was not present and completely lacking in involvement or responsibility for the crime. Cases of mistaken identity, in which the charged defendant is erroneous identified as the perpetrator despite not having been present, are a typical example of true factual innocence. However, factual innocence is not limited to cases of mistaken identity. By contrast, legal innocence, also known as procedural innocence (Findley 2010), is commonly understood to refer to the situation in which a defendant is at least partially, if not wholly, responsible for the crime of which he or she was tried and convicted, but some element of mandatory legal procedure was not properly followed during the investigation or prosecution of the case. Examples of these factually guilty and legally innocent persons include cases in which the state relied on illegally gathered evidence, access to counsel is denied, or the unbiased character of the jury is violated.

  6. In subsequent work they have expanded this approach to non-custodial populations (Sigurdsson and Gudjonsson 1996; Gudjonsson et al. 2006, 2009). In the U.S., Redlich and colleagues have also employed this methodology for understanding the predictors of false confessions (See, for example, Redlich et al. 2010).

  7. Pre-testing revealed that altering the order of the categories had little effect on the number of factual innocence claims but did redistribute other claims across similar categories. For analysis purposes, if respondents checked multiple categories, they were categorized by the highest level of responsibility they reported.

  8. While Spanish language copies of the instrument were available upon request, no effort, beyond pre-testing, was made to address other issues of respondent comprehension. This was intentional as other considered approaches to solving reading, language, or other comprehension problems would likely undermine assurances of anonymity.

  9. The DOC relies on demographic information provided by committing courts. Courts often classify groups such as Dominican individuals as Black while these individuals frequently self-identify as Hispanic on classification forms.

  10. Randomized response methods (RRM), and newer alternatives (Tan et al. 2009), rely on purposefully and transparently adding noise to each individual respondent’s data at the time of collection. Although this necessarily increases the variance of the estimator, measures of central tendency can still be recovered. However, these approaches do not actually verify that respondents are being truthful in their responses. If the respondents understand and believe these promises, it has the potential to produce more truthful responses. The trade-off, however, is increasingly complex surveys, which could theoretically lead to lower response rates or lower quality responses if respondents are confused or distrustful of the more elaborate procedures (See, for example, Berman et al. 1977; Boruch 1979). Putting aside this possible trade-off, at a more fundamental level, the confidence that researchers have in RRM or similar methods when used to measure an unverifiable quantity is only as strong as the researcher’s belief in the elimination of respondents’ remaining likelihood of misleading the researcher. As long as there remains a residual incentive to mislead, the aforementioned methods cannot guarantee an unbiased estimator. For more on randomized response methods, see generally (Warner 1965; Greenberg et al. 1971; Boruch 1972; Raghavarao and Federer 1979; Fox and Tracy 1980, 1984; Tracy and Fox 1981; Miller 1981; Tan et al. 2009; Coutts and Jann 2011).

  11. All reported confidence intervals were computed using bootstrapping (Efron and Tibshirani 1986). While incidence estimates reflect the population, and are therefore not subject to sampling error, these intervals are particularly useful when interpreting estimates conditional on covariates such as those reported in Figs. 3 and 4. For an alternative view of population statistics as samples from super-populations, see Deming and Stephan (1941) and (Thygesen and Ersbøll 2014). In addition, non-sampling error bounds were computed to account for the small degree of unit and item non-response in the survey administration. These confidence intervals were computed following Manski (2003), under the assumption that all non-respondents would have indicated each possible response with a P of 1. The resulting bounds (± 8%) were considerably larger than the bounds generated by the bootstrap. The reporting of these bounds was rejected after an examination of the correlation between response rates and population estimates by survey batch revealed a weakly positive relationship, contradicting the much stronger assumption under Manski.

  12. In many jurisdictions, including this setting for this study, crimes such as murder, manslaughter and rape may encompass a wide range of conduct linked by a common outcome (e.g., death of a victim, sexual contact without legal consent). These complex scenarios, often requiring the subjective testimony of witnesses or participants, may contribute to the increased rate for claims of partial involvement observed here. While beyond the scope of this analysis, this supposition warrants additional inquiry.

  13. Many of the rape convictions involve case circumstances quite different than those addressed by the Urban Institute study referred to earlier in this paper. In that study, stranger rape and the resulting blind search of a DNA database was the basis of their 3% prevalence estimate. The self-reported rape and sexual assault cases in the present study can be assumed to include a substantial number of non-stranger or non-disputed sexual contact cases. These involve a claim not of complete non-presence or non-involvement, which would trigger the collection and eventual analysis of DNA, but instead that the sexual contact was not criminal due to a missing legal element. While these are necessarily murkier cases than those described in the Virginia study, they are nonetheless claims of factual innocence.

  14. Similarly, these results do not address the probability or truthfulness of claims that any given individual defendant, whether within the jurisdiction in which these data were collected or beyond, has been wrongfully convicted or denied due process.

  15. Alternatively, a randomized response design could be employed for a randomly selected subset of cases, in order to establish whether this approach does in fact generate different estimates than the raw or adjusted CJES estimates (Coutts and Jann 2011; Jann et al. 2012).

References

  • Bedau HA, Radelet ML (1987) Miscarriages of justice in potentially capital cases. Stanford Law Rev 40:21–179

    Google Scholar 

  • Bergmann MM, Byers T, Freedman DS, Mokdad A (1998) Validity of self-reported diagnoses leading to hospitalization: a comparison of self-reports with hospital records in a prospective study of American adults. Am J Epidemiol 147:969–977

    Google Scholar 

  • Berman J, McCombs H, Boruch R (1977) Notes on the contamination method: two small experiments in assuring confidentiality of responses. Soc Methods Res 6:45–62

    Google Scholar 

  • Biderman AD (1967) Surveys of population samples for estimating crime incidence. Ann Am Acad Pol Soc Sci 374:16–33

    Google Scholar 

  • Biderman AD, Reiss AJ (1967) On exploring the “dark figure” of crime. Ann Am Acad Pol Soc Sci 374:1–15

    Google Scholar 

  • Blumberg AS (1967) The practice of law as confidence game: organizational cooptation of a profession. Law Soc Rev 1:15–39

    Google Scholar 

  • Borchard E (1932) Convicting the innocent; errors of criminal justice. Yale University Press, New Haven

    Google Scholar 

  • Boruch RF (1972) Relations among statistical methods for assuring confidentiality of social research data. Soc Sci Res 1:403–414

    Google Scholar 

  • Boruch RF (1979) Assuring the confidentiality of social research data. University of Pennsylvania Press, Philadelphia

    Google Scholar 

  • Borus ME (1966) Response error in survey reports of earnings information. J Am Stat Assoc 61:729–738

    Google Scholar 

  • Brandon R, Davies C (1973) Wrongful imprisonment: mistaken convictions and their consequences. Allen and Unwin, Crows Nest

    Google Scholar 

  • Carson EA (2014) Prisoners in 2013. Bureau of Justice Statistics, Washington, D.C.

    Google Scholar 

  • Cernkovich SA, Giordano PC, Pugh MD (1985) Chronic offenders: the missing cases in self-report delinquency research criminology. J Crim Law Criminol 76:705–732

    Google Scholar 

  • Chaiken JM, Chaiken MR, Peterson JE (1982) Varieties of criminal behavior. RAND Corporation, Santa Monica

    Google Scholar 

  • Coutts E, Jann B (2011) Sensitive questions in online surveys: experimental results for the randomized response technique (RRT) and the unmatched count technique (UCT). Soc Methods Res 40:169–193

    Google Scholar 

  • Deming WE, Stephan FF (1941) On the interpretation of censuses as samples. J Am Stat Assoc 36:45–49

    Google Scholar 

  • Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B Methodol 39:1–38

    Google Scholar 

  • Dwyer J (2000) Actual innocence: five days to execution and other dispatches from the wrongly convicted, 1st edn. Doubleday, New York

    Google Scholar 

  • Efron B, Tibshirani R (1986) Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Stat Sci 1:54–75

    Google Scholar 

  • Elliott DS (1995) Lies, damn lies, and arrest statistics. Center for the Study and Prevention of Violence, Boulder

    Google Scholar 

  • Erickson ML, Empey LT (1963) Court records, undetected delinquency and decision-making comments and research reports. J Crim Law Criminol Police Sci 54:456–469

    Google Scholar 

  • Farrington DP (1977) The effects of public labelling. Br J Criminol 17:112–125

    Google Scholar 

  • Findley KA (2010) Defining innocence. Albany Law Rev 74:1157–1173

    Google Scholar 

  • Fox JA, Tracy PE (1980) The randomized response approach applicability to criminal justice research and evaluation. Eval Rev 4:601–622

    Google Scholar 

  • Fox JA, Tracy PE (1984) Measuring associations with randomized response. Soc Sci Res 13:188–197

    Google Scholar 

  • Frank J (1957) Not guilty, 1st edn. Doubleday, Garden City

    Google Scholar 

  • Gardner ES (1952) The court of last resort. Doubleday, Princeton

    Google Scholar 

  • Garrett BL (2008) Judging Innocence. Columbia Law Rev 108:55–142

    Google Scholar 

  • Garrett BL (2011) Convicting the innocent. Harvard University Press, Cambridge

    Google Scholar 

  • Garrett BL (2017) End of its rope how killing the death penalty can revive criminal justice. Harvard University Press, Cambridge

    Google Scholar 

  • Gastwirth JL, Sinclair MD (1998) Diagnostic test methodology in the design and analysis of judge-jury agreement studies. Jurimetrics 39:59–78

    Google Scholar 

  • Gold M (1970) Delinquent behavior in an American city. Brooks/Cole PubCo, Belmont

    Google Scholar 

  • Gould JB, Leo RA (2010) One hundred years later: wrongful convictions after a century of research. J Crim Law Criminol 1973–100:825–868

    Google Scholar 

  • Gould JB, Carrano J, Leo RA, Hail-Jares K (2014) Predicting erroneous convictions. Iowa Law Rev 99:471–522

    Google Scholar 

  • Greenberg BG, Kuebler RR Jr, Abernathy JR, Horvitz DG (1971) Application of the randomized response technique in obtaining quantitative data. J Am Stat Assoc 66:243–250

    Google Scholar 

  • Gross SR (1998) Lost lives: miscarriages of justice in capital cases. Law Contemp Probl 61:125–152

    Google Scholar 

  • Gross SR (2013) How many false convictions are there? How many exonerations are there? In: Killias M (ed) Huff CR. Wrongful convictions and miscarriages of justice: causes and remedies in north American and European criminal justice systems, Routledge, pp 45–60

    Google Scholar 

  • Gross SR (2015) The staggering number of wrongful convictions in America. Washington Post, Washington

    Google Scholar 

  • Gross SR (2016) Exonerations in 2015. University of Michigan, Ann Arbor

    Google Scholar 

  • Gross SR, O’Brien B (2008) Frequency and predictors of false conviction: why we know so little, and new data on capital cases. J Empir Leg Stud 5:927–962

    Google Scholar 

  • Gross SR, O’Brien B, Hu C, Kennedy EH (2014) Rate of false conviction of criminal defendants who are sentenced to death. Proc Natl Acad Sci 111:7230–7235

    Google Scholar 

  • Groves RM, Lyberg L (2010) Total survey error: past, present, and future. Public Opin Q 74:849–879. https://doi.org/10.1093/poq/nfq065

    Google Scholar 

  • Gudjonsson GH, Sigurdsson JF (1994) How frequently do false confessions occur? an empirical study among prison inmates. Psychol Crime Law 1:21

    Google Scholar 

  • Gudjonsson GH, Sigurdsson JF, Asgeirsdottir BB, Sigfusdottir ID (2006) Custodial interrogation, false confession and individual differences: a national study among Icelandic youth. Pers Individ Differ 41:49–59

    Google Scholar 

  • Gudjonsson GH, Sigurdsson JF, Sigfusdottir ID (2009) Interrogation and false confessions among adolescents in seven European countries. What background and psychological variables best discriminate between false confessors and non-false confessors? Psychol Crime Law 15:711–728

    Google Scholar 

  • Hardt RH, Peterson-Hardt S (1977) On determining the quality of the delinquency self-report method. J Res Crime Delinq 14:247–259

    Google Scholar 

  • Harlow SD, Linet MS (1989) Agreement between questionnaire data and medical records the evidence for accuracy of recall. Am J Epidemiol 129:233–248

    Google Scholar 

  • Hill AP, Ross RK (1982) Reliability of recall of drug usage and other health-related information. Am J Epidemiol 116:114–122

    Google Scholar 

  • Hindelang MJ (1981) Measuring delinquency. Sage Publications, Beverly Hills

    Google Scholar 

  • Hindelang MJ, Hirschi T, Weis JG (1979) Correlates of delinquency: the illusion of discrepancy between self-report and official measures. Am Soc Rev 44:995–1014

    Google Scholar 

  • Hirschi T (1969) Causes of delinquency. University of California Press, Berkeley

    Google Scholar 

  • Hood R, Hoyle C (2015) The death penalty: a worldwide perspective. OUP Oxford, Oxford

    Google Scholar 

  • Huff CR, Rattner A, Sagarin E, MacNamara DEJ (1986) Guilty until proved innocent: wrongful conviction and public policy. Crime Delinq 32:518–544

    Google Scholar 

  • Huizinga D, Elliott DS (1986) Reassessing the reliability and validity of self-report delinquency measures. J Quant Criminol 2:293–327

    Google Scholar 

  • Jann B, Jerke J, Krumpal I (2012) Asking sensitive questions using the crosswise model an experimental survey measuring plagiarism. Public Opin Q 76:32–49

    Google Scholar 

  • Kaplowitz SA, Shlapentokh V, McGregor JP, Rabinovich L (1982) Possible falsification of survey data: an analysis of a mail survey in the soviet union. Public Opin Q 46:1–23

    Google Scholar 

  • Kirk DS (2006) Examining the divergence across self-report and official data sources on inferences about the adolescent life-course of crime. J Quant Criminol 22:107–129

    Google Scholar 

  • Krause K, Lategan (2016) Annual Statistical Report. Pennsylvania Department of Corrections, Bureau of Planning, Research and Statistics, Mechanicsburg, PA

  • Laird N (1978) Nonparametric maximum likelihood estimation of a mixing distribution. J Am Stat Assoc 73:805–811

    Google Scholar 

  • Laufer WS (1995) The rhetoric of innocence. Wash Law Rev 70:329

    Google Scholar 

  • Leo RA (2005) Rethinking the study of miscarriages of justice: developing a criminology of wrongful conviction. J Contemp Crim Justice 21:201–223

    Google Scholar 

  • Liebman JS, Fagan J, West V, Lloyd J (1999) Capital attrition: error rates in capital cases, 1973–1995. Tex Law Rev 78:1839

    Google Scholar 

  • Lustgarten E (1950) Verdict in dispute. Scribner’s Sons, New York

    Google Scholar 

  • Macnamara DEJ (1969) Convicting the innocent. Crime Delinq 15:57–61

    Google Scholar 

  • Manski CF (2003) Partial identification of probability distributions. Springer, New York

    Google Scholar 

  • Marquis KH, Ebener PA (1981) Quality of prisoner self-reports. Rand Corporation, Santa Monica

    Google Scholar 

  • Miller JD (1981) Complexities of the randomized response solution. Am Soc Rev 46:928–930

    Google Scholar 

  • Murphy FJ, Shirley MM, Witmer HL (1946) The incidence of hidden delinquency. Am J Orthopsychiatry 16:686–696

    Google Scholar 

  • Natapoff A (2012) Misdemeanors. South Calif Law Rev 85:1313–1375

    Google Scholar 

  • Natapoff A (2015) Misdemeanors. Annu Rev Law Soc Sci 11:255–267

    Google Scholar 

  • National Registry of Exonerations (2015) Misdemeanors. https://www.law.umich.edu/special/exoneration/Pages/Misdemeanors.aspx. Accessed 13 Nov 2017

  • Nye FI, Short JF (1957) Scaling delinquent behavior. Am Sociol Rev 22:326–331

    Google Scholar 

  • Peterson MA, Braiker HB, Polich SM (1980) Doing crime: a survey of California prison inmates. RAND Corporation, Santa Monica

    Google Scholar 

  • Peterson MA, Chaiken JM, Ebener PA, Honig P (1982) Survey of prison and jail inmates: background and method. Rand Corporation, Santa Monica

    Google Scholar 

  • Peterson J, Ryan JP, Houlden PJ, Mihajlovic S (1987) The uses and effects of forensic science in the adjudication of felony cases. J Forensic Sci 32:11231J

    Google Scholar 

  • Peterson J, Hickman MJ, Strom KJ, Johnson DJ (2013) Effect of forensic evidence on criminal justice case processing. J Forensic Sci 58:S78–S90

    Google Scholar 

  • Piquero AR, Schubert CA, Brame R (2014) Comparing official and self-report records of offending across gender and race/ethnicity in a longitudinal study of serious youthful offenders. J Res Crime Delinq 51:526–556

    Google Scholar 

  • Poveda TG (2001) Estimating wrongful convictions. Justice Q 18:689–708

    Google Scholar 

  • Radelet ML, Lofquist WS, Bedau HA (1996) Prisoners released from death rows since 1970 because of doubts about their guilt. Thomas M Cool Law Rev 13:907

    Google Scholar 

  • Radin ED (1964) The innocents. Morrow, New York

    Google Scholar 

  • Raghavarao D, Federer WT (1979) Block total response as an alternative to the randomized response method in surveys. J R Stat Soc Ser B Methodol 41:40–45

    Google Scholar 

  • Ramsey RJ, Frank J (2007) Wrongful conviction perceptions of criminal justice professionals regarding the frequency of wrongful conviction and the extent of system errors. Crime Delinq 53:436–470

    Google Scholar 

  • Rattner A (1988) Convicted but innocent: wrongful conviction and the criminal justice system. Law Hum Behav 12:283–293

    Google Scholar 

  • Redlich AD, Summers A, Hoover S (2010) Self-reported false confessions and false guilty pleas among offenders with mental illness. Law Hum Behav 34:79–90

    Google Scholar 

  • Reiss AJ, Rhodes AL (1961) The distribution of juvenile delinquency in the social class structure. Am Soc Rev 26:720–732

    Google Scholar 

  • Risinger DM (2007) Innocents convicted: an empirically justified factual wrongful conviction rate. J Crim Law Criminol 1973–97:761–806

    Google Scholar 

  • Robison SM (1936) Can delinquency be measured. Pub. for the Welfare council of New York city. Columbia University Press, New York

    Google Scholar 

  • Roman J, Reid SE, Chalfin AJ, Knight CR (2009) The DNA field experiment: a randomized trial of the cost-effectiveness of using DNA to solve property crimes. J Exp Criminol 5:345

    Google Scholar 

  • Roman J, Walsh K, Lachman P, Yahner J (2012) Post-conviction DNA testing and wrongful conviction. Urban Institute, Justice Policy Center, Washington, D.C.

    Google Scholar 

  • Rosenmerkel S, Durose M, Farole D (2010) Felony sentences in state courts, 2006-statistical tables. Bureau of Justice Statistics, Washington, D.C.

    Google Scholar 

  • Short J, Nye F (1959) Extent of unrecorded juvenile delinquency tentative conclusions. J Crim Law Criminol 49:296

    Google Scholar 

  • Sigurdsson JF, Gudjonsson GH (1996) The psychological characteristics of ‘false confessors’. A study among icelandic prison inmates and juvenile offenders. Pers Individ Differ 20:321–329

    Google Scholar 

  • Skogan W (1981) Issues in the measurement of victimization. Bureau of Justice Statistics, Washington, D.C.

    Google Scholar 

  • Snell T (2014) Capital punishment, 2013-statistical tables. Bureau of Justice Statistics, Washington, D.C.

    Google Scholar 

  • Spencer BD (2007) Estimating the accuracy of jury verdicts. J Empir Leg Stud 4:305–329

    Google Scholar 

  • Tan MT, Tian G-L, Tang M-L (2009) Sample surveys with sensitive questions: a nonrandomized response approach. Am Stat 63:9–16

    Google Scholar 

  • Thornberry TP, Krohn MD (2000) The self-report method for measuring delinquency and crime. National Institute of Justice, Washington, D.C.

    Google Scholar 

  • Thygesen LC, Ersbøll AK (2014) When the entire population is the sample: strengths and limitations in register-based epidemiology. Eur J Epidemiol 29:551–558

    Google Scholar 

  • Tourangeau R, Yan T (2007) Sensitive questions in surveys. Psychol Bull 133:859

    Google Scholar 

  • Tracy PE, Fox JA (1981) The validity of randomized response for sensitive measurements. Am Sociol Rev 46:187–200

    Google Scholar 

  • U.S. National Center for Health Statistics (1965a) Reporting of hospitalization in the health interview survey. Vital Health Stat Ser 1 Programs Collect Proced 1–71

  • U.S. National Center for Health Statistics (1965b) Health interview responses compared with medical records. Vital Health Stat Ser 1 Programs Collect Proced 1–74

  • U.S. National Center for Health Statistics (1966) Interview responses on health insurance compared with insurance records. Vital Health Stat 2:1–43

    Google Scholar 

  • U.S. National Center for Health Statistics (1967) Interview data on chronic conditions compared with information derived from medical records. Vital Health Stat 2:1–84

    Google Scholar 

  • Warner SL (1965) Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60:63–69

    Google Scholar 

  • Weiser B (2016) Trial by jury, a hallowed American right, is vanishing. N. Y. Times, New York

    Google Scholar 

  • Weiss CH (1968) Validity of welfare mothers’ interview responses. Public Opin Q 32:622–633

    Google Scholar 

  • Zalman M, Smith B, Kiger A (2008) Officials’ estimates of the incidence of “actual innocence” convictions. Justice Q 25:72–100

    Google Scholar 

  • Zalman M, Larson MJ, Smith B (2012) Citizens’ attitudes toward wrongful convictions. Crim Justice Rev 37:51–69

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Charles E. Loeffler.

Appendix: NMPLE Binomial Estimation of Implausible Responses

Appendix: NMPLE Binomial Estimation of Implausible Responses

To estimate F(p) we employ a non-parametric maximum likelihood estimator. While we place no restrictions on F(p), Laird (1978) proved that the NPMLE of the mixing distribution F is discrete under conditions satisfied by the binomial distribution. That is, the estimate \(\widehat{F}\left( p \right)\) will always be discrete; any continuous distribution choice for F will have a smaller likelihood. The EM algorithm can compute the NPMLE numerically. Initializing the algorithm with J point masses equally spaced at \(p_{1} , \ldots ,p_{J}\) on [0, 1], set \(\alpha_{j} = \frac{1}{J}\) for j in 1,…, J. Then iterating to convergence the equations

$$w_{ij} = \frac{{\alpha_{j} \left( {\begin{array}{*{20}c} {m_{i} } \\ {x_{i} } \\ \end{array} } \right)p_{j}^{{x_{i} }} \left( {1 - p_{j} } \right)^{{m_{i} - x_{i} }} }}{{\mathop \sum \nolimits_{k} \alpha_{k} \left( {\begin{array}{*{20}c} {m_{i} } \\ {x_{i} } \\ \end{array} } \right)p_{k}^{{x_{i} }} \left( {1 - p_{k} } \right)^{{m_{i} - x_{i} }} }},\quad \alpha_{j} = \frac{{\mathop \sum \nolimits_{i} w_{ij} }}{n},\quad {\text{and}}\quad p_{j} = \frac{{\mathop \sum \nolimits_{i} w_{ij} x_{i} }}{{\mathop \sum \nolimits_{i} w_{ij} m_{i} }}$$

produces \(\widehat{F}\left( p \right)\), having probability \(P\left( {p = p_{j} } \right) = \alpha_{j}\).

A simulated example demonstrates how this estimator performs on the three modeling choices we considered. We simulated data for n = 2000 respondents. For each respondent we generated the number of prior convictions, mi, as one plus a random draw from a negative binomial with mean 2 and standard deviation 2. Half of the simulated respondents had one or two convictions and 8% had seven or more. We randomly assigned 5% of the respondents to have p = 0 (reports all convictions as wrongful), 25% of respondents to have p = 1 (reports all convictions as correct), and for the remaining 70% we drew pi from a beta distribution with mean 0.7 and standard deviation 0.14. Lastly, we simulated the number of reported correct convictions from a Binomial (mi, pi).

If all simulated respondents were assumed to be honest, by ignoring the possibility that some respondents might lie and always report all convictions as wrongful (p = 0), then directly computing the proportion of convictions that simulated respondents report as correct yields \(\widehat{p} = 0.746\). The two-component mixture model produces estimates \(\widehat{p} = 0.790\) and \(\widehat{\alpha } = 0.061\), not far off from the true 5% with p = 0 that we simulated. We then estimated the NPLME:

$$d\widehat{F}\left( p \right) = \left\{ {\begin{array}{*{20}l} {0.044} \quad{p = 0} \\ {0.306} \quad{p = 0.553} \\ {0.412} \quad{p = 0.823} \\ {0.238} \quad {p = 1} \\ 0 \quad\quad\quad{\text{otherwise}} \\ \end{array} } \right.$$
(3)

The NPMLE recognizes that there are an excess number of simulated respondents for which p is 0 or 1 and closely estimates their proportion, 4.4% of respondents always indicate wrongful conviction (true simulated value was 5%) and 23.8% always indicate correct conviction (true simulated value was 25%). Then two point masses between 0 and 1 at p = 0.553 and p = 0.823 capture the remaining respondents as best as can be extracted from the observed data. Again, we did not specify that F(p) would be discrete, but evaluating Eq. (1) for any continuous distribution would have a lower likelihood than the discrete distribution. From this model the estimated fraction of respondents always reporting their convictions as wrongful is 4.4%, the closest to the true value of 5% for any of the modeling approaches.

The simulation demonstrates that the most flexible approach, the NPLME, offers the estimate of the fraction of respondents always reported innocence with the least bias.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Loeffler, C.E., Hyatt, J. & Ridgeway, G. Measuring Self-Reported Wrongful Convictions Among Prisoners. J Quant Criminol 35, 259–286 (2019). https://doi.org/10.1007/s10940-018-9381-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10940-018-9381-1

Keywords

Navigation