Abstract
This article presents a model wherein law enforcers propose sentences to maximize their likelihood of reelection, and shows that elections typically generate over-incarceration, i.e., longer than optimal sentences. It then studies the effects of disenfranchisement laws, which prohibit convicted felons from voting. The removal of ex-convicts from the pool of eligible voters reduces the pressure politicians may otherwise face to protect the interests of this group, and thereby causes the political process to push the sentences for criminal offenses upwards. Therefore, disenfranchisement further widens the gap between the optimal sentence and the equilibrium sentence, and thereby exacerbates the problem of over-incarceration. Moreover, this result is valid even when voter turnout is negatively correlated with people’s criminal tendencies, i.e., when criminals vote less frequently than non-criminals.
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04 May 2017
An erratum to this article has been published.
Notes
See, e.g., The American Civil Liberties Union’s web-site dedicated to mass incarceration, where “the war on drugs”, as well as addressing problems related to mental illness, substance use, and homelessness within the criminal justice system are listed as “current issues”.
See, e.g., Bandyopadhyay and McCannon (2014) and the sources cited therein.
Single-peaked preferences, which allow the application of the more widely known median voter theorem, are different from single-crossing preferences. The preferences considered in this article are quite intuitive and satisfy the single-crossing property without the need for imposing any additional restrictions. They become single-peaked preferences if additional restrictions are imposed upon them. However, the results presented do not require the application of the median voter theorem and, thus, I do not impose such restrictions. The differences between single-crossing preferences and single-peaked preferences (as well as the subtle difference between the representative voter theorem used here and the median voter theorem) are explained in greater detail in Gans and Smart (1996).
The median being smaller than the mean is a property that is typically met by right-skewed distributions. The exponential distribution, for instance, is among many well-known distributions that satisfy this property. The assumption that the median is smaller than the mean is invoked in other contexts, including income distributions (see, e.g., Meltzer and Richard 1981). The assumption is likely to hold for serious crimes, for which a conviction leads to disenfranchisement. Whether it holds for mere civil infractions, such as parking violations, is more questionable.
It is worth pointing out that some individuals who have inclinations to commit a particular type of crime may not have a tendency to commit other crimes. Thus, it would be erronous to suggest that all 6.1 million disenfranchised voters having similar preferences over sentences for any given crime. However, given the large number of individuals disenfranchised, the shift in the median voter’s criminal tendencies is likely to be non-negligible.
This is the standard imprisonment cost specification explained in greater detail in Polinsky and Shavell (2007), wherein punishment has no fixed costs.
An earlier version of this article, Mungan (2016), considers a population that grows at a constant rate. Incorporating this possibility does not affect any of the main results, and allows for comparative statics with respect to the growth rate. The only additional key finding is that the gap between the steady state sanction under disenfranchisement and the optimal sanction is decreasing in the growth rate.
An alternative assumption, which complicates the analysis, is that voters choose the policy that maximizes their lifetime payoffs. This leads to no change in the analysis of the case without disenfranchisement, nor does it affect the optimal sanction (Sects. 3.1–3.2). Moreover, all results that pertain to the effect of disenfranchisement (Sect. 3.3) emerge under this alternative assumption coupled with appropriate beliefs held by voters regarding the effects of sentences in the current period over the sentences elected in future periods.
See note 8, above.
One may wonder whether it is even possible for these assumptions simultaneously to hold. To demonstrate that this is possible, let \(F^{1}(x)=1-[1+\frac{x}{\gamma }]^{-\alpha }\) (a Pareto distribution) with \(\frac{1+\sigma }{h}\gamma<\alpha <1\). It follows that \(\varepsilon _{s}=-\frac{\theta _{s}s}{\theta }=\frac{f(ps)}{1-F^{1}(ps)} ps=\frac{\alpha ps}{\gamma +ps}<1\) for all s, since \(\alpha <1\). Moreover, \(U_{s}(0,\mu )=p\mu f(ps)h-p\mu (1+\sigma )(1-F^{1}(ps))>0\), because \(\alpha >\gamma \frac{1+\sigma }{h}\). Thus, both assumptions are satisfied. More generally, these assumptions are satisfied for distributions for which \(\lambda (x)x<1\) for all x, and \(\lambda (0)>\frac{1+\sigma }{h}\), where \(\lambda\) is the hazard function associated with the distribution.
This social welfare function is used as a benchmark and for comparing equilibrium sentences with the optimal sentence frequently derived in the law and economics literature.
This follows, because assumption 1 implies some \(s^{h}\) exists such that \(\frac{\partial W}{\partial s}<0\) for all \(s>s^{h}\), and, assumption 2 guarantees that some \(s^{l}\) exists such that \(\frac{\partial W}{\partial s}>0\) for all \(s<s^{l}\). Nevertheless, one may be interested in the characteristics of the first- and second- order conditions associated with W, which are given by:
$$\begin{aligned} \frac{\partial W}{\partial s}=p\mu [f(ps)(h+p\sigma s)-(\sigma +1)(1-F^{1}(ps))]=0 \end{aligned}$$and
$$\begin{aligned} \frac{\partial ^{2}W}{\partial s^{2}}=p^{2}\mu [f^{\prime }(ps)(h+p\sigma s)+f(ps)(2\sigma +1)]<0 \end{aligned}$$which reveals that \(f^{\prime }(ps)<0\) at the welfare maximizing sentence.
Specifically, Stigler (1970, p. 527) states: “what evidence is there that society sets a positive value upon the utility derived from a murder, rape, or arson? In fact the society has branded the utility derived from such activities as illicit”.
The bracketed parts are relevant if multiple sanctions maximize the median voter’s utility.
As previously pointed out in note 6, these include many well known distributions, among others, the exponential distribution. But, see von Hippel (2005) discussing exceptions to this rule, mostly when the distribution is discrete or not unimodal.
I am assuming, for simplicity, that disenfranchisement bars all ex-convicts from voting. In reality, different states have different policies. According to Uggen et al. (2016), among the 48 states that have some form of disenfranchisement 34 prohibit parolees and inmates from voting, whereas 12 states impose some form of post-sentence restriction.
References
Bandyopadhyay, S., & McCannon, B. C. (2014). The effect of the election of prosecutors on criminal trials. Public Choice, 161, 141–156.
Becker, G. (1968). Crime and punishment: an economic approach. Journal of Political Economy, 76, 169–217.
Clear, T., & Austin, J. (2009). Reducing mass incarceration: Implications of the iron law of prison populations. Harvard Law and Policy Review, 3, 307–324.
Curry, P., & Doyle, M. (2016). Integrating market alternatives into the economic theory of optimal deterrence. Economic Inquiry, 54, 1873–1883.
Drago, F., Galbiati, R., & Vertova, P. (2009). The deterrent effects of prison: Evidence from a natural experiment. Journal of Political Economy, 117, 257–280.
Gans, J., & Smart, M. (1996). Majority voting with single crossing preferences. Journal of Public Economics, 59, 219–237.
Giertz, J., & Nardulli, P. (1985). Prison overcrowding. Public Choice, 46, 71–78.
Helland, E., & Tabarrok, A. (2007). Does three strikes deter: A non-parametric investigation. Journal of Human Resources, 42, 309–330.
Hjalmarsson, R., & Lopez, M. (2010). The voting behavior of young disenfranchised felons: Would they vote if they could? American Law and Economics Review, 12, 356–393.
Langlais, E., & Obidzinski, M. (2016). Law enforcement with a democratic government. American Law and Economics Review, Forthcoming,. doi:10.1093/aler/ahw015.
Lee, D., & McCrary, J. (2016). The deterrence effect of prison: Dynamic theory and evidence. Mimeo.
Levitt, S. (1998). Juvenile crime and punishment. Journal of Political Economy, 106, 1156–1185.
Manza, J., & Uggen, C. (2004). Punishment and democracy: Disenfranchisement of nonincarcerated felons in the United States. Perspectives on Politics, 2, 491–505.
Meltzer, A., & Richard, S. (1981). A rational theory of the size of government. Journal of Political Economy, 89, 914–927.
Miles, T. (2004). Felon disenfranchisement and voter turnout. Journal of Legal Studies, 33, 85–129.
Mungan, M. (2016). Over-incarceration and disenfranchisement with population growth. George Mason Law & Economics Research Paper No. 16–43.
Polinsky, A., Shavell, S. (2007). Public enforcement of law. In A. M. Polinsky & S. Shavell (Eds.), Handbook of law and economics (pp. 403–454).
Rothstein, P. (1991). Representative voter theorems. Public Choice, 72, 193–212.
Spamann, H. (2016). The US crime puzzle: A comparative perspective on US crime and punishment. American Law and Economics Review, 18, 33–87.
Stigler, G. J. (1970). The Optimum Enforcement of Laws. Journal of Political Economy, 78(3), 526–536.
The American Civil Liberties Union. Mass Incarceration. ACLU. https://www.aclu.org/issues/mass-incarceration.
Traxler, C. (2009). Voting over taxes: The case of tax evasion. Public Choice, 140, 43–58.
Uggen, C., Larson, R., Shannon, S. (2016). 6 Million Lost Voters: State-Level Estimates of Felony Disenfranchisement. In The Sentencing Project, Washington, D.C.. http://www.sentencingproject.org/publications/6-million-lost-voters-state-level-estimates-felony-disenfranchisement-2016/
von Hippel, P. (2005). Mean, median, and skew: Correcting a textbook rule. Journal of Statistics Education, 13, n2.
Acknowledgements
I am grateful to two anonymous referees, William Shughart II, and Brandon Brice for useful comments and suggestions. I thank Kristen Harris for research assistance.
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The original version of this article was revised. The publisher regrets that due to an unfortunate turn of events in Eqs. (32) and (34) erroneous mathematical expression was introduced during article processing. Both equations have been corrected in the article and should be regarded as the final version by the reader.
An erratum to this article is available at https://doi.org/10.1007/s11127-017-0451-y.
Appendices
Appendix 1: Proofs of Lemma 1 and Proposition 3
Proof of Proposition 3
(i) \(t_{j}^{d}(s_{j-1})\) describes the criminal tendency of the median eligible voter as a function of the sanction and \(\overline{s}_{j}(t_{j}^{d})\) describes the sanction that is elected in period j. Given this notation, when ex-convicts are disenfranchised, a steady state is characterized by the condition:
That an \(s^{d}>0\) that satisfies this condition exists follows from the facts that \(\frac{d\overline{s}_{j}}{dt}<0\) [(as implied by (14)] and: (a) \(\frac{dt_{j}^{d}}{ds}>0\), (b) \(\overline{s}_{j}(t_{j}^{d}(0))>0\), and (c) \(\underset{s\rightarrow \infty }{\lim }\overline{s}_{j}(t_{j}^{d}(s))-s<0\). The validity of (b) and (c) follow easily from the observations that the sanctions preferred by all \(t\ge t^{m}\) are positive and finite. To demonstrate that \(\frac{dt_{j}^{d}}{ds}>0\), note that this condition is equivalent to \(\frac{\partial V_{j}(t,s)}{\partial s}<0\), owing to the definition of \(t^{d}\) expressed in (19). Differentiating \(V_{j}\) wrt s reveals that:
Thus, \(\frac{\partial V_{j}}{\partial s}<0\) iff
Proposition 2 demonstrates that \(V(t,s)>G(t)\); thus, a sufficient condition for (30) is that \(G(t)>\frac{\underset{\underline{t}}{\overset{t}{\int } }xg(x)dx}{\mu }\), which, as demonstrated in (21), holds. Hence, \(\frac{\partial V_{j}(t,s)}{\partial s}<0\), and, therefore, a unique steady state sentence \(s^{d}\) exists.
(ii) This claim follows directly from Proposition 2 (i): \(V_{j}(t,s)>G(t)\) for all s, and, in particular, \(V_{j}(t,s^{d})>G(t)\). Thus \(s^{d}>s^{n}\). \(\square\)
Proof of Lemma 1
The inequality in the lemma is
which holds if
or,
which holds if \(l^{\prime }<0\), since
\(\square\)
Appendix 2: Excluding criminal benefits
The previous analysis proceeds by comparing sanctions listed in (25). It is worth noting that the only sanction in this list that depends on the definition of social welfare is \(s^{o}\), i.e., the optimal sanction. Moreover, as Proposition 4 demonstrates, \(s^{d}<\min \{s^{n},s^{\nu },s^{\delta }\}\). Thus, if we let \(s^{c}\) denote the sanction that maximizes the sum of all utilities net of criminal benefits (or, equivalently, the cost minimizing sanction), it follows that all results presented in the previous sections are preserved (when criminal benefits are excluded from the social welfare function) if \(s^{d}>s^{c}\).
Note that when criminal benefits are excluded, social welfare (previously expressed in (10)) becomes:
which I will assume is single-peaked to simplify the analysis. Then \(\psi\) can be plugged into the median type’s utility as follows:
Therefore, \(U_{s}(s^{c},t^{m})>0\) if
This condition is equivalent to:
When this condition holds, it follows that \(U_{s}(s,t^{m})>0\) for all \(s<s^{c}\) whenever \(\psi\) is single peaked, and, thus, \(s^{d}>s^{c}\). Note that the right-hand side of (38) denotes the sanction elasticity of the crime rate. Thus, if this value is sufficiently smaller than the gap between the median and the mean criminal tendencies in the population, then the analysis extends to cases where criminal benefits are excluded from the welfare function.
The intuition for this result is somewhat convoluted, but relates to the misalignment between the median voter’s objective and the social objective, which is illustrated in (36). The punishment suffered by criminals is not internalized by the median type [this is denoted by \(ps\theta\) in (36)], but his own net criminal benefit (i.e., \(t^{m}\underset{ps}{\overset{\infty }{\int }}(b-ps)f(b)db\)) is. An increase in the sanction results in more punishment suffered by others [represented by \(p\theta\) in (37)] as well as the punishment that the median type expects to suffer [i.e., \(-\frac{t^{m}}{\mu }p\theta\) in (37)], and the magnitude of these changes are both proportional to the crime rate, because the crime rate is proportional to the probability with which each individual offends (i.e., \(\frac{t}{\mu }\theta\) for a type t individual). But, since the median type has a lesser criminal tendency, the personal costs associated with an increase in s are less than the costs he does not internalize. Thus, increasing the sanction beyond \(s^{c}\) leads to net benefits for the median type owing to increases in the severity of punishment. However, these benefits need to be weighed against the benefits generated by a reduction in the crime rate [represented by \(ps\theta _{s}\) in (37)], which the median voter does not internalize. These reductions are small compared to the net-benefits that are proportional to the crime rate, if the sanction elasticity of the crime rate is small.
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Mungan, M.C. Over-incarceration and disenfranchisement. Public Choice 172, 377–395 (2017). https://doi.org/10.1007/s11127-017-0448-6
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DOI: https://doi.org/10.1007/s11127-017-0448-6
Keywords
- Disenfranchisement
- Over-incarceration
- Mass incarceration
- Imprisonment
- Crime and deterrence
- Representative voter theorem