Punishment Deter Murder?
A brief look at the
by John Lamperti
Professor of Mathematics, emeritus
In light of the massive amount of evidence
before us, I see no alternative but to conclude that capital punishment cannot
be justified on the basis of its deterrent effect.
Justice Marshall, U.S. Supreme Court, Furman v.
Contrary to the views of some social theorists,
I am convinced that the death penalty can be an effective deterrent against
M. Nixon (March 10, 1973)
philosophical and religious values are central to the continuing controversy
over capital punishment. Nevertheless, factual evidence can and should inform
policymaking. The evidence for capital punishment as a uniquely effective
deterrent to murder is especially important, since deterrence is the only major
pragmatic argument on the pro-death penalty side.
The purpose of this paper is to survey and evaluate the evidence for
must define the question correctly. We are not asking whether the threat of
punishment, in general, deters crime, nor whether there should be heavy
penalties for murder. The issue at stake is this: Does capital punishment, in a
form that could be practiced in the United States, provide a better deterrent
to murder than long imprisonment? In particular, is it likely that expanding
the death penalty in New Hampshire would lead to fewer murders or eliminating
it to more? If not, capital punishment offers no practical benefits to weigh
against its social costs.
A small (but still substantial and
growing) portion of the vast literature on crime and prevention deals with
factual evidence about deterrence. This evidence is statistical and the
problems of interpretation are difficult. Nevertheless, there is a broad
consensus about the answer to our question. We will begin the survey after some
general remarks about statistical reasoning.
Kinds of statistical evidence
analysis is essential for interpreting complex data and making decisions in the
face of uncertainty. It's useful to recall two notable cases where statistics
helped form social policies.
1954 the Public Health Service organized "the biggest public health
experiment ever," a field test of the Salk polio vaccine. The goal was to
determine whether the new vaccine could substantially reduce the incidence of
paralytic polio. Several difficulties had to be overcome. The occurrence of
polio varied from year to year and place to place in a seemingly random manner.
Moreover, even without any preventive measures the incidence of the disease was
low, on the order of 50 cases per 100,000 susceptible children. This meant that
large chance variations in the number of cases were to be expected in the study
population, and these variations might either mask a positive effect from the
vaccine or produce the illusion of an effect where none existed.
overcome these problems a carefully designed experiment was performed,
involving nearly a million children. A "control group" received
placebo injections instead of the real vaccine; the rest, of course, were
inoculated with the Salk vaccine. The children in the control group were chosen
at random from all those who volunteered and qualified for the experiment, and
neither they, their parents, nor the doctors who examined them knew which
children had received the actual vaccine. This process insured that there were
no systematic differences between those receiving the vaccine and the placebo.
The incidence of paralytic polio in the control group turned out to be nearly
three times greater than that for the vaccinated children, and because of the
experimental design a clear conclusion emerged: It was virtually impossible
that such an outcome could have happened unless the treatment had a positive
effect. Thus the Salk vaccine, though not perfect, was judged a definite
second example is the problem of cigarette smoking and health, especially the
effect of smoking on the occurrence of lung cancer. A relationship was first
suspected during the 1920s and 30s when physicians in the U.S. and England
observed that nearly all their lung cancer patients were heavy smokers. A 1955 study compared smoking rates and
lung cancer deaths (lagged 20 years) for 11 countries, and found a high
positive correlation (0.7): higher lung cancer rates went with more smoking.
(This sort of correlation can be misleading however, since it is individuals,
not countries, who smoke and get cancer.)
Other studies compared groups of smokers with control groups of
non-smokers, chosen to be as similar as possible to the smokers in other
respects. These investigations made it clear that there is a strong association between heavy smoking and lung cancer,
but they do not prove that smoking causes the cancer.
The point is worth stressing, for similar problems arise in
investigating capital punishment. While smokers have a much higher incidence of
lung cancer than do people who have never smoked, this does not by itself prove
that smoking causes
cancer. It might happen that some third factor (or a combination of factors)
causes the cancer, and that this factor is also associated with smoking. If
that were true, then even though smokers would run higher risks of lung cancer
than non-smokers there would be no gain from quitting; smoking would only
indicate, but not cause, cancer proneness.
settle the question, something more was needed--either evidence for that
hypothetical third factor on one hand, in which case smoking would not be the
culprit, or clarity about the causal mechanism on the other. In the
smoking/lung cancer case no "third factor" has been found, and
additional evidence of a genuine link has indeed developed. For example, there was a dose/response
relationship–the more an individual smoked, the greater the chance of
lung cancer. Animal studies showed that exposure to cigarette smoke definitely
did cause lung cancer in dogs.
Considering this and other work, in 1963 a scientific commission
reported to the U.S. Surgeon General the conclusion that heavy smoking can cause lung cancer. That conclusion is
now almost universally accepted.
here is an imaginary (and somewhat facetious) example where a strong association
definitely does not
equal causation. Suppose someone
studied all the elementary school children in New Hampshire and compared their
reading test scores to their shoe sizes.
It’s certain that they would find a very strong positive
correlation—children who wear larger shoes have better scores. Does that mean that parents could help
their kids read better by getting them bigger shoes? Hardly! In this case there
obvious “third factor”: the children’s’ ages. Fifth and sixth graders are older and usually read better
than first and second graders, and they generally also have bigger feet. The association is certainly real, but buying your
daughter larger shoes will not make her a better reader.
Capital punishment in the United States
question of the death penalty and deterrence of homicide has something in
common with the smoking/lung cancer problem. Both deal with rare phenomena
subject to random fluctuations, and neither can be studied by a controlled
experiment like the Salk vaccine trial. In the case of smoking and cancer,
initial observations revealed a strong positive association between the two
variables, and subsequent research had to determine whether this association
was due to a causal relationship. In the capital punishment problem the data
are far less clear, and a first look suggests that executions are associated
with higher rates of
murder rather than lower as deterrence would indicate. Can any cause-and-effect relation be
established in this case?
For decades, murder has been more common in states with capital punishment than in those where it is not used. Data from 1973 to 1984 showed that murder rates in the states without the death penalty were consistently lower and averaged only 63% of the corresponding rates in the states retaining it. The gap has persisted since that time, and in 2008 the average murder rate in states with capital punishment was 5.2 (per 100,000 people) while in non-death penalty states it was 3.3. No deterrence can be seen here--but it might exist and yet be masked by other factors. Many things affect homicide rates; the problem is to separate the impact, if any, of capital punishment from that of all the other variables, known and unknown. How can this be done?
early approach consisted of comparing homicide rates in states with and without
capital punishment, choosing groups of neighboring states as nearly alike as
possible in other respects. Such comparisons were made by Thorsten Sellin for
the years from 1920 to 1958.
This method is a far cry from the controlled experiment performed to test the
Salk vaccine, since "other things being equal" is never exactly true
when comparing units as large and varied as states. Still, if deterrence plays
a significant role its effect should show up as lower homicide rates in the
death penalty states when compared to similar, neighboring abolition states.
Here are Sellin's conclusions:
The data examined reveal that
1. The level of the homicide death
rates varies in different groups of states. It is lowest in the New England
areas and in the northern states of the Middle West and lies somewhat higher in
Michigan, Indiana and Ohio.
2. Within each group of states having similar
social and economic conditions and populations, it is impossible to distinguish
the abolition state from the others.
3. The trends of the homicide death
rates of comparable states with or without the death penalty are similar.
The inevitable conclusion is that executions
have no discernible effect on homicide death rates which, as we have seen, are
regarded as adequate indicators of capital murder rates.
method is to follow the murder rate in a fixed state or jurisdiction and see
what happened when capital punishment was abolished, and, in some cases, when
it was reintroduced. Sellin and others did studies of this kind too. These
investigations again failed to reveal any additional deterrent effect due to
capital punishment. Both types
of study have been updated by other researchers and the changing practice of
executions since 1967 (first a ten year moratorium, then their resumption) has
been taken into account. The conclusions--no indications of deterrence--remain
studies should reveal a general, long-lasting deterrent effect of the death
penalty if it exists. Other investigators looked for short-term or special
kinds of deterrence. In 1935 Robert Dann published an analysis of homicides in
Philadelphia during 60 days before and 60 days after five highly publicized
executions. Dann argued that the deterrent effect of the executions should
result in lower homicide rates during the post-execution periods. The result
was the opposite; rates were higher than usual. Some 20 years later Leonard
Savitz did a similar study, although in his work the critical days were the
ones when death sentences were pronounced after well-publicized trials. Savitz
found no significant difference in homicides for the before and after periods.
Similar studies of short-term deterrence were carried out in Chicago and
California, and again no deterrent effect was found.
is sometimes suggested that capital punishment provides added protection for
police and prison guards, and a number of states that have abolished capital
punishment for “ordinary” murder retain it for the killing of police or prison
staff. This sort of deterrence has been investigated several times, and no
evidence was found that absence of capital punishment makes police or prison
work more dangerous.
One survey did, however, confirm that police in death penalty states believe it contributes to their safety.
Interestingly, the same survey showed police in the abolition states believing
by almost the same margin that absence of capital punishment did not add to the hazards of their jobs.
the mid 1970s investigators have used more sophisticated statistical methods
both to analyze new data and to reexamine older findings in new ways. With some
exceptions (see the next section) the results are consistent with the earlier
findings. Bailey and Peterson, for example, conclude that "Deterrence and
capital punishment studies have yielded a fairly consistent pattern of non-
deterrence." Although they find agreement that "the overall (general)
homicide rate is not responsive to capital punishment," they do call for
further research into particular types of crimes.
Regression models: Ehrlich and others
the mid 1970s, informed opinion agreed that existing data showed no increased
deterrence due to the death penalty. A study by economist Isaac Ehrlich broke
that pattern. Ehrlich considered U.S murder and execution statistics for the
period 1933-1969 together with measures of social factors such as unemployment
and per capita income, and then tried to establish a mathematical model
predicting the murder rate from all the other variables, national execution
rates among them. His model produced a negative coefficient for the execution
variable (i.e., more executions are associated with fewer homicides), which he
asserted was statistically significant.
Ehrlich concluded that "In light of these observations, one cannot
reject the hypothesis that punishment, in general, and execution, in
particular, exert a unique deterrent effect on potential murderers."
study was important for methodological reasons, since it was apparently the
first time multiple regression was used to investigate deterrence. (This
innovation made it hard for non-mathematicians to understand and evaluate the
paper.) Moreover, the fact that
Ehrlich was the first researcher to claim positive evidence for added
deterrence due to capital punishment guaranteed that his work would receive
data were soon studied by other investigators and his results reconsidered.
Peter Passell and John Taylor focused on Ehrlich's observed negative relation
between executions and homicide rates, and asked what happens when the time
period chosen for the model is changed. They also experimented with varying his
assumptions as to the model's functional form. In both cases they found that
some broad aspects of the model were unchanged, but the indication of a special
deterrent effect from executions disappeared completely. Passell and Taylor
concluded that whatever the other virtues of Ehrlich's work, no valid inference
about deterrence could be drawn from it.
Another research team, William Bowers and Glen Pierce, found much the same
Others have experimented with their own regression models for both time-series
and cross-sectional (interstate) studies. The results are mixed, but most of
the researchers failed to find any evidence for deterrence.
have had some personal experience with this issue. Students in a statistics
class I taught at Dartmouth experimented with Ehrlich's model and data during
our study of regression analysis. We confirmed Passell and Taylor's finding
that the indication of deterrence was extremely unstable when small changes
were made in Ehrlich's assumptions. My own conclusion is that regression on
nationally aggregated data can never yield reliable evidence on deterrence, pro
or con. The signal, if any, is hopelessly buried in the noise.
the final section of his paper, Ehrlich interpreted the negative correlation he
found as suggesting a "tradeoff between executions and murders," and
he estimated that over the period 1935-1969, "an additional execution per
year ... may have resulted, on average, in 7 or 8 fewer murders." This
dramatic statement was only slightly softened by his qualification that
"the expected trade-offs ... mainly serve a methodological purpose."
idea that one execution might prevent 7 or 8 murders is easily grasped and
remembered. This is unfortunate, because no such conclusion is justified by
Ehrlich's research. We have seen that the negative correlation between murders
and executions in his model disappears when minor changes are made in certain
assumptions. But even if the model were much more accurate and stable, the
"trade-off" idea would still be invalid. It requires the doubtful
assumption that all other factors could remain constant while the execution
rate alone was increased. Worse yet, it confounds association and causation.
himself surely understood this; that is presumably what he meant when he spoke
of a “methodological purpose."
But he did not stress or explain the need for caution, and predictably
some of his readers did not get the point. They were, in effect, ready to buy
their children larger shoes to improve their reading scores; that is, to step
up executions in order to prevent homicides. But the hope of saving seven, or
any number, of lives by one additional execution cannot be defended by
Ehrlich's work. The earlier conclusion, that U.S. murder statistics give no
evidence for an additional deterrent effect of capital punishment, still held.
work, like that of his critics, became possible in the 1970s because of access
to high-speed computing. Since
then much easier access to computing, as well as widespread access to
substantial data sets, have encouraged others to undertake econometric-style
investigations of capital punishment and deterrence. So far in the 21st century about 10 substantial
studies have been published. Their
findings have been mixed, with some claiming evidence of execution/murder
“trade-offs” similar to or larger than Ehrlich’s 7 or 8, while others found no
such evidence or even an effect in the opposite direction (so-called
“brutalization” hypothesis). A summary of these studies, together with a major
new investigation, can be found in a very recent article by three University of
Texas researchers. Their results “provide no empirical support for the argument
that the existence or application of the death penalty deters prospective
offenders from committing homicide.”
Deterrence--or the opposite?
capital punishment really has any effect on homicide rates, that effect must be
small. Worse, it might go the wrong way! There are cases where the death
penalty has been a cause
of homicide rather than a preventive.
could capital punishment be a cause of murder? In a medical paper, Dr. Louis
West has described what he calls "attempting suicide by homicide."
In these bizarre cases a person actually kills in order to court death by execution.
Here is one of them:
an Oklahoma truck driver had parked to have lunch in a Texas roadside cafe. A
total stranger--a farmer from nearby--walked through the door and blew him in
half with a shotgun. When the police finally disarmed the man and asked why he
had done it, he replied, "I was just tired of living."
have also documented examples of killing to invite execution; for example,
Clinton Duffy, the former warden of San Quentin prison, described several cases
in his 1963 book 88 Men and 2 Women.
In these instances the death penalty was a cause of homicide rather than a
possibility is the so-called "brutalization hypothesis," which
suggests that capital punishment can encourage homicide by seeming to legitimize
killing of enemies. Studies from London and New York State have found an
increase in homicides after highly publicized executions, rather than the
decrease consistent with deterrence.
How valid these findings are and how generally they might apply is not clear.
the other hand, there is also anecdotal evidence that some homicides may have
been deterred by the death penalty. For example, in 1971 the Los Angeles Police
Department reported that half of a group of suspects under arrest for robbery
stated that they had decided not to carry or not use weapons in their
"work" to avoid any risk of a killing which could lead to their own
execution. These statements to police can hardly be taken at face value, but
some such cases are probably genuine.
we acknowledge that there must be instances when capital punishment helps deter
a murder, we must also recognize that at other times it can encourage what it
is meant to prevent. Since neither effect can be measured directly we must turn
back to the statistical studies, which seek to determine the net effect. Their
evidence does not prove that the death penalty is no added deterrent to murder,
nor could it. It does show, I believe, that any special deterrent effect is
small in magnitude, and it might go in either direction. That is still probably
all that can be said.
do advocates of capital punishment reply to all this? Some rely uncritically on
investigations such as Ehrlich's or those of his successors that claim to find
evidence that deterrence is real.
Others state opinions like those of Professor Ernest van den Haag of New
York University. In an article "On deterrence and the death penalty''
van den Haag offered neither new data nor new analysis to support his belief
that capital punishment has a special deterrent value. Instead he gave
psychological and "common sense" arguments on its behalf, together
with a general criticism of the findings of "Professor Sellin et al."
He feels that the statistics are not good enough, that "the similar areas
are not similar enough, the periods are not long enough;....'' After more such
criticism van den Haag concludes: "I doubt that the presence or absence of
a deterrent effect of the death penalty is likely to be demonstrable by statistical
means. It is on our uncertainty that the case for deterrence must rest."
remarkable statement makes a weak case indeed. It is true that statistical
evidence cannot prove that any effect is precisely zero. If, for example, the
Salk vaccine had no impact whatever, this could not have been proved by the
trial described earlier. The experimental results would have indicated, with a
high degree of confidence, that any benefit from the vaccine must lie below a
certain level. As the amount of data increased that level would become smaller,
and zero effect would be the natural conclusion. It would be perverse to then decide to use the vaccine
anyhow because the tests did not exclude the possibility that there could be some benefit, however small. Such a decision would be even more
unreasonable if the vaccine was very costly or had dangerous side effects.
This, in effect, is just what van den Haag advocates in relation to capital
punishment. As negative evidence accumulates, it becomes more and more
implausible to base one's "case for deterrence" on the smaller and
smaller region of uncertainty that remains.
have surveyed a great deal of material; there is a lot more not mentioned here.
None of it has the clarity of a well-designed statistical experiment, nor could
it. And yet despite that uncertainty, I believe Justice Marshall was right, and
Richard Nixon wrong, in the judgments quoted at the start of this paper.
Marshall's view is today supported by an overwhelming majority among America's leading
criminologists, who believe that capital punishment does not contribute to
lower rates of homicide.
is a strong international trend against capital punishment. In recent years
Great Britain (1973), Canada (1976), France (1981), Australia (1985), Italy
(1994) and Spain (1995), among others, have eliminated capital punishment for
murder after extensive study and debate. Russia adopted a moratorium in 1996
and has not executed anyone since. South Africa abolished capital punishment in
1995 after its transition to democracy. In 1998 the European Union Council
reasserted the “opposition of the European Union to the death penalty in all
cases and in all circumstances.”
Executions have also become less frequent in many nations where the
death penalty remains on the books, and in 2009 no executions were carried out
anywhere in the Western Hemisphere—except in the United States.
trend toward abolition has not been observed to cause increases in homicide. In Canada, for example, around three
murders were committed per every 100,000 people before the death penalty was
abolished in 1976, while after that the rate consistently went down reaching
1.85 homicides per 100,000 people in 2003.
Other nations such as Great Britain have experienced
increases in murder--but even greater increases in other violent crimes that
were never subject to death sentences. Some years ago this passage from a
United Nations study summed it up: "It is generally agreed that the data
which now exist show no correlation between the existence of capital punishment
and lower rates of capital crime."
The conclusion still holds.
of those who defend the deterrent value of the death penalty rely on strong
intuitive feelings that capital punishment should be uniquely effective. When the
available evidence doesn't support that conclusion, they argue that the
evidence is imperfect. It is. But if there were a substantial net deterrent
effect from capital punishment under modern U.S. conditions, the studies we
have surveyed should clearly reveal it. They do not.
executions protected innocent lives through deterrence, that would weigh in the
balance against capital punishment's heavy social costs. But despite years of
trying, this benefit has not been proven to exist; the only certain effects of
capital punishment are its liabilities. The death penalty in New Hampshire
serves no social purpose, and its abolition would be a practical and a moral
Court Justice Blackmun, a Nixon appointee, ruled in the Furman case that capital punishment is not per
se unconstitutional. That does not mean it is a good policy. An excerpt from
Blackmun's Furman opinion can well conclude this paper:
yield to no one in the depth of my distaste, antipathy, and, indeed, abhorrence,
for the death penalty.... That distaste is buttressed by a belief that capital
punishment serves no useful purpose that can be demonstrated.
 It is often suggested that executing convicted murderers can
at least save money. This common belief is wrong; executions are far more
expensive than life imprisonment. See Mark Costanzo and Lawrence White,
"An overview of the death penalty and capital trials: history, current
status, legal procedures, and cost," Journal of Social Issues 50, no. 2 (summer
1994), pp, 1-18. More up to date research, summarized and cited in testimony
before the NH Commission, has reinforced that conclusion.
 The greatest cost is that innocent people have been
executed, and that others surely will be in the future. For a review of cases
in which people were wrongly sentenced to die, see chapter 25 in Hugo Adam
Bedau (ed.),The Death Penalty in America: Current Controversies (Oxford, 1997). See
also Charles Black, Capital Punishment: The Inevitability of Caprice and Mistake (Norton, 1974). In
recent years the case of Troy Davis, who has spent many years on death row in
Georgia for a crime he probably did not commit, has attracted considerable
attention. See also “Trial by Fire,” The New Yorker, Sept. 7 2009, for a detailed
account of the trial and execution of an almost surely innocent man in Texas.
 Data from Ruth Peterson and William Bailey, "Murder and
capital punishment in the evolving context of the post-Furman era," Social
March 1988, pp. 774-807. The exception to this pattern is the District of
Columbia, which has no death penalty and very high homicide rates. (Of course
D.C. is not a state, and special circumstances apply.)
 Thorsten Sellin, The Death Penalty (1959). Excerpts from
this book and many other sources were reprinted (along with some new material)
in a useful anthology The Death Penalty in America, edited by Hugo A.
Bedau (1964). Sellin was a leading
criminologist and a pioneer in death-penalty studies until his death in 1994.
 This work and that described below is summarized in William
Bailey and Ruth Peterson, "Murder,capital punishment, and deterrence: a
review of the literature," chapter 9 in Bedau (1997), note 2.
 See Peterson
and Bailey, op. cit. in note 4.
 A recent investigation is Bailey and Peterson, "Murder,
capital punishment, and deterrence: a review of the evidence and an examination
of police killings," Journal of Social Issues, summer
1994, pp. 53-74.
 Bailey and Peterson, op. cit.
deterrent effect of capital punishment: A question of life or death," American
Review June 1975, pp. 397-417.
 "The deterrence
controversy: a reconsideration of the time series evidence," in Capital
Punishment in the
H. Bedau and C. Pierce, editors, 1976.
 "The illusion of deterrence in Issac Ehrlich's research
on capital punishment," Yale Law Journal, Dec. 1975, pp. 187-208
Tomislav Kovanzik, Lynne
Vieraitis, and Denise Boots, “Does the death penalty save lives? New evidence from state panel data,
1977 to 2006,” Criminology and Public Policy, Vol. 8 (2009, Issue 4.
and Capital Punishment," in To Abolish the Death Penalty, Hearings before the
U.S. House Judiciary Committee, March and July, 1968, p. 124. Dr. West chaired
the Department of Psychiatry, Neurology and Behavioral Sciences at the
University of Oklahoma School of Medicine.
 Further examples are described by M. W. Espy Jr. in
"Capital punishment and deterrence: what the statistics cannot show,"
Crime & Delinquency, Oct. 1980, pp. 537-544.
 William Bowers and Glenn Pierce, "Deterrence or
brutalization: what is the effect of executions?" Crime and Delinquency, Oct. 1980, pp. 453-484.
 Journal of
Criminal Law, Criminology and Police Science 60 (1969), p.141.
 Michael Radelet and
Ronald Akers, "Deterrence and the death penalty: the views of the
experts," Journal of Criminal Law & Criminology 87, no.1 (1996), pp.
1-16. Radelet with another
collaborator, Traci Lacock, recently replicated this survey of leading
criminologists and again found an overwhelming consensus that executions do not
lower homicide rates. (The same Journal, vol. 99, 2009.)
 In addition to the United States,
nations carrying out sizable numbers of death sentences in 2009 include China
(the number of executions is a “state secret” but it is known to be more than
the rest of the world combined), Iran, Iraq, Saudi Arabia, Yemen, Sudan, Viet
Nam and Seria, in decreasing order.
The United States was in fifth position with 52.
 See “Canada online” at http://canadaonline.about.com/od/crime/a/abolitioncappun.htm.
Punishment, a United Nations study, 1968.