The morality of the death penalty, and friendly fire killings in the Hamas-on-Israel war -- a Signal Detection Theory analysis

Catchy title eh! Trigger warning: If the title makes it sound like what you will read below will be like a lecture in a psychology course -- it is.

Last week, Alabama carried out the first ever (in the U.S.) capital punishment execution using nitrogen gas. Like most people I know, I’m categorically opposed to the death penalty. As far as I know, most of the people I know are opposed to the death for the simple reason that they are morally opposed to state killing as a form of punishment for criminal acts. My own reasons are a bit different.

I actually have no moral opposition to the state taking the lives of individuals who have committed horrific murders. I had no moral opposition, for example, to the execution of Timothy McVeigh, who blew up the Alfred P. Murrah Federal Building in Oklahoma City, killing 168 people (including 19 children), and injuring more than 500 others. But – I AM opposed to executing people who are innocent of the crime for which they were convicted, and I long ago reached the conclusion that it is not possible to avoid executing the innocent while intending to execute only the guilty, and that belief is based upon, of all things, a theory of human perception that I was first exposed to (MANY years ago) in my freshman-level course in Introductory Psychology (thanks Barney Gilmore for a great class).

The theory is called Signal Detection Theory, and since first learning its precepts, I have found its lessons to be relevant to my understanding of a broad range of phenomena, including why there will always be some cases of the execution of the innocent as long as we have a death penalty. In the discussion below, I’ll discuss the theory, then apply its principles to judgments of criminal guilt and to an analysis of the tragedy of friendly fire killings in the Hamas-on-Israel war.

Signal Detection Theory

One of the earliest questions examined by people who called themselves experimental psychologists was the question of the absolute threshold of perception – that is, the question of the sensitivity of each of our perceptual systems. In the case of hearing, for example, the question is: What is the softest sound that a person can hear?

The obvious way to determine the absolute threshold for hearing would be to put someone in a soundproof room and then present brief sounds (the “signal”) of different levels of loudness (sound amplitude). Then, immediately after each signal is presented, a clear light is turned on briefly, telling the participant that it is time to indicate whether a sound has just been heard or not. The request for a response is also presented (for obvious reasons) an equal number of times when a signal has NOT just been presented.

There were a number of findings from this kind of research that led to the development of signal detection theory:

1. Some people had better, more sensitive, hearing than others.

2. Because the task was essentially one of distinguishing between the background level of sound and the sound of the signal against that background, the signals had to be louder to be detected against a noisy background than against a perfectly quiet background.

3. There was no “pure” absolute threshold for signal detection for any participant. Instead, with very soft and difficult-to-detect sounds, there was a range of sound amplitudes such that, within that range, the softer the sound, the less likely the participant was to indicate that they detected it. For example, within that range of amplitudes, a louder (but still difficult-to-detect) signal might be detected 80% of the times it was presented, whereas a softer sound might be detected only 20% of the times it was presented.

4. Even when no sound was presented, participants sometimes responded that they thought they had heard the signal.

5. Participants could be more or less cautious about deciding that they had heard the signal, depending upon their instructions and their own bias toward avoiding different kinds of errors.

In order to explain all of these findings (none of which is particularly surprising), Signal Detection Theory proposes that the likelihood that a participant will indicate that a signal has been detected is affected by three variables:

1. Signal Strength: The loudness of the sound relative to the background level of sound.

2. Sensitivity. The more sensitive the hearing of the participant, the more likely the individual will be to detect very faint sounds.

3. Response bias. Under some conditions, participants may be very wary about indicating that they have heard the signal unless they are absolutely certain, whereas under other conditions participants may be more likely to indicate that they have heard the signal any time they think it might have been presented – even if they are far from certain.

With any binary judgment task such as this one (binary in the sense that participants must make one of two response – heard or not heard – each time a response is requested), the effects of these factors on a participant’s performance can be analyzed in terms of four categories of responses:

HITS: The sound signal was presented, and the participant responded that the signal was presented (a correct response).

MISSES: The signal was presented, but the participant responded that the sound signal was not heard (an error)

CORRECT REJECTIONS: The sound signal was NOT presented, and the participant responded that no sound signal was heard (a correct response)

FALSE ALARMS: The sound signal was NOT presented, but the participant responded that the sound signal HAD been heard (an error).

How, then, do specific features of a perceptual judgment situation affect the rates of these different kinds of responses?

1. The more clearly the target signal differs from the background level of noise (that is — the greater the signal strength), the higher will be the hit rate and the lower will be the miss rate and the false alarm rate. Conversely, when the signal and noise are more similar to each other, then the hit rate and false alarm rate will be more similar to each other (and if there is really no discernable difference between the signal and the noise, the hit rate and the false alarm rate will be equivalent).

2. If participants are incentivized to maximize hits while minimizing misses, their hit rate can be increased, but AT THE COST OF AN INCREASE IN FALSE ALARMS AS WELL. Similarly, if participants are trying to be very cautious in order to minimize false alarms, they may be able to reduce their false alarm rate, but AT THE COST OF A DECREASE IN THE HIT RATE AS WELL. And ultimately, under any conditions in which performance cannot be perfect, the only way to reduce the false alarm rate to zero would be for the participant to have a zero hit rate as well.

Signal Detection Theory analysis of judgments of guilt and innocence

How can we apply this kind of analysis to jury judgments of guilt and innocence (another kind of imperfect binary judgment)? In this case, the four possible responses would be:

Hits: Guilty defendant found guilty (correct)

Misses: Guilty defendant found not guilty (error)

Correct rejections: Innocent defendant found not guilty (correct)

False Alarms: Innocent defendant found guilty (error)

and then:

Factors affecting the probability that a participant will make a correct determination of guilt or innocence::

1. Signal Strength. In a criminal case, signal strength corresponds with the quality of the evidence. Essentially, the issue is how well the evidence differentiates cases in which the defendant is really guilty from cases in which the defendant is really innocent. It must be kept in mind when considering this factor that the state does not bring charges against people unless the investigators are confident that the defendant is guilty. We know, however, that not all defendants are guilty.

2. Sensitivity. This factor corresponds with the ability of the jury to weigh different kinds of evidence in order to come to a correct decision. Humans are far from perfect at making these kinds of judgments, however, and we know, for instance, that one error that jurors tend to make is the overestimation of the validity of eyewitness testimony.

3. Response bias. Our criminal justice system is based upon the premise that it is better to let a guilty person go free (a “miss” in the parlance of signal detection theory) than to convict the innocent (a “false alarm”). Accordingly, jurors are instructed to try to minimize false alarms. I do not know how well most jurors are able to calibrate their response bias to be consistent with this principle.

Given this kind of analysis, how can we reduce the risk of false alarms, that is, of convictions of the innocent?

1. Increase Signal Strength by improving our forensic capabilities so that there is a clearer differentiation between cases in which the defendant is actually innocent from cases in which the defendant is actually guilty (but again, a reminder that people do not end up as defendants in a criminal cases unless the D.A. thinks the person is guilty).

2. Increase Sensitivity by, for example, training jurors in how to weigh different kinds of evidence (not an easy task).

3. Modify Response Bias by instructing jurors to do their best to avoid false alarms. The problem here, as was noted above, is that it is, according to this analysis, simply impossible to reduce the false alarm rate to zero without also bringing the hit rate (conviction of the guilty) down to an unacceptably low level.

The implications of this analysis for criminal cases is clear: As long as judgments of guilt and innocence are imperfect (which will always be the case), there will be “false alarms”, and that means that as long as we include the death penalty as one form of punishment, SOME of those executed will have been innocent. And yes – I know – an obvious rejoinder to this claim is that perhaps we could keep the death penalty as a possible form of punishment, but limit its use to cases in which we are perfectly and completely and 100% certain that the defendant is guilty of the crime for which s/he was accused. Sounds easy. For example, I have every reason to believe that Timothy McVeigh was guilty. But is this really possible? If it is — why have so many death row inmates been ultimately exonerated by the efforts of the Innocence Project? Wasn’t it the case that ALL of these “innocent but sentenced to death” inmates were – at the time of their sentencing – judged to be guilty with what was thought, at the time, to be 100% certainty?

According to Signal Detection Theory, and consistent with the evidence of the past 40 years, it simply is not possible to reduce the false alarm rate for capital punishment convictions to zero without doing away with the death penalty altogether. And THAT is why I’m categorically opposed to the death penalty – because as long as some are executed, it is likely that some of those will be people who are innocent, and THAT is what I find morally unacceptable.

Signal Detection Theory analysis of deaths by friendly fire in the Hamas-on-Israel war.

Deaths by friendly fire occur in every war, and at rates greater than most people realize. In a recent and well-publicized and particularly tragic case, for example, three Israelis who had been held hostage by Hamas but had somehow escaped were then mistaken for Hamas terrorists by IDF (Israeli Defense Force) soldiers and killed.

I find it helpful to think about a horrific event like this in terms of a Signal Detection Theory analysis. In this situation, as in any battle, the task for soldiers when seeing someone is to make a judgment about whether or not that individual is an enemy combatant and therefore a threat. That judgment (as is the case with any binary perceptual judgment) will, according to Signal Detection Theory, be affected by:

1. Signal Strength. In this case, signal strength refers to the degree to which the signal (the perceptual features of enemy combatants) differs from the perceptual features of people who are not enemy fighters and therefore not a threat.

2. Sensitivity. In this case, sensitivity refers to how well trained the soldiers are in how to distinguish enemy fighters from non-combatants.

3. Response Bias. In this case, response bias refers to the degree to which soldiers may be biased to categorize someone they see as a threat vs a non-combatant.

Because one of the keys to the protection of civilians in war is a clear and easy perceptual differentiation between civilians and combatants, it is a war crime for combatants to disguise themselves as non-combatants (soldiers are supposed to wear uniforms to distinguish them from civilians). The problem faced in this war by IDF soldiers is that, in direct defiance of this fundamental principle of the rules of war, Hamas fighters do not wear uniforms – thereby making the ability of IDF soldiers to detect the critical “signal” – that is, to determine whether someone they see is or is not a Hamas fighter – very difficult. Indeed, because of deliberate Hamas tactics, even the fact that someone that a soldier sees is a child is not clear evidence that the person does not pose a life-threatening threat to the IDF soldiers. As Sam Harris has noted in his superb must-read article “5 Myths About Israel And The War In Gaza”:

“…any conflict with jihadists is made immeasurably worse by the tactics they use. Why can’t Israeli soldiers simply trust people who appear unarmed and want to surrender or move to safety? Because they are confronting a culture of religious fanatics that has produced an endless supply of suicide bombers over the last 50 years. Just take a moment to contemplate how the tactic of suicide bombing changes everything. Nothing and no one can be taken at face value. Normally, if someone is driving a car or truck, you can be confident that he hasn’t rigged it to explode. Most people aren’t eager to die. We rely on the near universality of that attitude in all kinds of ways. But here we are talking about people who have literally rigged children to explode—this has happened in a dozen different conflicts with jihadists across the world—many of which had nothing to do with Israel or the West or even non-Muslims. How do you expect an army, or a police force, or any other organization, to deal with this possibility in a compassionate and civilized way—one that is recognized to be compassionate and civilized by all the innocent people who are subjected to it, day after day and year after year, at check points, and in other places where they have to be treated like they too might be suicide bombers? Just imagine what it is like to have to wonder whether a child is actually a bomb?”

What about Response Bias? In the context of an IDF soldier seeing someone emerge from a building or tunnel where Hamas terrorists might have been hiding, it is reasonable to assume that the bias on the part of the IDF soldiers would be toward identifying that individual as a threat – because there is a good chance the person IS a threat, and because in this case the risk to the soldier of a “miss” (that is – judging a person to be a safe non-combatant when the person really is a Hamas fighter) is the very real risk of the soldier being killed. And of course, given the specific context in which the IDF soldiers had to make their judgments, the true likelihood that someone emerging from a building would be an escaped hostage was EXTREMELY low, a fact which would contribute to a bias on their part away from a rapid perceptual categorization of someone in this situation as an escaped Israeli hostage.

Tragically, in the case of the three Israeli hostages killed by friendly fire, the IDF soldiers made a perceptual error – a “false alarm” – by falsely judging the men they saw as a threat. However, as tragic as an event like this may be, it is not surprising that such false alarms occur, given how important it is for the soldiers to avoid “misses” and given the war crime efforts by Hamas to weaken the critical signals that would enable IDF soldiers to distinguish Hamas fighters from civilians or hostages.