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Normative Models for Rational Suicide
A normative model of decision making is a theoretical suggestion for a way which people should go about making decisions. Such models are usually mathematical, however, our goal is not to have people actually be able to compute the values using these models. Indeed for the models which will be provided here it is probably impossible (even though there are numerous other models which try to make things easier). However, these models are presented since they might help us to think about the problem in a different, more concrete, manner.
The basic approach is humanistic, i.e. the main emphasis is on the well-being of the individual deliberating in a suicide decision.
Simplifying Assumptions
There are many issues involved in the decision of whether or not to exit.
- Is suicide good for the individual considering it?
- How to take fear into account?
- How to take into account the possibility of failure?
- How to take into account the suffering of those left behind?
Of course, we could use a model which compounds all these together. However, this doesn't help much to make a decision, since it will probably turn out to complex to get anything out of it.
Instead, this article considers only the first issue. For the sake of this article, lets assume that if one chooses suicide, there is no risk of failure and that relatives and friends do not exist. We take this approach in order to deal with the most fundamental question in it's simplest form: is suicide the right choice for you, when taking only yourself into consideration?
If the answer of this question is that suicide is not good for you, then your deliberation is done. There is no need to consider other issues. However, if the answer is that you should commit suicide, then we can start considering other issues. It may be the case that you conclude that suicide would indeed be good for you, but it would be too damaging to your family, and thus, overall, you would choose not to exit.
How to take into account fear and survivors, will be considered elsewhere. As for taking failure into account, the best way is to choose methods with extremely low failure rates. This will also be addressed elsewhere.
Expected Utility
Using the expected utility model, lets start to compare the two options we have: life and death. We need to calculate the utility of both outcomes. We are going to start using some mathematical notation. To make things easier, we use the following abbreviations:
- L - The option of life.
- D - The option of death (suicide).
- B - Your situation will get better in the future.
- NB - Your situation will not get better in the future.
Breaking things down into two future possibilities, that things get better, or not, may seem arbitrary. For example, things could get a just a little better, or the situation could even get worse. But the restriction to two options is just another attempt to simplify things. Essentially, we consider all futures which do not offer a significant improvement (i.e. an improvement which would make life worth living) as falling under the NB category.
As the first step we determine the utility of death as :
U(D) = 0
Because not being alive, nothing can have positive or negative utility, since you are not even aware of anything happening. (of course, we are assuming that there is no heaven or hell, etc...).
The difficult part is to determine the utility of the option of life. We do this by using probabilities. We use the notation P(outcome) for the probability that that outcome occur. So the utility of the outcome of choosing life is:
U(L) = P(NB) * U(NB) + P(B) * U(B)
Since P(NB) = 1 - P(B) we have 3 unknowns. Lets see how we can estimate each of U(NB), U(B), and P(B).
Estimating U(NB)
First lets focus on U(NB), i.e. the utility if things do not get better. This is something people are more able to estimate, because somebody trying to determine whether to exit is probably currently experiencing that situation. So they can evaluate how bad it is.
However, determining the value of U(NB) is quite difficult. U(NB) is supposed to be a number which represents how good the rest of one's life will be if things do not get better. One thing that could be said about U(NB), is that it is probably a negative value. If you are considering death, then this means that you would rather die than live on, (assuming the situation does not get better). And since the value of death is 0 ( U(D) = 0 ) then the value of living on must be less than 0.
But we still need to determine the size of this negative number, and this is not easy. Life usually lasts for many many years, it is difficult to see so far and make an estimation for your entire future life. One way to simplify things a bit is to try to break it down into smaller time periods such as months or days.
Lets define a function d which evaluates the utility for living one day in ones lifetime. For example, d(7) is how good your day will be in a week from now (i.e. in 7 days). Lets say that, assuming you do not exit, you have N more days to live. N can be assessed according to life expectancy for your gender. We could then estimate U(NB) by the following formula:
U(NB) = d(1) + d(2) + ... + d(N)
So we have broken down the utility of one's entire future life, into more manageable utilities for each day. Actually, to do this we need a further assumption of additivity. In real life there are many cases when additivity fails. For example, lets say that the utility of one portion of Ice Cream is 1. In mathematical notation we can say this as U(IC) = 1, where IC is one portion of ice cream. What is the utility of 50 portions of ice cream? If we assume additivity, we get that
U( 50 IC ) = U(IC) + .... + U(IC) = 50 * UD(IC) = 50 * 1 = 50
However, if we give a person 50 portions of ice cream, it is not likely that he will finish all of them. Maybe he will manage to eat three portions of ice cream. So he would not enjoy 50 portions of ice cream 50 times more than a single portion. This case is not additive. Non-additivity occurs when one event influences the utility of subsequent events. After eating one portion of ice-cream, the person would not gain much more enjoyment out of a second portion. Still we will assume additivity, since it simplifies things significantly, even though it reduces accuracy.
Lets return to our last estimation of U(NB):
U(NB) = d(1) + d(2) + ... + d(N)
How do we estimate d for future days? Not all days are the same. Some days are good and some days have negative value. A day with negative utility is a day that you would rather skip (or sleep through). One rule of thumb for estimating whether U(NB) is negative, is to ask whether you would rather skip most days of your life. You can estimate this, by keeping track of your days for a month. At the end of each day, go through what you have done, and how you felt, and try to grade it as either negative, neutral or positive, or you could add a scale with numeric values (-10 for a hellish day, and 10 for a great one).
Such a measurement is also possible for smaller time increments. There was an experiment where people were asked to go about their daily routines and were given timers that alerted them every half hour or so to just take down how they were feeling: bad (-), neutral (o) or good (+). The result of the study was that those people who were feeling good for less than 30% or of the time (even if they were feeling mostly neutral) were invariably suicidal. (if you know the reference for this, please mail the web master).
Lets assume that you manage to give grades from -10 to 10 for each day of the passing month. You can sum them up to determine the value of the entire month ( remember that we are assuming additivity ). Assuming that the situation will not change, the more you live the more the utility will continue in the current direction. For example, if the utility of your month was -10, then assuming you will live for 40 more years, the utility of your remaining life is
-10 * 12 * 40 = -4800
In such a case, death is better because U(D) = 0 is larger. In fact, using this analysis we can also estimate the cost of deliberation. If you give yourself a year to make the decision, yet you did not succeed to improve your situation, then you would have suffered for 12 months with utility of -10 * 12 = - 120 . In such a case, the sooner you die, the better. This is an example for the cost of deliberation. A cost which pro-life advocates do not acknowledge.
Estimating U(B)
Estimating U(B) is essentially the same as for U(NB), however, since you are probably not currently experiencing how living better is like, it is difficult for you to estimate. You could ask a life-loving friend to assess this for you. Note that even when life is better, there are better and worse days. Even when life gets better, it is never eternal bliss. It is, however, better than death.
Estimating P(B)
There are several ways of estimating the probability that your situation will improve. These depend on the situation of the individual. Our assumption is that the current situation of the individual is of suffering, and without some special event or process, this will not change. Thus estimating the probability of improvement is estimating the probability of that event or process occuring.
For example, assuming you are depressed, but haven't gone to any psychological treatment before, the chances of recovery can be estimated as the success rate of psychologists curing their patients. After you have received one or several forms of treatment, the assessment of the probability of improvement can change. If your depression was easy to cure, then any therapist would manage to improve your situation to some degree. The more treatments/drugs you have tried, and the more therapists you have gone through, the more difficult your problem is. Therefore, the more treatments you try, the probability of improvement decreases.
Applications
Using this model we can analyze many other cases, such as euthanasia, or someone who broke up with his girl friend.
Euthanasia
For somebody with a terminal disease, the probability of recovering is extremely low, perhaps even zero. Furthermore, the effects of the illness may cause pain and suffering which make U(NB) very negative. Calculating the utility of life, we get:
U(L) = P(NB) * U(NB) + P(B) * U(B) = 1 * U(NB) + 0 * U(B) = U(NB)
So U(L) is approximately equal to U(NB) which is extremely negative, thus life is a very bad option compared to death.
Break-up From Girl/Boy Friend
Most people manage to recuperate after breaking up, so the probability of things getting better is very high. Lets assume P(B) = 0.9 . If in addition we assume that U(B) = 100 and U(NB) = -100 , we get:
U(L) = P(NB) * U(NB) + P(B) * U(B) = 0.1 * -100 + 0.9 * 100 = 80
U(L) is positive, so life is better than death.
There is hope
Consider the argument: "there is always hope"? This would translate into "there is always a slight probability that things will turn better". Which, of course, assumes that the person in question wants to kill himself because the current situation is bad.
If U(NB) = -100, U(B) = 100, and P(B) = 0.1 (i.e. slight probability that things improve). We get
U(L) = P(NB) * U(NB) + P(B) * U(B) = 0.9 * -100 + 0.1 * 100 = -80
In this case, living is not rational, since it is worse than exiting. This indicates that just a slight probability for improvement, does not necessarily justify continuing to live.
More About Estimation
An additional resource for estimating U(B), U(NB) and P(B) is research about emotional well-being, also known as subjective well-being(SWB) [3]. Evaluating one's SWB means asking yourself "Is my life going well, according to the standards that I choose to use?". When evaluating SWB, the person himself is making the evaluation (hence the word "subjective").
Research about well-being has shown that the frequency, duration and intensity of mood and emotion all contribute to well-being, however, intensity plays only a secondary role. The amount of time (i.e., frequency and duration) of pleasant or unpleasant affect has greater importance [4]. It may be that for people who are considering suicide, the situation is different, but if we accept the former conclusion, then it means that the precise estimation of the value of function d, (which was mentioned above for evaluating U(NB), U(B)) is of less importance. It is more important to determine whether d is positive or negative, and to estimate the amount of positive and negative days.
SWB can be evaluated in several ways. The evaluation can be limited to a specific area in one's life (like work, or relationships) or it can have a broader scope (satisfaction with life). In addition, evaluations can be more cognitive ( i.e. judgments about what is happening in one's life) or more affective (moods and emotions, which are reactions to what is happening in one's life).
In addition, numerous scales and questionnaires have been developed. In particular, the following measures are related to the normative model of making a rational decision, since they take into account events which happen over a period of time:
- Experience sampling - how happy are you over time when we beep you at random moments, and then aggregate those moments?
- Memory measures - can you quickly recall good events (and not bad events) in a timed period.
As an example for a cognitive evaluation we present the following survey, which is in the public domain:
The Satisfaction with Life Scale survey(SWLS)[1][2] measures global cognitive judgments of one's lives. The questionnaire is as follows:
Below are five statements that you may agree or disagree with. Using the 1 - 7 scale below indicate your agreement with each item by placing the appropriate number on the line preceding that item. Please be open and honest in your responding.
- 7 - Strongly agree
- 6 - Agree
- 5 - Slightly agree
- 4 - Neither agree nor disagree
- 3 - Slightly disagree
- 2 - Disagree
- 1 - Strongly disagree
____ In most ways my life is close to my ideal.
____ The conditions of my life are excellent.
____ I am satisfied with my life.
____ So far I have gotten the important things I want in life.
____ If I could live my life over, I would change almost nothing.
Summarize the score and check the result:
- 35 - 31 Extremely satisfied
- 26 - 30 Satisfied
- 21 - 25 Slightly satisfied
- 20 Neutral
- 15 - 19 Slightly dissatisfied
- 10 - 14 Dissatisfied
- 5 - 9 Extremely dissatisfied
A questionnaire geared towards affective evaluations may have questions such as:
During the past 30 days for how many days have you felt sad or depressed? worried, tense or anxious? healthy and full of energy?
Conclusion
This article provided a sketch for the application of the normative model of expected utility to the decision of suicide. However, in order to apply these to specific cases, many estimations must be made. Although the practicality of these estimations may be questionable, they do provide new ways of thinking about one's own situation.
Perhaps even more important, the presentation of this model provides a concrete definition of rational choice in the context of suicide. The presentation asserts not only that choosing death may be rational at times, but it determines when it is rational, and when it is not. This provides us with concrete answers to some pro-life arguments, and a tool to analyze many common cases where suicide is considered.
EverDawn
REFERENCES
[1] Ed Diener, Satisfaction with Life Scale http://www.psych.uiuc.edu/~ediener/hottopic/hottopic.html
[2] Ed Diener, Robert A. Emmons, Randy J. Larsen, and Sharon Griffin, "The Satisfaction With Life Scale" Jonurnal of Personality Assessment Vol.49 No.1 1985
[3] Ed Diener, Frequently Asked Questions (FAQ's) About Subjective Well-Being (Happiness and Life Satisfaction), http://www.psych.uiuc.edu/~ediener/faq.html
[4] Diener E., Sandvik E., Pavot W., "Happiness is the frequency, not the intensity of positive versus negative affect", in Subjective Well-being: An interdisciplanary prespecitve (pp 119-139), 1991.
