Demographic Utility Comparison and Suicide

[Content Warning: suicide, rape, LGBT, economic inequality]


First of all, if you are contemplating suicide, please contact the national suicide prevention lifeline at 1-800-273-8255. Most people who survive attempting suicide are glad they survived.

Some people might want to take some of the conclusions I reach later to suggest that, perhaps, one group is somehow “worth less” than another group. However, this conclusion is really not accurate.

First of all, everything in this post (apart from the fact that suicide is generally bad) is super speculative. I don’t recommend anyone basing anything off it. This is intended to give a very rough ballpark estimate, mainly to demonstrate that analysis of utilities is actually possible, even if not always practical.

The second reason is that the idea that someone is “worth less” than someone else is extremely misleading within the utilitarian framework. If Alice is being tortured and Bob isn’t, then Bob’s life is “worth more” in that if you had to save one of their lives, you should probably choose Bob. However, Alice’s life is “worth more” in that it clearly much easier to vastly improve Alice’s life than it is to improve Bob’s, so that’s where we should focus our efforts. Finally, they (in some sense) are of equal “worth” in that (by definition) increasing one of their utilities by 4 is just as good as increasing the other’s utility by 4.

Finally, this post is (more-or-less) entirely statistical. I do not dwell on personal accounts and so, in addition to everything being super speculative, even to the extent that conclusions are accurate, they are averages and generally won’t apply well to random people.

Suicide and Utilitarianism

Still here? Okay, so one of the most widely cited issues with utilitarianism is that its realistically impossible to compare two people’s utilities. While some philosophers maintain that everyone intuitively recognizes that (for instance) Bill Gates values a cup of coffee less than I value not starving to death, this isn’t universally accepted

For the most part, I think this is a valid critique of utilitarianism, though I hope we will eventually overcome it with enough advances in psychology and neuroscience. I would, however, like to shed a modest degree of light on this subject using suicide statistics.

The reason I think the idea of suicide plays an important role in discussing utility comparisons is that while no one knows what “7 utils” means, we can agree to define 0 utils as the point at which someone is indifferent between continued existence and death. Someone who has attempted suicide has demonstrated that they crossed the line from positive to negative utility, or, rather, they temporarily believed that they had crossed that line.

Why This Matters

There are, however, some practical consequences of properly estimating the utilities of the general population and specific demographics. For instance, determining how much utility is lost due to suicide, rape, and income inequality, may be important in determining what the most effective balance is between funding groups that reduce these – though, of course, the effectiveness of these groups is just as important. Of course, in an ideal world, we’d have plenty of funding for both, but as it is, we must sadly figure out a balance.

Just as importantly, having proper utility estimates will allow us to make difficult choices concerning how high to raise taxes in order to fund redistribution efforts. On the one hand, the poor need the money more than the rich, on the other, taxes probably reduce economic activity, meaning there is less money to spread around. Finding the appropriate balance is definitely non-trivial.

Finally, I hope this contributes to the economic debate about whether utilities are comparable at all – a very undecided question.

Suicide is Generally Bad

First, I want to point out that the naïve analysis of “figure out how many people commit suicide and assume they all have negative utility” is invalid, as it runs contrary to the evidence. Of the people who jumped off San Francisco’s Golden Gate Bridge, all 29 said they regretted it as soon as they jumped. Four years after their initial attempt, only 26% of suicide survivors later attempt suicide, and only 3% eventually die this way (this increases to 7% later on, which is still quite small).

The fact that the number of people who don’t attempt suicide later is greater than those that do imply that most people regret their suicide attempt after-the-fact, which lends evidence to the theory that suicide (on average at least) runs contrary to most attempter’s long-term preferences. So, from a preference-utilitarian perspective, suicide should generally be prevented pretty much whenever possible.

The Utility “Floor”

First note that survivors of a single suicide attempt are just as likely as survivors of multiple suicide attempts to attempt suicide again. If you think of people’s utilities as being normally distributed with random noise added at any given time, this implies that regardless of how many times someone has committed suicide, only the first should lower our expectation for their utility. I therefore conclude that suicide attempts throughout life are best modeled as independent events (after the first attempt).

This is, in some sense, fortunate, because it mitigates the issues that inevitably crop up when trying to perform inter-person utility comparison – namely, if Alice’s has a utility of 10 and Bob has a utility of 1, then if you can either spend \$10,000 on a medical treatment to extend Alice’s life by 1 year, this is equally good as a treatment that extends Bob’s life by 10 years. However, if there is something resembling a long-term-utility minimum below which few people go, these types of occasions become exceedingly rare, and we achieve the kind of egalitarianism that most people find intuitively ethical.

Because a super-majority of people who attempt suicide regret it and don’t try again, we know it would be beyond the pale of even the most extreme pessimism to assume that everyone who commits suicide has a non-positive utility. Likewise, because we have now established that repeated suicide attempts do not correlate with a lower utility-per-year, we know that people who attempt suicide multiple times are similar to people who have attempted once (in terms of risk of future attempts), so even people who attempt suicide multiple times are unlikely to have a non-positive utility.

Normal Distribution

One more thing before we get to the analysis. Throughout this post, I'll mention multiple times that I'm assuming utility follows a normal distribution (also know as the bell curve), so I'd like to briefly explain what the normal distribution is and why this assumption is somewhat reasonable.

Theoretically, what makes a normal distribution special is that the average of a large sample of independent random numbers will always approximately follow the normal distribution. This comes up quite a bit in nature.

The bell curve and the percent of the population falling with in standard-deviation intervals.

For instance, many psychological traits like IQ and the big five personality traits follow the normal distribution. This is presumably because your intelligence and personality are the result of thousands of small genes and events, rather than a few big ones. Likewise, height is normally distributed.

I don't really know whether utilitarianism is normally distributed. I merely assume this to allow for further analysis. However, given that utility is a mental phenomenon, this seems like a reasonable assumption.

Estimating a Floor

The above analysis gives a (very high) upper-bound on the number of people who have non-positive utilities: the percent of people who attempt suicide.

At this point, we’re going to try to estimate the average utility in the population. The major assumption we will make now is that utility-per-year is normally distributed in the United States. Since utility is isomorphic up to scaling, we are going to define our own scale. We will define a standard util as the utility equal to a standard deviation of the US population’s utility-per-year. So, we’re going to try to try to place a lower bound on how many standard deviations the average American is above 0 utility.

By one estimate, 5% of people aged 15-54 have attempted suicide in their lives. Naturally, this is an underestimate, because some of those people will likely go on to attempt suicide later, but how much of an underestimate is it? To figure this out, we have to look at the various ages at which people first attempt suicide and adjust our 5% figure accordingly.

While I couldn’t find data on 12, 13, and 14 year-olds, I did find that suicide is thankfully very rare among children younger than 12 compared to the general population. Suicide attempts are most common among high schoolers (8% attempt each year), followed by young adults (1.3%), middle-aged adults (0.7%), and the elderly (0.3%). I should note that I estimated these 3 statistics by cutting the number who made a plan to attempt suicide in half. I feel the data supports this, but you can judge this yourself.

What does this mean? First, the fact that suicides becomes less likely as we age implies that our “5% of people have attempted suicide” figure is less an underestimate than we may have originally thought. According to the above data, by the time you reach the average age of the sample (34.5), the probability of you attempting suicide later has dropped to just 20% of the initial amount. I don’t have the actual data, so I’m going to naively just increase the “5%” figure by a fifth to “6%”.

Recall that we called the amount of utility equal to a standard deviation in the US population a standard-util. If we take the very pessimistic view that all people who attempt (or will attempt) suicide have non-positive utility, this implies (assuming a normal distribution) that the average American roughly 1.5 standard-utils. Because our assumption was pessimistic, we can conclude that the average American has at least 1.5 standard-utils.

> qnorm(0.06)
[1] -1.554774

Estimating a Ceiling

How, then can we find an upper-bound? I think a good place to start is with physician-assisted suicide. Due to the stigma associated with suicide and the difficulty of accomplishing it with a physician, I think it’s reasonable to believe that people who attempt physician-assisted suicide probably are likely to actually prefer death to life. I think this will provide us with an upper bound.

132 people died through physician-assisted suicide in Oregon in 2015. I sadly couldn’t find the number of total deaths in Oregon, but if we assume people are just as likely to die in Oregon as elsewhere in the US, we can estimate it to be about 32,000 deaths per year. Hence, about 0.4% of deaths in Oregon are due to physician-assisted suicide.

This implies an average population utility of 2.7 standard-utils.

> qnorm(0.004)
[1] -2.65207

On the other hand, you could correctly argue that most of people who use physician-assisted suicide would die soon anyway. Imagine, for instance, that everyone used physician-assisted suicide a few days before they died, would this imply that everyone secretly had negative utility – of course, not.

I turn, then, to the United Kingdom. Physician-assisted suicide is illegal in the UK, so many Brits travel abroad to obtain it. About 16% who do so had no underlying health problem.

Bringing this back to Oregon data, we can estimate that about 0.07% of deaths are due to physician-assisted suicide of people without health problems. Using this gives us a better upper bound on average population utility: 3.2 standard-utils.

> qnorm(0.0007)
[1] -3.194651

So, we have finally put a range on the average population utility: between 1.5 and 3.2 standard-utils. This is, sadly, quite large.

Demographic Examples

Of course, we can continue making assumptions. If, for instance, we assume that a specific demographic group has

  1. A normally distributed utility
  2. the same standard deviation as the general population
  3. equal fluctuations in day-to-day utility
then we can estimate the utilities of each demographic group by looking at its suicide-attempt rate. Of course, the accuracy of these estimates depends a great deal on how accurate our assumptions are.

For instance, 13% of rape victims attempt suicide, this would imply (assuming rape victims are typical to begin with) that rape reduces utility by an average of 0.4 standard-utils. Note, however, that this does not include the utility lost do directly to the rape, only the psychological aftereffects.

> qnorm(0.13)-qnorm(0.06)
[1] 0.4283825

We can similarly compare the suicide-attempting differences between LGBT youth and non-LGBT youth to estimate the utility lost due to cultural stigma associated with non-conventional sexual orientations (assuming there would be no difference if our culture was neutral). Using the cited data, we find a difference of 0.9 standard-utils, though this is probably an overestimate, because their data assumes LGBT youth are 5.1 times as likely to attempt suicide, but studies find the ratio ranges from 2 to 5 times as likely. Using the twice-as-high figure, we can establish a lower bound at 0.3 standard-utils.

> qnorm(0.215)-qnorm(0.042)
> qnorm(0.084)-qnorm(0.042)
[1] 0.3492756

I would strongly caution trying to use any of these numbers to imply one group has it worse than another. First, there’s the obvious problem that the LGBT range contains the rape statistic, allowing no such inference. But, more importantly, all of these are very rough estimates and are probably not accurate to the significant figures written.

We can similarly estimate the cost of war-trauma on soldiers to be 0.4 standard utils, based on the fact that they are more than twice as likely to attempt suicide as the general population.

> qnorm(0.05*30/14)-qnorm(0.05)
[1] 0.4029868

Consider one more categorization: income. If we assume that the rich and poor are similar except for income, then we can figure out how much utility extra income yields. It has been found (again, sorry for secondary source), that people making less than \$34,000 per year were “50 percent more likely to commit suicide” and that people with incomes between \$34,000 and \$102,000 were 10% more likely. If we assume that the lethality rate is equal, then these are proportional to attempts and we get something like 0.21 standard-utils for moving from below \$34,000 to between \$34,000 and \$102,000 and about 0.05 standard-utils for moving from that to over \$102,000.

> qnorm(0.05*1.5)-qnorm(0.05)
[1] 0.2053222
> qnorm(0.05*1.1)-qnorm(0.05)
[1] 0.04666049

Note, that this is in keeping with the evidence that income generally makes you happier (at least within a nation), but that there are diminishing returns – though, all this changes depending on how you word the questions.

Sadly, it looks like having rich neighbors increases your odds of suicide, so increases someone’s financial well-being isn’t completely a win-win. By the by, this helps explain the apparent paradox that higher incomes correlate with higher reported well-being within a nation, but that as nations gain income, their well-being generally remains flat (cited above).


Like I said, drawing concrete economic/political/social conclusions from this post is just bad critical thinking. The main point of this post was to demonstrate that utility comparisons between groups can, in fact, be estimated, even though I do it poorly. Everything else is just examples.