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Moral Aggregation: What do headaches and speed limits have in common?

By Jack Walker - Philosophy Student @ Churchill College, Cambridge


When making ethical decisions, not everybody can win out. Sometimes, we are forced to make decisions where one group must be disadvantaged in order to help some other group. For example, think of a situation where we only have a limited amount of a drug used for treating some common disease. In this case, we will need some way of deciding who gets helped and who doesn’t. When philosophers start thinking about how to make these kinds of decisions, tricky cases tend to come out of the woodwork, especially those involving aggregationof harms across different people. By ‘aggregation of harms’ here I just mean combining harms that different people experience in order to make something bigger. Aggregation is an idea we make use of all the time in ethical decision making, since it seems to be the thing we appeal to when making certain kinds of trade-offs. For example, we might think it would be better to cure fifty people with headaches than just one person with a sprained ankle, or to save five people from an oncoming train rather than a single individual, because in both cases the former can be added together to make something many times worse than the latter.


This seems plausible enough so far but quickly runs into difficulties. For example, consider a situation that Alastair Norcross describes where, “a vast number of people are experiencing fairly minor head- aches, which will continue unabated for another hour, unless an innocent person is killed, in which case they will cease immediately. There is no other way to avoid the headaches.” The question that Norcross asks when posing this scenario is whether we are allowed to kill the innocent person in order to prevent the headaches. In other words, is there some number of headaches such that when we aggregate them, they could be more important than the moral value of an innocent life? Let’s say that if we answer ‘yes’ here then we accept the principle ‘Lives for Headaches’.


Accepting Lives for Headaches is hugely counterintuitive. How could it possibly ever be right to kill an innocent person in order to spare others the pain of having a headache? Even if there were a lot of headaches going on, it seems unconscionable that something so small and inconsequential could possibly outweigh something so important. We might be tempted to say that the two types of harm are just incomparable. However, this seems like a difficult argument to make if we accept the idea of continuity. Continuity here means that for every harm, there is some lesser harm a big enough amount of which will outweigh the first harm. For example, it might be better to cure fifty cases of full body paralysis than to save one life. However, we might then next think that it is better to cure fifty cases of partial paralysis than one case of full body paralysis. This can then be repeated on and on until we get to situations where we are dealing with very large numbers of very small harms e.g. it is better to cure fifty headaches than a sprained ankle. At this point it seems like the thing at the top and the bottom of the chain must be comparable since they are linked by all the steps in between. In other words, if we accept continuity and aggregation then it seems like we must agree that there is some number of headaches at which we must accept Lives for Headaches.  


One classic response here is to deny that we can aggregate harms across people, but this also seems problematic. We appeal to aggregation as a standard part of our moral decision making and it gives us a really compelling explanation as to why it is, for example, better to save five people than one person in cases like the Trolley Problem.


To my mind, the best response here is just to bite the bullet and accept that Lives for Headaches is true for some very high number of headaches. Indeed, accepting this principle isn’t quite so counterintuitive as we might at first think. One reason for this is that we are already committed to similar principles in other cases which seem unproblematic (this is what is known as a ‘Companions in Guilt’ style argument). For example, think about speed limits on motorways. Thousands of people die in accidents on motorways every year and having lower speed limits would likely lead to fewer deaths. If we set the speed limit on motorways to 50mph, many lives would be saved. However, this would also lead to small inconveniences for many people, such as longer journeys. This is the same trade off as Lives for Headaches – many small inconveniences weighing against one big harm - yet it seems much more plausible when put in these terms.


Unless we can find a principled difference between the two cases, it seems like we need to adjust either our attitudes towards the morality of higher speed limits or our intuitions regarding Lives for Headaches. In my opinion, it seems much easier to accept that our intuitions are wrong about the latter, especially when we consider how our intuitions about harm are often unreliable when it comes to matters of scope. Yudkowsky gives a strong example of scope insensitivity when he references a study examining peoples’ moral decision making regarding saving birds from drowning in oil spills. When asked how much they would pay to save 2,000 birds vs 200,000 birds from drowning, subjects responded with an average of $80 and $88 respectively. Even though the latter is a hundred times worse, the amount that people were willing to spend only increased by 10%. This shows that the scope of the harm at issue actually had little effect on how people felt to respond to it. Here the problem is a failure ofconceptualisation – nobody can possibly imagine 2,000 birds at one time, let alone a hundred times that. As such, we find it difficult to generate an intuition that accurately reflects the stakes at hand. We can apply the same insight to the comparison between headaches and lives. The reason why people are intuitively so inclined to reject the Headaches for Lives trade-off is because they are unable to adequately conceptualise the true harm that, say, a billion headaches represents.


This debate may seem abstract and academic but is important for real life cases where we weigh the major interests of the many against the major interests of the few. Where we stand on these philosophical debate will affect how we feel about a wide range of issues, from speed limits to minority rights to mask mandates. As such, it is important that we are able to think about aggregation deeply and rigorously – lives (and headaches) may well be on the line.

Further reading:

  1. Johann Frick’s lectures on ethics on YouTube -

  2. Alastair Norcross – Comparing Harms: Headaches and Human Lives

  3. Dale Dorsey – Headaches, Lives and Value

  4. Eliezer Yudkowsky – Scope Insensitivity -


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