Saving the Many or the Few: The Moral Relevance of Numbers

Author: Theron Pummer
Category: Ethics 
Word Count: 1000

To your left, three strangers are drowning. To your right, one other stranger is drowning. You can effortlessly save the three by throwing a lifebuoy to your left. Alternatively, you can save the one by throwing the lifebuoy to your right. You cannot save all four.

What should you do? It’s wrong to do nothing, but is it wrong to save just the one stranger? Are you morally required to save the three?

Many claim that, when those you can help are innocent strangers with similar interests at stake, you’re required to save the greater number.

Is this claim justified? This essay reviews some doubts.

Four strangers: you can either save the three (left) or the one (right).
Four strangers: you can either save the three (left) or the one (right).

1. Who Is Wronged?

If there is a requirement to save the three drowning strangers over the one, then it must be wrong to save the one. But consider the following skeptical argument:[1]

  1. Saving the one does not wrong anyone.
  2. If saving the one is wrong, there must be someone it wrongs.
  3. Therefore, saving the one is not wrong.

First, consider (1). If you save the one, who is wronged? Take any one of the three. It may seem this person cannot reasonably complain about the fact that you saved the one instead. After all, were it between saving this person and saving the one, you’d wrong neither one if you saved the other—at least, assuming you used a fair method of selection, like flipping a coin.[2] 

But arguably, if you save the one over the three, each of the three could reasonably complain that you didn’t appropriately value her life. For example, each could ask, “Why’d you save that person at the cost of three lives, but didn’t save me at the cost of just one life?” So, contrary to (1), you would be wronging someone by saving the one. In fact, you’d be wronging each of the three.[3]

Some reject (2), claiming that saving the one is wrong because it fails to bring about the most happiness. But if it’s wrong not to bring about the most happiness, it’d be wrong to save the life of a moderately happy person instead of saving the life of a very happy person. Many deny this.[4]

2. Limited Addition

Does the requirement to save the greater number hold only when the interests at stake for each are similar?

Suppose the interests are very different. Suppose we’re scheduled to air a surprise commercial at the end of the World Cup, bringing laughs to billions. But then Jones gets trapped under some of our equipment, causing him extremely painful electrical shocks. We can still air our funny commercial, but only if we leave Jones in agony for an hour.[5]

Many believe we’re morally required to save Jones from agony rather than bring laughs to billions.

Some take cases like this to support a “limited addition” view, according to which:

  • when what is at stake for each person is sufficiently similar (deaths versus deaths), you are required to save many more over fewer; but,
  • when what is at stake for each is sufficiently different (deaths versus headaches), you are required to save those with more major interests at stake, regardless of the numbers.[6]

This view may be unstable. Suppose you have three alternatives:

(i)   save one person from intense pain;
(ii)  save many people from moderate pain;
(iii) save many many people from mild pain.

Assume intense pain is sufficiently similar to moderate pain, moderate pain is sufficiently similar to mild pain, and intense pain and mild pain are sufficiently different.[7] Given this, the limited addition view seems to have the implausible implication that you must choose (ii) over (i), (iii) over (ii), and (i) over (iii).[8]

Defenders of the limited addition view might respond that, while you must choose (ii) over (i) when these are the only alternatives, and while you must choose (iii) over (ii) when these are the only alternatives, things are importantly different when all three alternatives are available.[9]

We could instead try to limit the requirement to save the greater number to cases in which the interests at stake for each are exactly similar, but then you’d almost never be required to save a group in virtue of its containing a greater number of people. And that seems implausible.

3. Favoring the Few

According to another skeptical argument, if it’s not wrong to save your friend over three strangers, then it’s not wrong to save one stranger over three others.[10]

It is hard to deny that the special connection you have to your friend makes it permissible to favor them over strangers. But then it’s at least questionable whether you have a sufficiently special connection to the one stranger.[11] 

What sorts of connections between you and the one can make it permissible to favor them over others? Suppose that, while the one is not your close friend, they are an acquaintance—you wave to each other on your journey to work. And arguably you can form a relevant connection without any shared history, as in love at first sight.[12] Or you might empathize with the one in particular.

Even if such minimal connections could make it permissible to save the few, they apply to a limited range of cases. Suppose that four strangers are drowning: three a mile west, one a mile east. You can send a rescue team in either direction. That’s all you know. Here it seems you’d have no basis for favoring the one. Many cases of charitable giving are like this in that your information is impersonal—one charity saves one life on average per $X donated whereas another saves three.[13] 

Finally, suppose your choice is between saving one nearby stranger, who is looking into your eyes while drowning, or saving three anonymous distant strangers. Must you then save the one?[14]

4. Conclusion

Here we’ve reviewed some doubts about the requirement to save the many over the few.[15] Determining the plausibility and scope of this requirement may have important implications not only for emergency rescues, but also for issues like charitable giving and healthcare allocation.[16]


[1] From Anscombe 1967. Also see Munoz-Dardé 2005.

[2] On selecting fairly, see Broome 1990 and Walden 2014. Some believe it’s permissible to select based on facts like who’s to your left, who’s closer, or who you see first, rather than employ a randomizing procedure like a coin flip.

[3] For discussion, see Otsuka 2006 and Kumar 2011. See Zhang (unpublished) on the complaint from each of the three that you didn’t save her at the cost of one life, but saved the one at the cost of three lives.

[4] For example, see Doggett 2013 and Pummer 2023 (chapter 2).

[5] This is a modified version of a famous case from Scanlon 1998 (235).

[6] Defenders of this sort of view include Kamm 1993, Scanlon 1998, and Voorhoeve 2014. What I’m calling a “limited addition” view is better known in the literature as a “limited aggregation” view, “restricted aggregation” view, or “partially aggregative” view. See Horton 2021 for a comprehensive discussion of such views and objections to them.

[7] Rather than three pains (intense, moderate, and mild), we could appeal to a sequence of pains, beginning with very intense pain and ending with very mild pain, where each pain in the sequence is only slightly less bad than its predecessor. This would make it very difficult to deny that adjacent pains are sufficiently similar. See, for example, Norcross 1997.

[8] When your alternatives include (i), (ii), and (iii), the fact that you must choose (ii) over (i) seems to imply that (i) is impermissible, the fact that you must choose (iii) over (ii) seems to imply that (ii) is impermissible, and the fact that you must choose (i) over (iii) seems to imply that (iii) is impermissible. The result is that each of your alternatives is impermissible. But even if the choice between (i), (ii), and (iii) is a difficult one, it’s hard to believe you’re doomed to choose impermissibly.

[9] For further discussion, see Kamm 1993, Voorhoeve 2014, and Horton 2021.

[10] From Taurek 1977.

[11] See Parfit 1978.

[12] See Setiya 2014.

[13] For example, see GiveWell is an organization devoted to assessing charities that help people in extreme poverty in terms of average benefit delivered per dollar donated.

[14] See Woollard 2015 (156), Mogensen 2019, and Pummer 2023 (chapters 5 and 6).

[15] Sung 2022 argues that, even if you’re almost certain that it’s permissible to save the few, you still ought to save the many just in case.

[16] I explore the scope of this requirement in Pummer 2023, with a focus on donating time and money to help strangers living in extreme poverty. On the relevance of numbers in the context of healthcare allocation, see Kamm 2013.


Anscombe, Elizabeth. 1967. “Who Is Wronged?” Oxford Review 5: 16–17.

Broome, John. 1990. “Fairness.” Proceedings of the Aristotelian Society 91: 87–101.

Doggett, Tyler. 2013. “Saving the Few.” Nous 47: 302–315.

Horton, Joe. 2021. “Partial Aggregation in Ethics.” Philosophy Compass 16: 1–12.

Kamm, Frances. 1993. Morality, Mortality. Volume I: Death and Whom to Save from It. New York: Oxford University Press.

Kamm, Frances. 2013. “Aggregation, Allocating Scarce Resources, and the Disabled.” In Bioethical Prescriptions: To Create, End, Choose, and Improve Lives. New York: Oxford University Press.

Kumar, Rahul. 2011. “Contractualism on the Shoal of Aggregation.” In Reasons and Recognition: Essays on the Philosophy of T. M. Scanlon, eds. R. Jay Wallace, Rahul Kumar, and Samuel Freeman, New York: Oxford University Press, pp. 129–154.

Mogensen, Andreas. 2019. “The Callousness Objection.” In Effective Altruism: Philosophical Issues, eds. Hilary Greaves and Theron Pummer, Oxford: Oxford University Press, pp. 227–243.

Munoz-Dardé, Véronique. “The Distribution of Numbers and the Comprehensiveness of Reasons.” Proceedings of the Aristotelian Society 105 (2005): 191–217.

Norcross, Alastair. 1997. “Comparing Harms: Headaches and Human Lives.” Philosophy and Public Affairs 26: 135–16.

Otsuka, Michael. 2006. “Saving Lives, Moral Theory, and the Claims of Individuals.” Philosophy and Public Affairs 34: 109–135.

Parfit, Derek. 1978. “Innumerate Ethics.” Philosophy and Public Affairs 7: 285–301.

Pummer, Theron. 2023. The Rules of Rescue: Cost, Distance, and Effective Altruism. New York: Oxford University Press.

Scanlon, T. M. 1998. What We Owe to Each Other. Cambridge, MA: Harvard University Press.

Setiya, Kieran. 2014. “Love and the Value of a Life.” Philosophical Review 123: 251–280.

Sung, Leora. 2022. “Never Just Save the Few.” Utilitas 34: 275–288.

Taurek, John. 1977. “Should the Numbers Count?” Philosophy and Public Affairs 6: 293–316.

Voorhoeve, Alex. 2014. “How Should We Aggregate Competing Claims?” Ethics 125: 64–87.

Walden, Kenneth. 2014. “The Aid That Leaves Something to Chance.” Ethics 124: 231–241.

Woollard, Fiona. 2015. Doing and Allowing Harm. Oxford: Oxford University Press.

Zhang, Erik. Unpublished. “Individualist Moral Theories and Interpersonal Aggregation.”

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About the Author

Theron Pummer is a Senior Lecturer in Philosophy at the University of St Andrews. Previously he was a Junior Research Fellow in Philosophy at the University of Oxford. He is the author of The Rules of Rescue: Cost, Distance, and Effective Altruism (Oxford University Press, 2023). His articles have appeared in The Journal of Philosophy, Philosophical Review, Ethics, Philosophy and Public Affairs, and Philosophy and Phenomenological Research.

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