Ten thousand and a million feel the same when a decision is being made

The response that refuses to scale

Ask people what they would pay to prevent some harm, and vary the number of cases the payment would prevent across a wide range. The stated amounts move remarkably little. Studies using this design, most famously with the number of birds saved from oil-contaminated ponds, have found that multiplying the quantity affected by a large factor produces only a small change in what people say they would give.

The pattern has been reproduced with different goods and different populations, and it’s one of the awkward results underneath the long-running dispute about whether surveys asking people to value things they don’t buy produce meaningful numbers at all. That dispute is genuine and unresolved. What isn’t in much doubt is the shape of the response: quantity is barely read.

What the mind is doing instead

The leading account is that the response is generated by an image rather than by a count. Asked about harm to birds, a person forms a representation of an affected bird, feels something about it, and translates the feeling into a figure. The number in the question never enters that process, because a mental image of one case and a mental image of many cases are much the same image.

This account also predicts the asymmetry people notice in their own reactions to news. A single identified individual in difficulty produces a strong response; a statistic covering a large population produces a weaker one, sometimes weaker in absolute terms despite describing vastly more harm. The identified case supplies the image directly. The statistic asks the mind to do arithmetic it does not do.

Where this quietly governs decisions

Anywhere resources are allocated between problems of different sizes. If the felt urgency of a problem is roughly independent of how many people it affects, then attention distributes according to vividness, proximity and how easily a case can be pictured, which are properties of the presentation rather than of the problem.

It also governs how individuals give and volunteer, and the effect there isn’t a moral failing so much as an unavoidable feature of a system that runs on images. A person moved by one case and unmoved by ten thousand isn’t being inconsistent on purpose. The two inputs are being processed by different faculties, only one of which was ever consulted.

The arithmetic correction, and why it feels wrong

The available fix is to insist on the calculation explicitly: cost per case, cases affected, harm avoided per unit spent. Doing this reliably changes the answer, because it routes the question through a system that can actually count. It is also uncomfortable, and the discomfort is worth taking seriously rather than dismissing as squeamishness.

Part of the discomfort is that the calculation ignores things people legitimately value — who is responsible, whether a duty was owed, whether the harm was inflicted or merely allowed. Those are real considerations that a per-case figure discards. The honest position is that scope insensitivity is a defect in how magnitude is perceived, and that correcting it does not by itself settle the moral questions the numbers were standing in for.

Detecting it in a presentation

A useful check on any appeal, pitch or proposal is to ask whether the number would change your response if it were ten times larger or ten times smaller. If not, the number is decoration and the response is being produced by something else, which is worth knowing before you act on it.

The reverse check is just as useful. When a proposal is described entirely in aggregate terms, ask what a single instance looks like, because a figure with no image attached tends to be underweighted just as badly in the other direction. Neither presentation is honest by itself. A description that includes both the case and the count is asking the reader to use both faculties, which is the most anyone can do.

The limit of the criticism

It would be a mistake to conclude from this that human responses are simply broken and should be replaced by spreadsheets. The image-based response is what makes anybody care about anything at all, and a purely computational allocation would be paralysed by the absence of any reason to prefer one outcome to another.

What the finding supports is narrower and more workable. Feeling is a good detector of whether something matters and a poor instrument for measuring how much. Use it to notice the problem and use arithmetic to size it, and be suspicious of any presentation that is careful to supply only one of the two.