Once upon a time, three groups of subjects were asked how much they would pay to save 2,000 / 20,000 / 200,000 migrating birds from drowning in uncovered oil ponds. The groups respectively answered $80, $78, and $88.1 This is scope insensitivity or scope neglect: the number of birds saved—the scope of the altruistic action—had little effect on willingness to pay.
Similar experiments showed that Toronto residents would pay little more to clean up all polluted lakes in Ontario than polluted lakes in a particular region of Ontario, or that residents of four western US states would pay only 28% more to protect all 57 wilderness areas in those states than to protect a single area.2 People visualize “a single exhausted bird, its feathers soaked in black oil, unable to escape.”3 This image, or prototype, calls forth some level of emotional arousal that is primarily responsible for willingness-to-pay—and the image is the same in all cases. As for scope, it gets tossed out the window—no human can visualize 2,000 birds at once, let alone 200,000. The usual finding is that exponential increases in scope create linear increases in willingness-to-pay—perhaps corresponding to the linear time for our eyes to glaze over the zeroes; this small amount of affect is added, not multiplied, with the prototype affect. This hypothesis is known as “valuation by prototype.”
An alternative hypothesis is “purchase of moral satisfaction.” People spend enough money to create a warm glow in themselves, a sense of having done their duty. The level of spending needed to purchase a warm glow depends on personality and financial situation, but it certainly has nothing to do with the number of birds.
We are insensitive to scope even when human lives are at stake: Increasing the alleged risk of chlorinated drinking water from 0.004 to 2.43 annual deaths per 1,000—a factor of 600—increased willingness-to-pay from $3.78 to $15.23.4 Baron and Greene found no effect from varying lives saved by a factor of 10.5
A paper entitled “Insensitivity to the value of human life: A study of psychophysical numbing” collected evidence that our perception of human deaths follows Weber’s Law—obeys a logarithmic scale where the “just noticeable difference” is a constant fraction of the whole. A proposed health program to save the lives of Rwandan refugees garnered far higher support when it promised to save 4,500 lives in a camp of 11,000 refugees, rather than 4,500 in a camp of 250,000. A potential disease cure had to promise to save far more lives in order to be judged worthy of funding, if the disease was originally stated to have killed 290,000 rather than 160,000 or 15,000 people per year.6
The moral: If you want to be an effective altruist, you have to think it through with the part of your brain that processes those unexciting inky zeroes on paper, not just the part that gets real worked up about that poor struggling oil-soaked bird.
1 William H. Desvousges et al., Measuring Nonuse Damages Using Contingent Valuation: An Experimental Evaluation of Accuracy, technical report (Research Triangle Park, NC: RTI International, 2010).
2 Daniel Kahneman, “Comments by Professor Daniel Kahneman,” in Valuing Environmental Goods: An Assessment of the Contingent Valuation Method, ed. Ronald G. Cummings, David S. Brookshire, and William D. Schulze, vol. 1.B, Experimental Methods for Assessing Environmental Benefits (Totowa, NJ: Rowman & Allanheld, 1986), 226–235; Daniel L. McFadden and Gregory K. Leonard, “Issues in the Contingent Valuation of Environmental Goods: Methodologies for Data Collection and Analysis,” in Contingent Valuation: A Critical Assessment, ed. Jerry A. Hausman, Contributions to Economic Analysis 220 (New York: North-Holland, 1993), 165–215.
3 Daniel Kahneman, Ilana Ritov, and David Schkade, “Economic Preferences or Attitude Expressions?: An Analysis of Dollar Responses to Public Issues,” Journal of Risk and Uncertainty 19, nos. 1–3 (1999): 203–235.
4 Richard T. Carson and Robert Cameron Mitchell, “Sequencing and Nesting in Contingent Valuation Surveys,” Journal of Environmental Economics and Management 28, no. 2 (1995): 155–173.
5 Jonathan Baron and Joshua D. Greene, “Determinants of Insensitivity to Quantity in Valuation of Public Goods: Contribution, Warm Glow, Budget Constraints, Availability, and Prominence,” Journal of Experimental Psychology: Applied 2, no. 2 (1996): 107–125.
6 David Fetherstonhaugh et al., “Insensitivity to the Value of Human Life: A Study of Psychophysical Numbing,” Journal of Risk and Uncertainty 14, no. 3 (1997): 283–300.
I'm not sure I buy that this is completely about scope insensitivity rather than marginal utility and people thinking in terms of their fair share of a kantian solution. Or put differently, I think the scope insensitivity is partly inherent in the question, rather than a bias of the people answering.
Let's say I'd be willing to spend $100 to save 10 swans from gruesome deaths. How much should I, personally, be willing to spend to save 100 swans from the same fate? $1000? $10,000 for 1,000 swans? What about 100,000 swans -- $1,000,000?
But I don't have $1,000,000, so I can't agree to spend that much, even if I believe that it is somehow intrinsically worth that much. When I'm looking at what I personally spend, I'm comparing my ideas about the value of saving swans to the personal utility I give up by spending that money. $100 is a night out. $1000 is a piece of furniture or a small vacation. $10,000 is a car or a year's rent. $100,000 is a big chunk of my net worth and a sizable percentage of what I consider FU money. As I go up the scale my pain increases non-linearly, and my personal pain is what I'm measuring here.
So considering a massive problem like saving 2 million swans, I might take the Kantian approach. If say, 10% of people were willing to put $50 toward it, that seems like it would be enough money, so I'll put $50 toward it figuring that I'd rather live in a world where people are willing to do that than not.
Like many interpretations of studies like this, I think you're pulling to trigger on an irrationality explanation too fast. I believe that what people are thinking here is much more complicated than you're giving them credit for and with an appropriate model their responses might not appear to be innumerate.
It's a hard question to ask in a way that scales appropriately, because money only has value based on scarcity, so you can't say "If you are emperor of a region with unlimited money to spend, what it is worth to save N swans?" because the answer is just "as much as it takes". Money only has value if it is scarce, and what you're really interested in is "Using 2007 US dollars as units: How much other consumption should be foregone to save N swans?". But people can only judge that accurately from their own limited perspective where they have only so much consumption capacity to go around.
Exactly what I was thinking while I was reading this! Perhaps the example used isn't a good one.