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Adding Up Small Benefits

July 26th, 2014
giving  [html]
If you could give everyone in the world one extra second, would that be more or less helpful than dividing those seconds among fewer people? For example, with the same number of seconds you could give 81k people each an extra day. My initial impression is that a second is nearly useless while a day lets you do all sorts of things, but is 81k people so much less than 7b that it makes up for this?

One contributing factor here is scope insensitivity. People are good about thinking about things at human scale, but as the numbers get bigger our capacity to visualize and make intuitive comparisons stops working well. If we hear that one person was injured in a flood vs four people we can imagine clearly the difference between one person and four, but if we hear that it was 100k vs 10k people we think in both cases "that's horrible!" and "huge numbers of people!". We can resort to simple math and see that 10x people being injured is probably something like 10x worse, but emotionally 100k and 10k just feel enormous.

For me at least, scope insensitivity does explain a big part of my confusion over seconds vs days. The same intuition that tells me an extra day for 81k people is better than an extra second for everyone tells me that this is even true if it's only one person that gets the extra day. My brain just doesn't intuitively understand numbers as big as seven billion. There has to be, however, some number of people large enough that giving them all seconds is better than giving one person a day, and I doubt a second that comes as part of an entire extra day is tens of thousands of times more useful than an extra second that comes on its own.

What is the conversion? Do we have increasing or decreasing marginal returns on additional time? Would you rather have a 1% chance of getting an extra day or a 50% chance of getting an extra half hour? The simple thing to do would be to treat every second as about as valuable, linear returns, but is that actually what's going on?

(This comes up with evaluating optimizations that speed things up for users. If your optimization saves someone a half a second 1B times a day, that's fifteen extra years of life worth of seconds per day. But is this equivalent to giving fifteen people each an extra year of life?)

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