I think the example works fine with numbers like “the welfare effect of $1 is a hundred times larger for this poor person than that rich person”
Let’s say each noble has 10000 dollars, each peasant has 1 dollar, and peasants get 100x more utility per dollar. Then each noble’s utility is simply 10000+1x100, because each of 1000000 peasants has weight 1/1000000 which cancels out. Now let’s take 1 dollar from each noble and distribute it to peasants. That’s 1000 dollars total, so 0.001 dollars per peasant. Now each noble’s utility is 9999+(1+0.001)x100, which is a decrease. What am I missing?
There are a billion rich people and a billion poor people (and a bunch in the middle we’ll ignore)
Each rich person cares about themselves 5x as much as all poor people put together
The poor people get 100x the welfare from $1 as the rich people
Then the rich people care so little about the poor people that they wouldn’t want to donate unilaterally, but they would still support taxes to fund foreign aid until they reached the level where the poorest billion valued money only 5x more than the richest billion.
Yeah, this makes more sense. For the scheme to work, the proportion of rich people multiplied by the disparity between rich and poor has to be high enough.
Let’s say each noble has 10000 dollars, each peasant has 1 dollar, and peasants get 100x more utility per dollar. Then each noble’s utility is simply 10000+1x100, because each of 1000000 peasants has weight 1/1000000 which cancels out. Now let’s take 1 dollar from each noble and distribute it to peasants. That’s 1000 dollars total, so 0.001 dollars per peasant. Now each noble’s utility is 9999+(1+0.001)x100, which is a decrease. What am I missing?
If you want an example with more modest numbers:
There are a billion rich people and a billion poor people (and a bunch in the middle we’ll ignore)
Each rich person cares about themselves 5x as much as all poor people put together
The poor people get 100x the welfare from $1 as the rich people
Then the rich people care so little about the poor people that they wouldn’t want to donate unilaterally, but they would still support taxes to fund foreign aid until they reached the level where the poorest billion valued money only 5x more than the richest billion.
Yeah, this makes more sense. For the scheme to work, the proportion of rich people multiplied by the disparity between rich and poor has to be high enough.