My Answer to the 1% Question

A couple of days ago, I raised the 1% question, holding off on my answer. Here it is:

I would clearly take the $1 million/year over raising everyone's income by 1%. I'm not sure how high the number would have to be in order for me to decline the $1 million, but it's at least 10%. Why is this?

1. 1% is very, very little. I don't think I'd really notice a 1% increase in my income. (If I got it in a lump sum, I would, but if it was spread out over the year, I would not notice.) So I don't see a 1% increase as doing much for anyone. I understand that we would be adding those small utility increases over a lot of people, but this is not convincing to me. Because I know that I get a huge utility increase from $1 million/year. (This maybe means that I do not have additive utility in my social welfare function.)
2. With $1 million/year, I can take a nice increase in my personal utility, and still have a very strong social impact locally. I can't raise the income of the poor by $10 billion or whatever, but I could build house for the poor in my community, or buy mosquito nets in Africa, or create scholarship programs, etc. There's two benefits here, one selfish and one not. The selfish benefit is that I get to observe, witness, participate in, and be recognized for these local gifts; the Chinese gift is anonymous and abstract to me. The non-selfish benefit relates to #1: I don't believe the 1% really helps much (if at all) and these gifts have large impacts, even if on a small number of people. (Again, it seems that I do not have a additive social welfare function.)

What bothers me about my choice?

1. What do I believe about individual utility functions then? I don't think that a 1% increase in income is really going to make a difference for anyone. I can convince myself that there are some people who are on the margin for big needs (paying for housing/schooling/food/medical care/etc), but I can't convince myself that there are many like this. Shouldn't I believe that utility functions are increasing? If so, then even a tiny increase, accumulated over a billion Chinese, is a lot of increased happiness...
2. As suggested above, the way to reconcile this is that I have some sort of non-additive social welfare function such that a huge increase for a small number of people is more valuable than a small increase for a huge number of people; I don't think this is crazy. I can handle it. But what is the functional form of this welfare function? Would I be consistent in applying it? For example, doesn't this imply that I would vote for a re-distribution that takes 1% percent away from everyone in China and gives it to me? Or to someone else?
   
3. I'm destroying a lot of wealth. As noted in the last post, a 1% increase in everyone's income in China is something on the order of $70-$90 billion. That's 70,000 to 90,000 times larger than my income increase! That is, the price ratio is hugely in favor of giving the 1% increase to the Chinese. Framing the question that way makes me question my choice. Even a 0.1% increase is a price ratio of approximately 7,000-9,000.

But I can't get around the fact that I think the world (ok, my world) is better off with me having $1 million/year more rather than the Chinese having 1% more. The next question for me to determine is if I would make the same choice if the $1 million went to someone like me, who is not me. I think I would, but am obviously less sure. I want to say yes, because this suggests my choice is based primarily on my beliefs about utility functions and social welfare functions rather than greed.