Possibly something like "All else being equal, a poor person will gain more utility from a dollar than a rich person would"? Even that has problems but that seems slightly better.
Actually, that's semantically equivalent to rephrasing #1, and as such semantically contradictory to rephrasing #2.
A rich person might for example still base much of his self-worth on how much money he has but each dollar will be a smaller amount of self-worth.
I figured someone might raise this objection. :)
Let's define the "rich" person as owning 10,000,000 dollars, and the poor person as owning 1,000. If the rich person places a high proportion on his self-worth on how much money he owns (say, 80% of his self-worth) then 10,000,000+1 yields an increase of self-evaluation by 0.00000008. If, however, the poor person places .001% of his self-worth on how much money he owns, then 1,000+1 yields an increase of 0.00000001. So the rich person's "self-worth score" in this scenario is increased by a factor of 8 as compared to the poor person's.
Now, is it likely that poor people, lacking money, will place any but the weakest of weightings onto how they judge themselves as people based on the amount of money they currently possess? Is the opposite likely?
That, then, becomes the nature of the question.
You fail to understand what rich and poor mean. While a rich person may be using dollars to keep score, a poor person is using them to stay alive.
Do you really think that someone with a million dollars could care about each one of them as much as someone who has only one dollar cares about his one dollar? That the million dollar owner could be more devastated by the loss of two of his million dollars than the one-dollar owner will be by the prospect of not eating if he loses his one dollar?
A article in the Atlantic, linked to by someone on the unofficial LW IRC channel caught my eye. Nothing all that new for LessWrong readers, but still it is good to see any mention of such biases in mainstream media.
I break here to comment that I don't see why we would expect this to be so given the reality of academia.