If I didn’t make a calculation error, the nobles in general recommend up to a 100*max(0, 1 - (the factor by which peasants outnumber nobles)/(the factor by which each noble is richer than each peasant))% tax (which is also equivalent to 100*max(0, 2-1/(the fraction of total wealth collectively owned by the nobles))%). With the numbers given in the post, this produces 100*max(0, 1 − 1000/10000)% = 90%. But for example with a billion times as many peasants as nobles, and each noble a billion times richer than each peasant, the nobles collectively recommend no tax. When I query my intuitions though, these two situations don’t feel different. I like the symmetry in “Each noble cares about as much about themselves as they do about all peasants put together”, and I’m wondering if there’s some way to preserve that while making the tax percentage match my intuitions better.
In this model the nobles don’t recommend a further tax if in aggregate they have 50% of the total income, utility is logarithmic, and they care about themselves as much as everyone else put together.
(This is a good argument that this model may just not capture your intuition. But I do think the case for taxes is in fact quite a lot better when the nobles collectively control a large share of the income rather than just being individually wealthy.)
If I didn’t make a calculation error, the nobles in general recommend up to a 100*max(0, 1 - (the factor by which peasants outnumber nobles)/(the factor by which each noble is richer than each peasant))% tax (which is also equivalent to 100*max(0, 2-1/(the fraction of total wealth collectively owned by the nobles))%). With the numbers given in the post, this produces 100*max(0, 1 − 1000/10000)% = 90%. But for example with a billion times as many peasants as nobles, and each noble a billion times richer than each peasant, the nobles collectively recommend no tax. When I query my intuitions though, these two situations don’t feel different. I like the symmetry in “Each noble cares about as much about themselves as they do about all peasants put together”, and I’m wondering if there’s some way to preserve that while making the tax percentage match my intuitions better.
In this model the nobles don’t recommend a further tax if in aggregate they have 50% of the total income, utility is logarithmic, and they care about themselves as much as everyone else put together.
(This is a good argument that this model may just not capture your intuition. But I do think the case for taxes is in fact quite a lot better when the nobles collectively control a large share of the income rather than just being individually wealthy.)