# What percentage of utils do the top 1% pay in tax

A commonly cited statistic in American politics is the top 1% of Americans earn 20% of all income, but may 40% of all income taxes. This is measured in dollars, however, and a dollar is worth more to a poor man than a rich man.

So my question is, what percentage of the total utility loss of income taxation does the top 1% incur by paying income taxes?

Now I’m aware of issues like heterogeneity of preferences and interpersonal utility comparisons that make it hard to calculate a fully accurate figure, but are there estimates of diminishing marginal utility and the like that would allow us to get some kind of ballpark estimate at least?

We cannot perform the desired comparison.

Namely, it's not clear that one can sum utilities over multiple individuals in a meaningful way.

Utility is an ordinal measure, meaning it only cares about order. The reason the utility functions exist is because I can perform a mapping to a utility function for any list of preferences.

Example of the Mapping: If my preferences are, in order:

2. Go to Movies.
3. Play Games.

Then I can map this to the values:

1. Answer SO questions. (5 utility points)
2. Go to Movies. (3 utility points)
3. Play Games. (1 utility point)

But the points themselves are meaningless, and the difference between them and relative magnitudes are also equally meaningless. I could have also assigned them 200/3/-100 and the order and structure would be the same, this means they are ordinal. But because I can perform an ordinal assignment we can easily construct a function for lists like:

1. Consume 100 units of widgets.
2. Consume 99 units of widgets...
3. Consume 0 units of widgets...

Economics is not explicitly committed to the idea that individuals assign utility points in a remotely comparable pattern. Even if this were the case, there is no way to perform this calculation.

As an aside, however, we can look at the decline in consumption that occurs from taxation for wealthy people.

I would argue that utility theory is unfortunately meaningless in this context. As you point out, interpersonal utility comparisons don't work, I can always multiply a utility function by 10 and it will represent the same preferences.

In some studies they assume quasilinear utilites and say that money has the same value to everyone, but this assumption would go against what you are trying to measure, as you specifically want to move away from money and on to utils.

A comment on an implicit assumption of your question: taxes also pay for public goods, so it is possible that everyone gains by paying taxes compared to no one paying taxes.

My unpopular opinion is that utility theory is just a storytelling tool, which is useful if the students have a good grasp of math, but the theory is flawed in many ways. People seem to use heuristics rather than maximizitation in general contexts, preferences are sometimes revealed as non-transitive, etc.

• While I disagree with @Giskards opinion of utility theory as merely a storytelling tool, one cannot argue that comparing utility between two people in this manner cannot be done. It not just practically impossible - it may even be categorically impossible, as well. Oct 22 at 16:24
• @RegressForward I recommend you expand this comment into an answer; my unpopular opinion understandably scares voters away from mine :) Oct 22 at 21:44