Intepersonal comparisons of utility

I occasionally run into someone expressing skepticism about the validity of Warren Smith's Bayesian regret calculations, due to the fact that they employ a Utilitarian or "Benthamite" social welfare function (i.e. the social welfare for is the sum of the utilities of the members of the group). The particular criticism I refer to is that individual utilities cannot be summed because they are not "interpersonally comparable".

Let's assume, for the sake of argument, that utilities are not interpersonally comparable. In that case, the uniquely best social welfare function is the one which maximizes the expected utility of a randomly chosen voter, in his own personal units of utility. That is, the best option is the one that maximizes the average of all voters' utilities. But note that this is mathematically identical to simply summing the utilities, for any given group of voters! And therefore the complaint about not being able to perform interpersonal comparisons of utility is academic, and doesn't invalidate the social choice function Smith employed for his BR calculations.

Regarding the aforementioned Twitter conversation, this also some bearing on the applicability of "labels" to the scores listed on a Score Voting ballot. That is, some folks would like to have something like:

0 - terrible, 1 - poor, 2 - mediocre, 3 - good, 4 - great

The most obvious problem, to anyone acquainted with basic economic theory, is that this introduces error. For instance, suppose that my subjective connotation with these words is such that

u(great) - u(good) = u(good) - u(terrible)

And suppose that my utilities for some set of options are such that

u(x) - u(y) = u(y) - u(z)

Without labels, I would vote (assuming I'm a sincere voter)

x = 4, y = 2, z = 0

But if I vote using the labels, that would be

x = 4, y = 3, z = 0

This would produce a lower expected utility for me, making me worse off. Of course, if I'm a tactical voter, then it doesn't matter anyway. But why add more text than is absolutely necessary to a ballot, if it reduces the expected utility of voters? Why make the voters worse off?

There is a potential counter to this. But it appears to require that you accept the validity of interpersonal utility comparisons. Here's how it works. Suppose that Bob and Alice have the following utilities, on a universal scale.

u(x) = 8, u(y) = 6, u(z) = 0
u(x) = 8, u(y) = 6, u(z) = 4

Their sincere votes (on a 0-4 scale) would look like

x = 4, y = 3, z = 0
x = 4, y = 2, z = 0

The scaling distortion makes it appear as though they have different opinions on y, but the same opinions on z—which is precisely backwards. But suppose those labels, like "great" and "mediocre", have highly similar mappings to actual utility values for both Bob and Alice. In that case, the labels could prevent more loss than they caused—by nullifying some component of the normalization loss.

The irony here is that our friend on Twitter supported the use of labels, but opposed the validity of interpersonal utility comparisons!

The caveat is, as I said at the beginning, that a welfare function that maximizes the sum of all individuals' utilities also maximizes the expected utility of any individual voter, even if we disallow interpersonal comparisons of utility. So my aforementioned defense of labels is still equally valid, even if we don't permit interpersonal utility comparisons.

@selylidne can thank me for offering at least some evidence in support of his own argument.

The economic consequences of an economically irrational decision-making system

Amidst the hype surrounding the "fiscal cliff", some calm voices have emerged to challenge the fear mongering. One of them is Stephanie Kelton, an assistant professor of macroeconomics, finance, and money and banking at UMKC. Kelton has pointed out that the cliff is in large part a manufactured crisis. She suggests we start to address it by (among other things) repealing the Budget Control Act of 2011, whose key provisions established the cliff in the first place. She further suggests that the government should spend, and generally avoid tax increases, in order to increase the GDP (the oft-ignored denominator in debt-to-GDP ratio)—basically the opposite of what a lot of the mainstream pundits are advising.

I now want to take a step back and look at this issue from a very different perspective. The gravest danger in any calamity like this is not that we fail to fix it, but that we fail to detect underlying causes (i.e. calamity generators). Join me for a bit of abstract thinking...

Let's assume that Kelton is correct, and society is generally convinced that we need to implement the policies she's advocating. How do we do that? Well, primarily by electing people to public office who we believe will implement those policies. But imagine we're faced with an election for some highly influential position, and the preferences look like this:

33% Keltonite 1 > Keltonite 2 > Boehnerite
32% Keltonite 2 > Keltonite 1 > Boehnerite
35% Boehnerite > others

In this election, a massive 65% majority of the voters wants Keltonite policies. But if we use the ordinary vote-for-one "Plurality Voting" system, the Boeherite candidate wins with 35% of the votes. The lives of hundreds of millions of people are then significantly worse because of an obvious defect of the voting system.

But this is preventable! There are numerous other ways to vote. And voting systems can be objectively measured for "economic efficiency" using a metric called "Bayesian regret", which effectively measures average voter satisfaction. Here are some sample Bayesian regret figures from William Poundstone's book Gaming the Vote (2008).

Observe that a change from Plurality Voting to Range Voting (aka Score Voting) or Approval Voting virtually doubles the improvement gotten by the invention of democracy in the first place (the performance of Plurality Voting minus the performance of random non-democratic selection).

And these systems are very simple. Approval Voting just uses an ordinary ballot, but lets voters vote for as many candidates as they wish. The candidate with the most votes still wins. Score Voting is like Yelp reviews—you rate the candidates and the one with the most points wins. Not as simple, but more expressive.

So the question is, why aren't these economists who want to save the world talking about voting reform? If they're interested, I recommend they check out The Center for Election Science.