## Does "utility" exist?

by Clay Shentrup & Warren D. Smith

We've encountered a surprisingly large number of people who claim "utility does not exist" – or that while it may exist for one person, it is invalid or meaningless to compare utilities between persons – or that while you can talk about one person's preferring A over B ("ordinal preference"), it is invalid or meaningless to quantify the intensity of such preferences.

If that is really their (un)belief, we have trouble understanding how those people manage to survive and handle the challenges of everyday life. We suspect they actually do believe in and use interpersonal numerical utility all the time, they simply don't realize they are doing so.

We are now going to give two quick arguments why quantitative multiperson utility is a necessary idea – foolishly demanding it be ignored would hurt humanity hugely. These arguments are not intended to be a "mathematical proof" nor intended to be a complete discussion about utility arguments, concepts, axioms, and limitations. They intend merely to provide a few quick insights.

### Revealed preference

The economic concept of "revealed preference" is illustrated by the phrase "put your money where your mouth is." E.g, if someone claims his dog is worth more than a million dollars, we could test his sincerity by offering him a million dollars for the dog. For those who claim disbelief in interpersonal utility comparisons, we say: "Would you prefer to

1. deprive two people of their dessert, or
2. deprive one of his next week of food."

If you agree that the former option is more benevolent, then you are acknowledging it is kinder to cause harm to more people if the intensity of the harm is less, or at least acknowledging that intensity can be interpersonally compared, and doing so can be important.

### Lotteries

Which would you prefer for 1000 people?

1. 10 people are killed while 990 are left alone
2. 200 are killed, but only with probability=p; otherwise all 1000 are awarded a bag of gold and magical cures for their current health problems.

If you agree that the choice of which is better, depends on the precise value of p (e.g. if p=100% or nearly enough, then the first choice is better; if p=0 or nearly enough then the second choice is better) – and if you agree your choice of p depends on the precise kind of harm-or-help the people experience (e.g. would be affected by replacing "200 die" by "200 lose a shilling" and/or "bag of gold" by "a peanut") – then you've conceded that some quantitative notion of utility for those 1000 people exists. You seem to need numerical utility measures to compare such choices sensibly in the presence of uncertainty ("probability p").

### Were those realistic?

Yes. The first example is the sort of thing any judge, or lawmaker making laws about crime, needs to (or ought to) consider. The second is the sort of thing everybody involved in a medical experiment needs to consider. Would you really prefer that everybody making these decisions ought to start with the view that he/she should refuse to think about utility or quantitative utility for multi-person sets because that's invalid and meaningless??

About the history of utility concepts