Your Utility Function Does Not Compute

Last week, I wrote about some of the ways that we show that we don’t truly value everyone equally, despite the prevalence of such principles in popular discourse and the Declaration of Independence that we celebrated on Tuesday.

This week, I’d like to take a look at a couple more aspects of modern life that don’t make any sense to me from this perspective.


Growing up in a somewhat suburban neighborhood, my only interactions with most neighbors came when I would knock on their door on two yearly occasions: Halloween, and whenever my baseball team had a popcorn fundraiser.

These fundraisers were clearly optimized to act like a game to us kids, with the standard “All of the following, plus…” reward structure. It was fun to try to hit those targets and get the rewards.

Looking back on it now, though, it all seems like a huge waste of effort. Kids go around to their neighbors essentially begging for a small donation to their cause in exchange for some small treat. They then have to put in a lot of work to distribute those treats to their neighbors. You then have to reward the kids for all of this effort with prizes, when then take a cut out of the value that the organization was originally trying to get, yet still criminally underpaying the kids for the effort.

It gets even more ridiculous to see teenagers and adults holding bake sales or car washes to raise a meager amount of money for some cause. As the Babylon Bee appropriately satirized, Successful Bake Sale Raises Over Two Dollars for Missions Trip.

I’m sure that bake sales and similar sorts of fundraisers started out as innocent attempts to try to make asking for money a little less awkward. Instead of simply donating, you get this token of appreciation in return. Given the difference between the cost of ingredients and of baked goods in typical grocery stores, this seemed to some like a reasonable way to turn some spare time into money.

But taking a step back, we have another word for activities that we spend time on to make money: work. And seen in that context, baking, washing cars, and distributing goods to neighbors is either a criminally underpaid profession or simply a way to get around restrictions on child labor.

If you want to support some cause, just give money. If your cause needs support, just be up-front and ask for money. At our church, when a couple of the women wanted support to go on a missions trip, they just spoke about what they’d be doing and people designated their donations in the weekly offering. I was counting the offering that day, and we simply recorded those funds under a separate account for them. Simple as that.

Sometimes you can ask for money from an appropriate organization to support you. When my school’s Science Olympiad team made it to nationals (which happened pretty much every year), our coach would ask the district school board for funding to pay for our flights, which also gave him a chance to brag about us and give the school board a chance to learn about something positive going on at their schools. We heard stories, however of other schools having to put more effort into fundraising than preparing for the actual competition. In my view, that ruined the whole point of it all, which was the time spent learning through preparing for the competition.

You’d be surprised how generous some people can be. For the first two issues of our MIT Et Spiritus publication, the Day Foundation, an organization devoted to (among other things) starting up journals like these around the country, covered all of our publication costs. As we mature, though, they’re trying to wean us off of that funding, so we’ve been seeking a broader donor base of churches and MIT Christian fellowships to support us. In the process of asking around, one of our co-editors-in-chief went to the pastor of Park Street Church to ask for a donation, and he offered to pay for an entire issue. It’s a one-time solution, but will help us bridge the gap to that broad base of local donors to ultimately sustain the journal long-term.


Last post, when explaining what the ethic of equality means, I offered utility functions as a way to understand it:

In utilitarian terms, this means that we should act in order to maximize the sum of everyone’s personal utilities. Perhaps we should add a slight discount term on other people’s preferences due to our uncertainty about them. Otherwise, we might end up like the proverbial long-married couple who always split a piece of bread opposite to their preferences because they were just trying to be loving and thought the other person shared their preferences. But apart from those lower-order terms, this ethic means that we should be just as satisfied with someone else getting some benefit than ourselves.

Utilitarianism is sometimes seen as controversial, but I don’t think people fully grasp why. The claim that you can write down which states of the world you prefer over which other states of the world you prefer into a total ordering that can be mapped onto the real numbers should not be controversial; it actually follows from some simple assumptions like transitivity. The more important assumption is that this function isn’t completely opaque, and can actually be reasoned about.

The ethic of summing utility functions plays off of this more subtle assumption. Of course, we’d have to put everyone’s utility function on the same (differential) scale to do so, and we’d need a definition for that. Rather trying to write one that covers all edge cases, I chose to simply switch back to heuristic ethical language and extract the core principle without getting bogged down in those technical details.

Even if you assume we can map our assessments onto the same scale and accurately assess our own individual utility functions (a tall order to say the least), there’s still the individualist assumption that the collective good is exactly equal to the sum of its parts. This obviously doesn’t allow us to capture any arbitrary utility function, but sometimes we can add interaction terms whether positive (feedback loops) or negative (jealousy) to better approximate reality.

Still, I think it’s giving away too much to believe claims that people’s utility functions take arbitrary shapes. I think it’s reasonable to assert that we have some degree of smoothness and continuity in most circumstances, for instance. Apart from minimums imposed by banks, I think we actually value an extra $10 in our bank accounts to a similar degree under similar financial circumstances, and any policies we set for ourselves should accurately reflect that reality.

It’s in this context that the concept of budgeting simply doesn’t make sense to me, especially in personal finances. Instead of smooth gradients, polynomials or splines, budgeting tries to approximate your utility function with step functions. Spend no more than $X on food, $Y on transportation, $Z on housing. If you go over in any of those categories, you failed.

Think about it: If you’re near the end of the month but haven’t spent your full budget, is it suddenly okay to splurge up to the limit? If you’re almost at your limit but need one more ingredient for dinner tonight, should you try to do without just to fit within the budget? And if you used up your food budget but still have money left that you won’t be using in the transportation budget, do you really want to say that no, you can only spend that money on transportation?

Now, I completely understand that some people have such a poor grasp of the value of money that the practice of setting limits at all is the only way to actually encourage them to spend less. Setting a tangible goal also gives the satisfaction that comes with achieving the goal, or the reality check when it isn’t met.

But in the long run, we all need to develop the character trait of frugality. This is the approach that has guided how Grace and I have been approaching our finances together. We go over every purchase made in the past week (compiled from our bank accounts by Mint) and if anything is out of the ordinary, we talk about it. Sometimes we make changes to our habits, like prioritizing cooking over eating out, in order to spend less.

And I think that’s what all financially mature individuals and families should do. Develop a consistent intuition of what’s worth it to buy for what price, and apply the intuition to each purchase. After all, that’s probably much closer to what your utility function actually looks like.

I’m still not sure how to translate this approach to larger organizations like companies and churches. It’s difficult to compare spending habits across different individuals, and budgets are one somewhat reasonable way of communicating expectations, especially if the expenditures are fairly predictable. But they’re still crude approximations and lead to the same sorts of errors on the organizational level.

Perhaps a replacement to budgets could look like a training session for new volunteers or employees in charge of spending the organization’s finances. Maybe it would take the form of policies like “Buy store brand whenever possible.” Perhaps instead of reimbursing all meal expenses up to a certain price, companies could agree to reimburse only some designated percentage (half? or maybe only half after a certain amount), to generally encourage employees to keep their costs low. Of course, this would need to be paired with a corresponding increase in pay for jobs that require it. As is, though, it seems to me that budgeting per diems encourage people to spend far more than necessary.

A dollar saved is a dollar earned is a dollar given

I keep referencing it because this post really can’t be viewed on its own apart from last week’s. The main motivation I have for saving money is to be able to give more in the future, after taking care of my own needs and those of my family. While we haven’t explicitly tied our giving to our spending in that way because our future needs are uncertain, that’s the ultimate calculation to be done, assuming our spending habits stay the same.

And that’s really the other key to all of this: Preventing value drift. Moving from a budgeting system to something less explicit but more appropriate of course lends with it the possibility that the intuitions guiding our purchases will become warped by a consumerist culture and companies that want us to buy more and more. It’s in this context that Grace and I have found living in a small apartment to be a blessing.

But going forward in the future, I think the best hope for keeping those priorities does not lie in explicit budgets that we can change anyways if we end up making a bit more. Instead, as a whole, we need to do our best to keep each other accountable and set good examples for each other. Where Randian libertarians see groupthink, I see healthy community.

Last week’s post also helps paint the picture of why fundraisers seem so wasteful to me. If we actually do share money freely among our communities, we shouldn’t need to literally sugar coat requests for help. It should be commonplace, accepted, and part of community norms to ask for help and, in turn, give that help when asked.

And all who believed were together and had all things in common. And they were selling their possessions and belongings and distributing the proceeds to all, as any had need. (Acts 2:44-45 ESV)

One response to “Your Utility Function Does Not Compute

  1. David Haile July 7, 2017 at 6:36 pm

    Your topic reminds me of a few thoughts within Malcom Gladwell’s podcast, “My Little Hundred Million”. It is worth a review.


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