by Brian Tomasik
First written: 2005; last update: 28 Nov. 2013

## Summary

This piece illustrates how to compare the cost-effectiveness of different ways to reduce suffering: how much good is accomplished per unit resource, and how to convert between resources.

## Introduction

In this piece, I frequently make use of example values for changes in aggregated utility that result from given actions. I do so for the sake of clarity. In reality, of course, it is impossible to assign a precise numerical value in utils to the consequences of an action. Sometimes numbers given in more concrete units can help to approximate magnitudes of different effects -- for example, one might say that refraining from the purchase of a store-bought chicken prevents around 45 days of suffering in a factory farm and subsequent slaughter, among other things. And in some situations, no numbers are necessary at all. Thus, utilitarianism is not just an abstract nice idea; often, it can be approximated in practice.

The procedure for making a utilitarian evaluation is to estimate the net change in aggregated utility that would result from each of several possible actions that one might undertake. While it would be theoretically desirable to know the magnitude of the change in aggregated utility that results from every tiny effect that one's action might have, it is generally sufficient to consider the most significant impacts. This is not to say that one should never consider the smaller effects of any given action; indeed, there may be seemingly negligible details that turn out to be important. One ought to devote some time to exploring these possibilities. However, doing so for every decision would be a waste of time that could be better spent on other pursuits.

## Resource equalization

Estimating changes in aggregated utility for each option is the first step, but one must also consider the opportunities that one will give up in the process of undertaking each action. All actions require some amount of resources (even if only a few seconds of time), and in using resources to undertake action A, one forgoes resources that might have been applied to action B. The easiest way to factor this into one's deliberations is to consider options for which resource use has been equalized. To take an example, suppose that Charles is unsure whether he should walk to a nearby protest or stay at home and write a letter to Congress. The former option would take five hours and would result in an expected 40 utils, while the latter would take one hour and produce an expected 15 utils. Naively, Charles might say, "Oh, well if I go to the protest, I can effect a bigger expected change in aggregated utility. I ought to do that." But such an analysis is flawed because the two options being considered utilize different amounts of resources. Assuming that time is the only resource involved, Charles can set equal the resource use of the two possibilities by imagining that he wrote five letters in five hours. Now the utility comparison for the two applications of equal resources are 40 utils for the protest and 75 utils for the letters. In this case, using only the options and numbers given, Charles should write to Congress.

## Marginal aggregated utility

Resource equalization is one way to do back-of-the-envelope comparisons. The following approach is another way to take account of resource expenditures.

Definition. "Marginal aggregated utility" is the change in aggregated utility that results from application of a unit of resources.

There are subtleties in applying this principle, though. For example, Charles might think, "Marginal aggregated utility is the bang that I get for the buck, so to speak. So clearly, I should always choose the option for which marginal aggregated utility is highest."

In general, this thinking is correct. Consider, for instance, the protest-versus-letters scenario above. Assuming that marginal aggregated utility is constant over the five hours spent writing letters and going to the protest,

• marginal aggregated utility for the protest = (40 utils)/(5 hours) = 8 utils/hour, while
• marginal aggregated utility for writing letters = (75 utils)/(5 hours) = 15 utils/hour.

Choosing the option with higher marginal aggregated utility does indeed give the right answer. However, consider this situation.

Example. Suppose that, in rummaging around an old stack of papers, Charles finds an already-written advocacy letter to McDonald's that will bring about an expected 370 utils. However, the letter still needs a 46-cent stamp in order to be sent. If we let "cents" be our unit for amount of resources used, the marginal aggregated utility that results from the first cent is 0 (since the letter can't be sent). Similarly, for any amount less than or equal to 45 cents, marginal aggregated utility is 0. But when Charles applies 46 cents, he can finally send the letter -- thereby effecting an expected increase of 370 utils. However, Charles wouldn't have come to that conclusion only by looking at the initial value of marginal aggregated utility.

Another way to say this is that the amount of aggregated utility accomplished as a function of resource expenditure is discrete and rather than fully continuous and differentiable as is typically assumed in economics for ease of analysis.

## Interconversion of resources

What if different options require utilization of different types of resources? For instance, how does one compare donating money to an altruist organization with spending time handing out literature on important issues? Resources can be converted into one another given the specifics of the situation. Assuming that the most efficient way to convert time into money is to work at one's job (say the pay rate is $15/hour), then one can compare spending two hours handing out brochures against two hours of working at one's job, the latter being equivalent to donating$30 toward the organization.

Resources can also create more resources. For instance, time spent exercising now may mean a longer life in which to do good later. Time spent networking can mean higher earnings to donate in the future. And so on.