boxethics.org is a free web application to generate box diagrams from utility distribution tables and is developed by Daniel Ramöller. Such diagrams are popular to visualize scenarios in distribution ethics, and, in particular, in the ethics of future generations. (These scenarios are often highly simplified in order to study specific features.) The diagrams can be exported to different formats for use in all popular word processors and presentation programs, and online content. Below are several examples. Click on a diagram to open it in the web application.

Figure 1: A population-size diagram.

Figure 1 illustrates two important features in one common type of diagram. It illustrates both the size as well as the welfare level of a population (or future generation), p. The broken top line indicates that the box could be much wider than shown and hence the population size much greater.

Figure 2 illustrates a version of the, so called, Mere Addition Paradox by Derek Parfit (1984). It consist in a sequence of alternative outcomes, A, A+, and B, each consisting of one or more populations at certain welfare levels. The basic idea is that the three seemingly plausible evaluations that (1) A is not better than outcome A+, i.e. an additional isolated population with positive welfare does not make things worse, (2) B is better than A+, i.e. having equality and higher overall welfare is better, and (3) A is better than B, i.e. doubling the population by lowering welfare drastically is worse, are inconsistent since (2) and (3) together imply that A is better than A+ which contradicts (1). One task in the ethics of future generations is to solve this paradox.

Figure 2: Illustration of the Mere Addition Paradox.

Figure 3 illustrates an impossibility due to Gustaf Arrhenius (2000). Arrhenius assumes that, given certain specifications, it seems plausible that (1) AHE is at least as good as AB, (2) AHF is at least as good as AHE, (3) G is at least as good as AHF, and (4) CB is better than G. However, (1) to (4) imply that CB is better than AB, a version of the, so called, Repugnant Conclusion: For every population with very high welfare level, there is a population with lives barely worth living which is better.

Figure 3: Illustration of the Third Impossibility Theorem.
Figure 4: A time diagram.

Figure 4 illustrates the usage of boxes in another common type of diagram, see e.g. John Broome (2004). In contrast to the previous type, it illustrates the welfare changes of a generation, g, over time but not its size. The generation exists in time periods t-1 to t1 but ceased to exist in t2. The vertical line, “Now”, indicates the point in time where a certain decision is to be made.

Figure 5 illustrates a version of Derek Parfit (1984)'s Risky Policy. The first generation, g1, can decide to choose the Risky Policy or the Save Policy. Compared to the Save Policy, over the next century, from t0 to t2, the welfare is slightly higher. But with the Risky Policy the lives of the third generations, g3, will be severely shortened. Furthermore, due to the changes in the standard of living people will have children at different times under the different policies. Because of this fact, different people will exist under different policies in the further future. And under the Risky Policy, g3 will not be worse off than they would have been under the Save Policy because they would not have existed. The problem of finding a plausible objection to the Risky Policy is (part of) the, so called, Non-identity Problem.

Figure 5: Illustration of the Risky Policy.


Arrhenius, Gustaf (2000). Future Generations: A Challenge for Moral Theory.

Broome, John (2004). Weighing Lives.

Parfit, Derek (1984). Reasons and Persons.