Abstract
In Incomparable Values: Analysis, Axiomatics, and Applications, John Nolt provides a rich and illuminating framework for examining incomparable values understood as those values that allow for items to be neither better than, worse than, nor exactly equal to one another. Nolt divides his discussion of such incomparable values into axiology on the one hand and decision theory on the other. The former focuses on understanding the nature of incomparable values while the latter focuses on understanding how we should choose between items of incomparable value. On both fronts, Nolt presents novel tools, arguments, and insights far too numerous to mention, let alone to do justice to, in this short space. I here highlight only a handful of the many valuable ideas developed in this book.
With respect to axiology, Nolt examines the nature of incomparability stemming from multi-dimensionality (Chapter 1). The idea here is that some values consist of multiple distinct dimensions and two items can be incomparable with respect to that value when each is better in one dimension, but worse in another. As a toy example (modified from pp. 164–166), suppose the overall welfare of an individual is determined by the two dimensions of physical health and mental health. Here, the welfare of some individuals might be made better (worse) by improving (worsening) one or both dimensions. However, improving their physical health while also reducing their mental health would not make their overall welfare better than, worse than, or exactly equal to what it was before.
Nolt demonstrates how such incomparability can be modeled using a Cartesian coordinate system with each axis representing one dimension of that value so long as each dimension is itself linear and has an absolute zero point (Chapters 4 and 5). In the above example, an individual's welfare could be represented on a two-dimensional Cartesian plane with the x-axis representing physical health and the y-axis representing mental health. So the initial overall welfare of some particular individual might be represented by, say, the <6, 8> position on this plane while their welfare with increased physical health but decreased mental health might be represented by the <9, 6> position.
Such a Cartesian model is useful for better understanding the boundaries between incomparable items (Chapters 2 and 12). For instance, while the individual's overall welfares in those two situations are incomparable, we can use this model to identify which other situations would be better (worse) than both. Here a welfare value in the <9, 8> position would be better than both given that it would be at least as good and sometimes better with respect to both physical and mental health dimensions. Moreover, this position serves as the pair's Lowest Upper Bound insofar as any better welfare level would also be better than both incomparable welfare levels. On the other end, the pair's Greatest Lower Bound is <6, 6>. The incomparability of the two welfare levels is then “contained” within these boundaries. In this way, the Cartesian method allows us to indirectly determine the distance between two incomparable items.
Nolt also shows how this idea of incomparability due to multi-dimensionality can help avoid the Repugnant Conclusion, which arises when aggregating individual welfare to determine the value of an entire population (Chapter 8). The idea is that if the value of a population is determined by simply adding up the welfare of each individual in that population, we will be forced to accept the repugnant conclusion that a massive population whose members each have an exceedingly low (but positive) welfare can turn out to be better than a smaller moderate sized population whose members each have a very high level of welfare so long as the total aggregate welfare of the massive population is higher.
Nolt demonstrates how this conclusion might be avoided if we understand the value of a population to be determined by multiple dimensions that allow for incomparability (pp. 211–214). If the value of a population has two dimensions, one being the total aggregate welfare and the other being the average per capita welfare, then it will turn out that the massive population with low average welfare is not better than the moderate population with high average welfare. Each population is better on one dimension and worse on another, resulting in the two being incomparable with each other and thus avoiding the repugnant conclusion.
Turning to decision theory, one might think that when faced with a choice between incomparable items there would be no way to favor one over another. However, Nolt proposes an interesting two-step method for discriminating between such items (Chapter 10). The first step is a process called equilibration that involves rescaling the value's multiple dimensions such that each unit of each dimension is roughly as important for the choice at hand. This process does not set the units of each dimension as equal in terms of their value contribution as this would eliminate incomparability altogether, but rather sets each dimensional unit in a way that gives them rough equality in terms of their practical significance.
The second step is to set an appropriate adequacy standard for selecting between incomparable items. Given equilibration, one might be tempted to choose whichever item had the most aggregate units of all dimensions combined. The problem is that equilibration only provides imprecise equality between different dimensional units so we cannot be confident that these units can be traded off in a one-to-one exchange such that the sum is all that matters for the choice at hand. Nolt then proposes an adequacy standard that allows for tradeoffs between different dimensional units given their rough equality but nonetheless favors more equal distributions of dimensional units. The idea here seems to be that given some, but not complete, confidence in the equality between dimensional units, we should generally favor items that score roughly the same in all their dimensions over items that score high on certain dimensions but low on others.
Nolt then demonstrates how such an adequacy standard can provide a further response to the Repugnant Conclusion (pp. 288–289). As mentioned above, taking a population's value to be determined by two dimensions allows us to avoid the conclusion that the massive population with low average welfare is better than the moderate population with high average welfare. However, that still leaves the conclusion that the two populations are incomparable with one another. Nolt's adequacy standard though allows us to further discriminate between these populations in choice situations. That is, despite their incomparability, we can be justified in choosing the moderate population over the massive population since it does not trade off one dimension for another like the massive population does.
Finally, I should note here that much of this book is devoted to precisely defining concepts and principles as well as providing proofs for the numerous theorems that follow from nine central axioms. While at times quite technical, Nolt's thoroughness and rigor are not only admirable but also provide a level of clarity that will allow for fruitful engagement and discussion. The ideas presented in this book will be of great value and interest to anyone hoping to better understand value incomparability and how we should respond to it.
