1. Introduction
Quantification is a divisive topic. Traditional proponents of quantification stress its epistemic value and historical importance in physical science. Traditional skeptics highlight how quantification can black-box value judgments and transfer illegitimate power to scientists and technocrats. Recent work in the philosophy of measurement aims for an optimistic compromise. We should pursue the epistemic benefits of quantification but ensure its political legitimacy by aligning value-laden choices with the values of relevant stakeholders. In what follows, I argue that this compromise fails.
My argument consists of two parts. The first part illustrates what I call the alignment approach to quantification and shows that it presumes a basic but unsubstantiated premise. Proponents of the alignment approach argue that political legitimacy should be added “as an additional layer of security […] to the familiar scientific process covered in textbooks on measurement” (Alexandrova and Fabian Reference Alexandrova and Fabian2022, 6; similarly: Duque et al. Reference Duque, Tal and Pamela Barbic2024, 9). While proponents disagree on how to operationalize legitimacy, they agree that it requires a procedure for aligning value-laden choices with the values of relevant stakeholders. All operationalizations of the alignment approach presume that the empirical constraints on quantitative measurement are loose enough to reach quantification along multiple, stakeholder-specific pathways. Proponents of the alignment approach have yet to provide evidence that this basic premise is correct.
The second part of my argument casts doubts on the basic premise. I use seismology as an exemplary case in which a value-laden concept was quantified successfully. To design and test quantitative scales, seismologists had to disregard stakeholder values for overwhelmingly theoretical concerns. The case study suggests that value alignment will frequently be incompatible with successful quantification. Hence, the alignment approach falls short of its goal. To achieve politically legitimate and successful quantification, we need to look for alternative sources of legitimacy.
The plan is as follows. Section 2 introduces the problem of value-ladenness in quantification. Section 3 introduces the alignment approach to quantification and argues that all its proponents are committed to an unsubstantiated premise. Section 4 reconstructs quantification in seismology to challenge that premise. I conclude with an optimistic but merely promissory outlook on alternative sources of political legitimacy in measurement.
2. Quantifying value-laden concepts
Philosophers speak about quantification in at least two different senses. In a descriptive sense, quantifying simply means representing an attribute (mass, time, biodiversity, etc.) in quantitative terms. I am here concerned with a second, normative meaning of quantification. To quantify an attribute, in this second sense, means being justified in describing that attribute in quantitative terms (following Helmholtz Reference Helmholtz1887; Michell Reference Michell1997; Trendler Reference Trendler2009).
To justify quantitative descriptions of an attribute, we need to justify quantitative scales for comparing instances of that attribute. Scales are quantitative if they produce measurement outcomes that contain sufficient relational structure for scientists to calculate differences between these outcomes via addition or subtraction. The basic quantitative scale is an interval scale, which presumes that all instances of an attribute stand in transitive and monotonic distance relations. To justify propositions like “If object X is 5°C warmer than object Y and 10°C warmer than object Z, then object Y is 5°C warmer than object Z,” we need to justify the Celsius (interval) scale. Hence, quantifying means being justified in measuring an attribute on an interval scale.Footnote 1
Here, I am not concerned with the general epistemological debate about how quantitative scales can be tested empirically. Scientists and philosophers continue to disagree about the exact theoretical and experimental presuppositions of such tests (Trendler Reference Trendler2009, Reference Trendler2019; Sherry Reference Sherry2011; Michell Reference Michell2019; Tal Reference Tal2019; Vessonen Reference Vessonen2020; Thalos Reference Thalos2023). It suffices to note that there is sufficient common ground to identify clear examples of successfully quantified attributes in the history of science, ranging from temperature to electric current. The distance relations between specific instances of these attributes were shown to (i) remain stable in controlled conditions and (ii) converge across instruments and background conditions to a sufficiently high level of precision. In many successful cases, presupposing quantitative scales further allowed scientists to discover new and highly specific details of the empirical world (Smith Reference Smith, Biener and Schliesser2014; Miyake Reference Miyake2017; Smith and Seth Reference Smith and Seth2020). It is also commonly agreed that quantitative scales—if empirically justified—are epistemically valuable. They allow us to mathematically derive and empirically test predictions at a higher degree of specificity.
In many scientific disciplines, the general problem of testing quantitative scales is compounded by a second, more specific problem: (How) Should quantification be pursued if it involves value-laden choices? I assume that choices can be considered value-laden if and only if they are epistemically unforced and have morally significant consequences. This definition excludes epistemically unforced choices that do not have morally significant consequences (e.g., whether we should use a Fahrenheit or Celsius temperature scale), as well as consequential choices that are clearly determined by the evidence (e.g., whether global temperature should be measured through instruments or subjective reports).
Value-laden choices in designing quantitative scales abound in many areas of science. Prominent cases typically fall into two overlapping classes. A first class of cases concerns the quantification of “thick” qualitative concepts that serve descriptive and evaluative purposes (Alexandrova Reference Alexandrova2018; Alexandrova and Fabian Reference Alexandrova and Fabian2022). Here, researchers make choices about the definition of their measurand and its indicators that determine which (and whose) moral values are reflected in their measure. For example, should our questionaries assume that well-being is simply the ratio of reported positive to negative emotions in a standardized questionnaire, or is it a complex aggregate of disposable income, employment rate, self-reported health, and several other indicators? If the measure should preserve these different evaluative components, how much weight should scientists assign to each component when calculating a final well-being number?
A second, related class of cases concerns choices between alternative indicators and definitions that lead to highly differential consequences for different stakeholders. Such choices can occur even if our pre-quantitative concepts are purely descriptive and do not usually express moral valuations. For example, carbon emissions per country can be defined and measured in alternative, purely descriptive ways, but these alternative definitions will lead to highly different policy outcomes. The CO2 emitted in the life cycle of a commodity may be assigned to the country it was produced or consumed in, very likely leading to different policy decisions about who is held politically accountable for these emissions (Karakaya et al. Reference Karakaya, Yılmaz and Alataş2019).
Two proposals for dealing with value-laden choices in quantification have long dominated the scientific and philosophical literature. The first proposal is a simple extension of an influential account of value neutrality in scientific research (e.g., Nagel Reference Nagel1961, 492–93): Scientists can and should avoid value judgments by making them conditional on a standardized measurement procedure and a standardized definition of the measurand. Science funders or policy makers may worry about “appraising” such standards on ethical grounds, but scientists themselves merely “estimate” how well they are approximated by empirical phenomena. The appeal of this approach is apparent: We can pursue the epistemic benefits of quantification without deferring undue authority to scientists.
The second influential proposal can be read as a response to the first proposal: Reject attempts at quantification because they confer illegitimate power to scientific experts. Drawing on historical and contemporary cases, many researchers have become convinced that value judgments cannot be avoided by standardization and, for the sake of democracy or justice, should not be black-boxed by seemingly objective standards. Newfield et al. (Reference Newfield, Alexandrova and John2022) call this the “original critique” of quantification. It is implicit (although rarely endorsed) in classic scholarship in history and social studies of science (Hacking Reference Hacking1990; Rusnock Reference Rusnock and Norton Wise1995; Porter Reference Porter1996; Muller Reference Muller2018).
Few philosophers today endorse either of the two canonical proposals. Instead, recent work has taken inspiration from a growing literature on the role of moral and political values in science. The result has been a newfound optimism that we can exploit the epistemic benefits of quantification while avoiding its political risks. The proposed solution is what I will call the alignment approach.
3. The alignment approach
If quantification involves value-laden choices, institutions designing quantitative measures wield power over those affected by the outcomes of measurements. We frequently defer power to institutions like governments, courts, or even supranational entities if we consider these institutions politically legitimate. It has been a key aim of recent work on quantification to spell out how quantification may be legitimized.Footnote 2 The result is a growing literature aimed at combining the pursuit of quantitative measurement with norms governing the epistemically unforced and consequential choices made during measure construction. Recent contributions to this literature explicitly or implicitly commit to a specific criterion for political legitimacy:
LegitimacyA: Measures are politically legitimate if the value judgments during their design were subject to procedural constraints that aligned those judgments with the values of relevant stakeholders.
LegitimacyA forms the core of what I will call the alignment approach to value-laden quantification—adopting a notion used widely in debates about the role of moral and political values in science (Parker and Lusk Reference Parker and Lusk2019; Schroeder Reference Schroeder2021; Elabbar Reference Elabbar2023). LegitimacyA can be operationalized in different ways, depending on how narrowly the class of appropriate procedures is drawn and who is considered as the relevant stakeholders of measurements. I will spell out the different proposals for operationalizing it in what follows, if only to show that all of them presume a basic but unsubstantiated premise to be criticized in the following section.
3.1 Participative versus indirect alignment
Proponents of alignment approaches disagree on how directly stakeholders have to confer legitimacy on quantitative measures. Some philosophers argue that scientists can legitimize value-laden choices by relying on surveys of stakeholder values. Others call for alignment procedures that directly involve the relevant stakeholders in designing, executing, and evaluating measurements. I will illustrate the distinction by discussing some exemplary approaches that fall on different ends of the spectrum.
Alexandrova’s (Reference Alexandrova2018, 440) “deliberative polls of normative presuppositions” illustrate an indirect alignment procedure. She argues that such polls can ground the procedural objectivity of value-laden measures. Her example is an online poll from the UK Office of National Statistics (ONS) titled “What matters to you?,” in which citizens could judge the normative aptness of different well-being measures. The ONS then consulted the survey responses to make value-laden choices between alternative measures. For Alexandrova, “the honest effort to canvass the diverse views shows that the value presuppositions on this measure have arguably passed the sort of test I have in mind” (Alexandrova Reference Alexandrova2018, 439).
There are two recent pilot projects that attempt to align quantitative measures with stakeholder values by directly involving them in the measurement process. The first is Fabian and Alexandrova’s (Reference Alexandrova and Fabian2022) proposal for an “ideal of participatory measurement.” Their participatory measure of well-being involved employees and beneficiaries of a UK charity. Beneficiaries contributed directly to the choice of a definition of well-being and helped choose questionnaire items to calculate a well-being value. Duque et al. (Reference Duque, Tal and Pamela Barbic2024) have also argued for a direct involvement of stakeholders in psychosocial measurement. They launched an exemplary project with a Canadian mental health services provider, which aimed to implement collective “ethical iterations.” In such iterations, scientists, service providers, and participants collectively deliberate the appropriate values for making epistemically unforced choices and revise these choices in light of service outcomes.
3.2 Wide versus narrow scoping of stakeholders
Proponents of the alignment approach also disagree on how to best scope the relevant group of stakeholders. This disagreement, essentially, concerns whether the values of users and subjects of measurement deserve any privileged consideration over and above the values of the general public. Philosophers linking legitimacy to alignment with user and subject values endorse narrow scoping, whereas philosophers urging alignment with public values endorse wide scoping.
The two pilot projects of participatory measurements are excellent examples of narrow scoping (Alexandrova and Fabian Reference Alexandrova and Fabian2022; Duque et al. Reference Duque, Tal and Pamela Barbic2024). In both cases, the processes used to align epistemically unforced choices with stakeholder values involved scientists, service providers, and most importantly, subjects of quantitative well-being or mental health assessments.
Schroeder (Reference Schroeder2019) endorses wide scoping for economic measures. For him, epistemically unforced choices in quality-of-life measures should be based on egalitarian considerations because most citizens hold egalitarian views about health. Schroeder has argued repeatedly that wide scoping is strongly preferable to narrow scoping in and beyond quantitative measurement (Schroeder Reference Schroeder2017, Reference Schroeder2021). If scientists adapt their value-laden choices to specific groups of stakeholders, they risk undercutting public trust in science. With few exceptions (explicitly antidemocratic values such as racism), value-laden choices should therefore be aligned with democratic values—that is, the values held by the public of a particular democratic society or its elected representatives (Schroeder Reference Schroeder2022).
It should now be clear that there are several influential proposals for how value-laden choices in quantification may be legitimized by aligning them with stakeholder values. Philosophers disagree on which procedure for value alignment can secure political legitimacy and thus scope the class of relevant stakeholders differently. My goal is not to intervene in these debates. Instead, I will argue that they share a basic but unsubstantiated premise.
3.3 The basic premise of the alignment approach
Defenders of the alignment approach value quantitative measurement but share traditional critics’ sense that quantification can be highly consequential and, hence, requires political legitimacy. They are optimistic that their favored procedures for value alignment can confer political legitimacy on quantitative measures. This optimism raises a basic but crucial question that, to my knowledge, has not been addressed in the literature. Values differ across groups, countries, and time. Quantitative measures need to be adjusted to different groups, countries, or historical periods so that they don’t sacrifice their political legitimacy. Clearly, however, quantification is incredibly hard, and even physical scientists often took decades or centuries to develop a quantitative scale that passes empirical scrutiny (Yoder Reference Yoder1989; Chang Reference Chang2004; Schlaudt Reference Schlaudt2009; Sherry Reference Sherry2011; Luchetti Reference Luchetti2020). The question, then, is whether quantification is empirically unconstrained enough to be achievable along such stakeholder-specific pathways. Surely, we can define and operationalize mental health or well-being in line with stakeholder values, but can the quantitative scales thus constructed pass empirical scrutiny?
The basic premise of the alignment approach to quantification: The process of quantification is sufficiently unconstrained empirically for quantitative measurement to be achievable along multiple, stakeholder-specific pathways.
Proponents of the alignment approach presume that this question can be answered positively but provide no evidence for such a proposition. The resulting optimism about legitimate and successful quantification rests on a premise in need of scrutiny. It is, indeed, the basic premise of the alignment approach because it sets it apart from both traditional proponents and traditional critics of quantification.
Existing arguments for aligning quantitative measures are, in principle, not sufficient to substantiate the basic premise. Such arguments take two forms. First, some proponents of value alignment are content with criticizing the harmful consequences of aspiring toward an unattainable value-free ideal (Bocchi Reference Bocchi2024) or arguing for the superiority of their specific alignment procedures (Schroeder Reference Schroeder2021). Such work provides valuable insights into the merits of specific alignment procedures vis-à-vis the value-free ideal or competing proposals. It does not bear on the epistemic warrant for such stakeholder-dependent scales’ correctness and, ipso facto, the basic premise of value alignment.
The second type of argument provided for value alignment takes the form of practical demonstrations (Alexandrova and Fabian Reference Alexandrova and Fabian2022; Duque et al. Reference Duque, Tal and Pamela Barbic2024). Even concrete pilot projects for aligning measures, however, fail to substantiate the basic premise because they concern psychosocial attributes whose quantitative status remains highly questionable on empirical grounds (Michell Reference Michell1999; Trendler Reference Trendler2009, Reference Trendler2019; Wolff Reference Wolff2023). Contrary to cases of successful quantification, (quantitative) distance relations postulated between well-being or mental health have not been tested via stable, convergent, and sufficiently precise measurements, nor have such measurements led to the discovery of further quantitative details of the empirical world. The pilot projects demonstrate realistic procedures for aligning value-laden choices in quantification scales with stakeholder values. They do not demonstrate that the resulting scales of well-being and mental health will eventually satisfy the empirical requirements of quantitative measurement.
4. Against alignment
In the previous section, I have argued that existing versions of the alignment approach do not substantiate that approach’s basic premise. The most developed proposals for value alignment focus on measures whose quantitative status remains disputed. My approach in what follows is the inverse. I focus on a rare case of a value-laden but epistemically successful quantification: seismological scales of earthquake size. Seismology’s historical development motivates my counterfactual contention that we would not have been able to quantify earthquake size along stakeholder-specific pathways. This suggests that the basic premise is, at least sometimes, false.
4.1 Quantification in seismology
It is a central aim of modern seismology to measure “earthquake size.” The first widely used scales of earthquake size were intensity scales. Their basic assumption is that earthquake size is proportional to ground motion and its direct effects. For example, the famous Rossi–Forel scale (fig. 1) ranks earthquakes by sorting them into 10 different levels of intensity based on criteria ranging from seismograph readings to “general panic” or the occurrence of a “great disaster.” Intensity is a spatial quantity, meaning that the same earthquake will have different intensities at different places.
Rossi–Forel scale of earthquake intensity. Reproduced from Howell (Reference Howell2005).
Intensity scales clearly do not pass empirical tests of quantitativeness. Even conceptually, a close reading of the Rossi–Forel scale suggests that there is no clear way to compare distances between different intensities additively. Why would we assume that the increase in intensity from level III to V is of the same size as that from levels VII to VII? If it is not of the same size, we cannot compare earthquakes by adding or subtracting their intensities. As seismologists soon realized, the different indications in the scale also do not covary monotonically, meaning that seismograph recordings, social reactions, and architectural destruction may lead to different intensity assignments for the same earthquake at the same location.
Pre-quantitative scales were nonetheless very valuable to stakeholders and often designed in close collaboration with citizens in earthquake-prone regions (Coen Reference Coen2013). The indications for different intensity levels were based on events that stakeholders cared about and could verify themselves. Recording these indications (through seismographs and subject reports by affected citizens) allowed scientists to track and understand the physical and social effects most threatening to them. Mapping of intensity across different locations provided an excellent method for locating seismic faults and identifying future risk areas. For that reason, the main media for communicating intensity were so-called isoseismal maps, which can successfully guide future hazard mitigation by relocating citizens or implementing special construction laws (fig. 2). Intensity scales are a fantastic example of successful value alignment in measurement, where stakeholder values affected the choice of indicators and stakeholders directly participated in the process of measurement by submitting intensity reports and qualitative commentary to scientists.
Isoseismal intensity map of the 1906 San Francisco Earthquake, where different shadings represent different intensities on the Rossi–Forel scale. Reproduced from Lawson et al. (Reference Lawson and Earthquake Commission1908).
Intensity scales gradually lost importance after Charles Richter published the first magnitude scale of earthquake size in 1935. Magnitude scales assign a single value to each earthquake, which can be inferred from the maximum amplitude
$A$
of a seismogram at a distance d from the epicenter of an earthquake:
$$M = {\log _{10}}\left[ {{A \over {{A_0}\left( d \right)}}} \right],$$
where
${A_0}$
is the conventionally chosen amplitude of a standard shock (assigned 0 M) at d (Richter Reference Richter1935). Initially, the scale was only used at epicentral distances of up to about 600 km in Southern California and, by implication, based on amplitudes of specific seismic waves (mostly shear body waves) originating in earthquakes with a specific hypocentral depth. Richter and his colleague Beno Gutenberg subsequently extended the scale for use across the world. They achieved this feat by modeling the effects of variations in Earth’s internal structure and crust, earthquake focus depth, wave type, and instrument design on recorded amplitude (Gutenberg and Richter Reference Gutenberg and Richter1942, Reference Gutenberg and Richter1956).
Seismologists’ hope was that the magnitude scale approximately tracked the energy released during an earthquake, providing a single physical standard for comparing earthquakes across time and space. This hope was eventually realized by the scale’s successor, Keiiti Aki’s moment scale, which directly links a specific spectrum in the seismogram to an earthquake’s moment
${M_{0}}$
— the product of the area, displacement, and rigidity of the fault dislocation—a reasonable approximation of the released energy:
$${M_0} = 4\pi pv_s^3\Delta {\Omega _0}$$
where
${\Omega _0}$
is a particular shear wave signature in the seismogram, p is the density of the transmission media in Earth’s body or crust,
${v_s}\;$
is the shear wave pulse’s velocity, and
$\Delta $
is the distance to the hypocenter. Earthquakes could now be compared based on a (modeled) parameter of their physical mechanism rather than their heterogeneous effects at Earth’s surface. The moment of specific earthquakes can be measured consistently across regions and instruments, there is a clear physical meaning to distances between values on the scale, and the scale has been successfully used to discover quantitative details of Earth’s internal structure (Miyake Reference Miyake2017; Giacomo et al., Reference Giacomo, Domenico and Storchak2021).
The key takeaway of this history is that quantifying earthquake size involved redefining what “earthquake size” meant. The moment of an earthquake refers to the physical mechanism at the earthquake source, whereas intensity refers to ground motion and its destructiveness. This semantic change went hand in hand with a change in what data the scales produced and whose interests these data served. While intensity is indexed to particular places across an affected area, its quantitative successor scales assign only one number to each earthquake that is indexed to its hypocenter. The new and elegant quantitative values for earthquake size were of little use in mapping hazard risk and, ipso facto, mitigating those risks in future earthquakes. Indeed, 21st-century seismologists had to revive intensity scales based on subjective reports to make progress in mitigating earthquake risk and better understand the physical links between earthquake moment and local ground motion (Hough Reference Hough2000; Atkinson and Wald Reference Atkinson and Wald2007).
4.2 The alignment dilemma
The development of seismology illustrates that heavily value-laden concepts can be quantified successfully. It suggests, however, that such quantification might require scientists to make epistemically unforced choices that do not align with stakeholder values, hence sacrificing legitimacyA. There is no purely epistemic reason for pursuing a quantitative scale instead of qualitatively recording, understanding, and mitigating earthquake effects. Yet if quantification is the goal, such a redefinition appeared necessary—after all, intensity had previously been studied for about a century, without any clear progress toward quantification. Seismologists excluded stakeholders and their preferences from measurement design and evaluation, and they redefined earthquake size to refer to a property of overwhelmingly theoretical and surprisingly little practical interest.
It is a widely known insight from other historical studies that quantitative measurement often involves serious meaning change and that this meaning change is heavily constrained empirically (Chang Reference Chang2004; Smith and Seth Reference Smith and Seth2020). What seismology illustrates is that such meaning change may well require scientists to abandon stakeholder values. Because we have no positive example of quantification along stakeholder-specific pathways, this observation calls into question the basic premise of the alignment approach to quantification. If the basic premise is not correct, proponents of the alignment approach are left with a dilemma, which can be put in argument form as follows.
The Alignment Dilemma:
(P1) Scientists should align value-laden choices in the design of quantitative measures with stakeholder values.
(P2) Quantifying attributes requires scientists to alter the definition and scope of pre-quantitative concepts.
(P3) Frequently, the stakeholder values served by pre-quantitative concepts cannot be served by their quantitative successors (the basic premise is, frequently, false).
(C): Frequently, scientists should not quantify attributes.
Note that the point of this argument is not to convince you of its conclusion. Rather, it maps out a dilemma: If you want to pursue quantification (hence, not accept C), you cannot accept the argument illustrated by my case study (P2 and P3) and require scientists to align value-laden choices with stakeholder values (P1). The dilemma suggests that the alignment approach to quantification will often, if not always, be unfeasible on empirical grounds.
5. Conclusion
I have argued that the alignment approach to quantification fails because it relies on an unsubstantiated premise. Its proponents assume that quantification is sufficiently unconstrained to be achievable among multiple, stakeholder-specific pathways. The history of seismology—a rare success case of value-laden quantification—casts strong doubts on this premise. Quantification is difficult to achieve on empirical grounds and will frequently require choices that do not align with stakeholder values.
This conclusion does not call into question the basic intuition of recent work on quantification: We should insist that quantitative measures meet the demands of political legitimacy. Twentieth-century seismology illustrates the shortcomings of the alignment approach to quantification but is surely no model of how quantification ought to look (for similar views: Hough Reference Hough2000; Coen Reference Coen2013). The challenge, as I see it, is to work out a criterion of legitimacy that grants researchers sufficient freedom to make nonaligned choices during quantification but ensures that quantitative scales serve the interests of stakeholders in the medium or long term. Such a criterion should draw from a recent interest in the diverse sources of institutional legitimacy beyond the nation-state by political philosophers (Adams Reference Adams2018). I lack the space to spell out such a criterion here but hope to have illustrated its relevance.
Acknowledgements
Special thanks are due to Cristian Larroulet Philippi for many hours of discussing measurement in seismology together, and to Ahmad Elabbar for pushing me to write up my worries about value alignment in measurement. For feedback on earlier versions of this article, I thank Aja Watkins, Alisa Bokulich, Anna Alexandrova, Eran Tal, Federica Bocchi, Pieter Beck, and Ruward Moulder. Finally, I thank all other attendees of the Values in Science workshop at Pembroke College, University of Cambridge, in March 2024 and the “Science and the Public” session at the Philosophy of Science Association 2024 meeting, members of the Philosophy of the Geosciences Research Group at Boston University, and Hasok Chang’s research group at the University of Cambridge, all of whom provided me with helpful questions and comments. The research for this article was funded by the British Academy (PFSS24\240061).
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