A concept of diversity, as we use the term, is an understanding of what makes a group diverse that may be applicable in a variety of contexts. Specifically, concepts of diversity need not be tied to an attribute, such as gender, theoretical perspective, and so forth. Thus, we do not review distinctions drawn among attributes, such as surface versus deep, demographic versus cognitive, task-related versus non-task-related, or functional versus identity (Harrison and Sin 2006: 2; Harrison and Klein 2007: 1199; Hong and Page 2004). In addition, we distinguish concepts from measures of diversity, which we understand as mathematical formulas for quantifying the degree to which a group is diverse. Usually, the relationship between concepts and measures of diversity is one to many: for a given diversity concept, several measures may be reasonably taken to quantify it (McDonald and Dimmick 2003; Solanas et al. 2012; Teachman 1980). Since concepts, as opposed to contexts, of diversity have not been clearly distinguished in philosophical literature on diversity among scientists, we review other literatures where they have been, namely, social science and ecology.
Discussions of diversity concepts can be found in social science literature, usually in connection with measures of diversity (Harrison and Klein 2007; McDonald and Dimmick 2003; Solanas et al. 2012; Teachman 1980). Teachman (1980) provides an early and influential example of such work, defining “population diversity” as “the distribution of population elements (which are not limited to humans or the characteristics of humans) along a continuum of homogeneity to heterogeneity with respect to one or more variables” (Teachman 1980, 341). Three observations about this definition are helpful.
First, Teachman’s definition expresses a diversity concept in the sense described above. It explicitly abstracts from particular contexts and attributes, but it does not indicate a mathematical formula for quantifying degrees of diversity. Second, population diversity is a broad umbrella under which more specific diversity concepts might fall. The distinctive feature of these concepts is that, once the relevant variables or attributes are provided, the diversity of a population (or group) depends only on their distribution within that population (or group). Such diversity concepts differ only in terms of which distributions they take to exhibit greater or lesser heterogeneity. In this way, Teachman’s population diversity is very similar to our concept of within group diversity discussed in section 3. Third, the label “population diversity,” rather than simply “diversity,” suggests that other diversity concepts may exist. What we call comparative diversity concepts diverge from Teachman’s notion of population diversity insofar as they depend on a comparison with a reference population.
Consider a more specific diversity concept suggested by Teachman himself under the guise of “desirable properties of a measure of qualitative variation” (Teachman 1980, 342). The term “qualitative variation” refers to variation in qualitative attributes, such as gender or religious affiliation, rather than variation along a quantitative scale, as might be used for income or height. Let A = {a1, …, an} represent a qualitative attribute, where A is a label for the attribute and a1, …, an are the mutually exclusive categories into which it subdivides. For example, if the attribute is religious affiliation, then the categories might be {Buddhism, Christianity, Hinduism, Islam, Judaism, Secularism, Sikhism}.Footnote 2 While multiple attributes (e.g., gender, ethnicity, and religion) might be considered in a single case, as Teachman notes, for simplicity we limit attention here to examples involving only one. Finally, let G denote the focal group, or population, whose diversity is in question. Focal groups can be almost any collection of people (inhabitants of a town, students at a university, a committee, a board of directors, a legislature, a research team, an expert panel, etc.) or other entities (e.g., species in an ecosystem, segments of time devoted to distinct perspectives in media coverage of a topic, etc.).
Teachman’s “desirable properties” for a measure of diversity for qualitative variables, then, are as follows (Teachman 1980, 342):
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1)
Diversity is minimized when everyone (or everything) in G falls in a single category ai ∈ A;
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2)
Diversity is maximized when each category in A is present in G at a proportion of 1/n, and
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3)
For any groups G and G’, if i categories of A are present in G at proportions of 1/i each, j categories of A are present in G’ at proportions of 1/j each, and i > j, then G is more diverse than G’.
In the above example above, diversity would be minimized if everyone in the group had the same religious affiliation, for instance, if all were Buddhists. Conversely, diversity would be maximized if all affiliations were present in equal proportions. The third property tells us something about intermediate cases. Consider a group composed of equal numbers of Buddhists, Christians, Hindus, and Muslims, and a second group composed of equal numbers of Jews, Muslims, and Sikhs. Then (3) tells us that the first group is more diverse than the second.
Properties (1) through (3) suggest that diversity entails a uniform distribution over the full set of attribute categories. The more flat and spread the distribution is, the closer it approximates a uniform distribution, and hence the greater the diversity. The more concentrated the distribution is on a single category, the further removed it is from a uniform distribution, and consequently the less the diversity. This diversity concept is labeled “variety” by Harrison and Klein (2007) and “dual concept”Footnote 3 by McDonald and Dimmick (2003, 64). We call the diversity concept picked out by Teachman’s three desirable properties “egalitarian,” which we take to be a more descriptive label. Numerous measures of egalitarian diversity for qualitative attributes exist, of which Blau’s index is the most common (Harrison and Klein 2007; Joshi et al. 2011, 525; McDonald and Dimmick 2003; Solanas et al. 2012; Teachman 1980).Footnote 4
Egalitarian diversity is not the only diversity concept that has been proposed. Harrison and Klein propose three concepts of diversity—separation, variety, and disparity—and suggest that different measures are appropriate for each (Harrison and Klein 2007, 1202–1203, 1210–1214). As noted, “variety” is Harrison and Klein’s name for egalitarian diversity. Harrison and Klein’s innovation is to suggest that an egalitarian diversity concept is appropriate only for cases involving qualitative attributes, and that distinct concepts—separation and disparity—are associated with quantitative variables.
Diversity as separation is difference among group members “along a single continuous [and lateral] attribute” (Harrison and Klein 2007, 1203). The key idea is that separation involves difference of degree, but without any clear difference of social status. Examples include the degree of group members’ “organizational commitment” and “perceptions of leader charisma” (Harrison and Klein 2007, 1203). In these examples, diversity depends on the extent of divergence among the viewpoints or attitudes present in the group. Consequently, diversity as separation is maximized by polarization, that is, when the group is divided into equal numbers at opposite extremes (Harrison and Klein 2007, 1204). Finally, diversity as disparity is difference along a single continuous attribute, albeit a “vertical” attribute that is both socially valued and socially consequential (Harrison and Klein 2007, 1206). Examples include “power” and “pay” (Harrison and Klein 2007, 1206). Intuitively, diversity as disparity is the extent of imbalance between the best off and everyone else. Consequently, it is maximized by a positively skewed distribution, that is, by a distribution in which one individual occupies the highest point of the scale and all others the lowest (Harrison and Klein 2007, 1203).
The literature reviewed thus far, then, specifies egalitarian diversity for qualitative attributes but suggests that there may be other diversity concepts for quantitative variables. However, it is problematic to use the distinction between qualitative and quantitative attributes as a basis for categorizing diversity concepts. First, whether qualitative or quantitative variables are used is a practical decision of representation and modeling, not underlying concepts. For example, income can be represented by a quantitative variable, but it can also be represented by a set of qualitative categories (e.g., low income, middle income, high income). Yet in either case, the undelying concept might be that the more flat and spread the distribution, the greater the diversity. Second, the distinction between qualitative categories and quantitative variables is not always as sharp as some diversity researchers appear to suggest. There is now a burgeoning literature offering various, quantitatively well-specified models of qualitative categories (Minda and Smith 2001; Danks 2014; Gopnik and Wellman 2012). These quantitative models can provide similarity measures for comparing different qualitative categories, which suggests that one could add a measure of similarity to an egalitarian concept. For example, when the attribute is religious affiliation, Christianity and Judaism might be judged more similar than Christianity and Sikhism, and consequently a group consisting of equal numbers of Christians and Jews might be considered less diverse than a group consisting of equal numbers of Christians and Sikhs. Degrees of similarity are closely linked to Harrison and Klein’s (2007) notion of diversity as separation. However, we think it is more fruitful to see similarity as a conceptual ingredient that might be incorporated in several diversity concepts, rather than as a stand-alone diversity concept tied to quantitative variables. In fact, one contributor to the literature on diversity concepts proposes that “the manner and degree” of similarity (or difference) is an essential dimension of diversity generally (Stirling 2007, 709; Stirling 1998, 39–40, 58).
Multiple diversity concepts are also found in debates about biodiversity. In ecology, a major question has been whether there is any place for concepts of diversity that are not tied in some way to the biological context (Pielou 1980; Sugihara 1982; Molinari 1989; Ricotta 2005). One aspect of this debate is about whether an egalitarian diversity concept is appropriate for the study of biodiversity (Junge 1994, 19). The alleged problem with conceiving of diversity in this way is that it separates ecological diversity from the very reason it is thought to be worth studying in the first place—namely, “its possible connection with the functioning and organization of communities” (Sugihara 1982, 564). In conservation biology, some also insist that concepts of diversity take into account the degree to which the elements (e.g., species) at a particular site are similar to each other, so that diversity is linked to the preservation of unique ecological components of a given community (Maclaurin and Sterelny 2008; Vane-Wright et al. 1991, 236–241).
Moreover, conservation biologists also often require a diversity concept that takes into account rarity relative to other sites (Margules et al. 1988; Vane-Wright et al. 1991, 241–245). Thus, conservation biologists, following Whittaker (1960), often distinguish between “α-diversity, the diversity within a site, β-diversity, that between sites, and γ-diversity, or the total diversity of a region, including both α- and β-diversity” (Sarkar 2006, 136). Sarkar argues that only the latter two concepts are relevant to biodiversity, and that the most common β-diversity concept is complementarity (Sarkar 2006, 137; Sarkar 2002, 153). If species are the relevant attribute, then an ecosystem at site S is complementary with respect to an ecosystem located in region R to the extent that it possesses species that are rare in R. Complementarity, then, is an example of what we call comparative diversity.
Some conservation biologists also argue that their field is, or should be, primarily concerned with the preservation of “native” species, “native” population structures of particular species, or some other “native” aspect, or aspects, of the ecosystem (see, e.g., Angermeier 1994). These conservation biologists are struck by the allegedly counterintuitive possibility of maintaining or even increasing the biodiversity of a community by introducing new species, modifying a species’ population structure, fragmenting a landscape, etc.—that is, actions that are supposedly at odds with the goals of the field (Angermeier 1994; Angermeier and Karr 1994, 694; Thompson and Starzomski 2007). One response to this situation is to adopt alternative diversity concepts that, as Angermeier and Karr put it, “incorporate explicit native criteria” (1994, 694).
In sum, this section has shown that (a) multiple diversity concepts exist, (b) some depend only on the distribution within the focal group, while others depend on a comparison with a reference population, (c) these concepts might or might not incorporate a similarity weighting, and (d) some depend on non-distributional considerations (e.g., “nativeness”). In what follows, we explain how all of these conceptual complexities also arise in discussions of diversity among scientists.