This post was initially published in French in September 2021.
The essential role of an actuary in charge of pricing is the segmentation of the portfolio (or “insurance classification” in English), corresponding to a discrimination activity (mathematically speaking) in the sense that the actuary will look for the most “discriminating” variables, to explain another one (in relation with the loss experience). But in the legal sense, discrimination is forbidden by law, which places the actuary in an often delicate and complex position.
Ethnic and racial origin
In France, the term “ethnic statistics” is a sensitive subject. However, censuses traditionally (for more than a century) ask for nationality at birth, thus distinguishing between French by birth and French by acquisition. And, for the past thirty years, the variable “parents’ country of birth” has been introduced in a growing number of public surveys. The word “ethnic”, often used in legal texts, seems to be a “euphemistic substitute for ‘racial'”, as the Committee for the Measurement of Diversity and the Evaluation of Discrimination states [Comedd, 2010]. The former has an anthropological basis, an “ethnic group” designating a group of people whose existence is attested even though they have no state (thus going beyond the “country of birth” requested in the questionnaires), whereas the latter seems to be associated with a relatively recent biological term, related to the classification of species. In 1978, the Data Protection Act used the expression “racial or ethnic origins”: “ethnic” is any reference to a foreign origin, whether it be nationality at birth, the nationality of the parents, or “reconstitution” based on surname or physical appearance.
In the United States, according to the Census, race is a concept of identification, where U.S. residents choose the race (or races, as of 2000) with which they best identify. This self-reporting principle was instituted in 1970, and prior to that, Census officials themselves associated U.S. residents with various categories. The “primary races” have long been “White,” “Black and African American,” and “Asian.
As Wolff  recalls, in 1896 Frederick L. Hoffman, an actuary with Prudential Life Insurance, published a book that demonstrated, with statistics, that the Black American was uninsurable. Although this work was criticized as soon as it was published – the main criticism was that it aggregated all sorts of data, preventing a more detailed analysis of other causes of (possible) excess mortality – it played an important role at a time when many anti-discrimination laws were being passed. At that time, several states in the United States passed laws prohibiting the charging of different premiums on the basis of racial information. For example, as Wiggins  points out, in the summer of 1884, the Massachusetts state legislature passed a law to prevent discrimination by life insurance companies against people of color. This law prevented life insurers operating in the state from making “any distinction or discrimination between white persons and colored persons wholly or partly of African descent, with respect to the premiums or rates charged on policies of life insurance for such persons.” The law also required insurers to pay full benefits to African-American policyholders as long as they paid the same monthly payments. It was on the basis of these laws that the uninsurability argument was made: insuring blacks at the same rate as whites would be statistically inequitable, Hoffman argued , and not insuring blacks was the only way to comply with the law.
While anti-discrimination laws have existed for over a century in the United States, many studies regularly question, based on spatial data, the existence of “red lining,” that is, the existence of geographic discrimination, which would be racial discrimination in disguise. For example, Heller  showed that predominantly African American neighborhoods pay 70% more, on average, for auto insurance premiums than other neighborhoods. And by analyzing 30 million premium quotes, by zip code, for major insurance companies across the United States, Larson et al.  confirmed that a gap existed, albeit smaller than the 70% mentioned. For example, in Illinois, insurance companies charged, on average, more than 10 percent more in auto liability premiums for “majority minority” zip codes (in the sense that the rate of minorities was highest) than in majority white zip codes. Historically, as Squires  reminds us, many financial institutions have engaged in such discrimination by refusing to serve predominantly African American geographic areas. While many analyses, such as Ong and Stoll (2007), have challenged these conclusions on the basis of covariates correlated with race, the question of how to establish, on the basis of observed data, the existence of discrimination remains a complex one; Charpentier (2022) reviews different approaches.
Discriminating between smokers and non-smokers
Another, more anecdotal, but important topic in the history of statistics is related to tobacco, as many debates took place between 1930 and 1990 on whether tobacco “causes” cancer, or whether it is simply a correlation. Many legal texts related to discrimination emphasize the importance of two factors in establishing discrimination: the absence of a causal relationship and the absence of choice. Also, smoking has been problematic: first, it took a long time to establish its health hazard (and the causal relationship between smoking and certain cancers), but more importantly, the debate over lack of choice is far from settled, as Baumeister  notes.
Patterson  recalls that, as early as 1930, insurers had observed that smoking had a negative impact on health. In particular, Frederick L. Hoffman , after having collected racial statistics as mentioned in the previous section, had started to collect statistics related to cancers from 1915. He stated that “smoking habits unquestionably increase the susceptibility to cancer of the mouth, throat, esophagus, larynx and lungs”, while pointing out the incredible heterogeneity of the “smoking” group (both in terms of quantity and quality of the product smoked). But nothing is said about the actuarial consequences. Here again, the conclusions were criticized by Ronald Fisher in 1958 and 1959, who stated that “there is no doubt that the genotype has a considerable influence on smoking”; in other words, smoking is explained genetically. And since cancers are often linked to genetic predispositions, if there is a correlation, it is only because there are common genetic factors. Fisher’s analysis was later challenged, as Stolley  recounts, and smoking was finally recognized as a probable cause of many cancers. Cowell and Hirst  re-launched the debate in the actuarial community, by constructing the first mortality tables for non-smokers and smokers.
Lawyers and actuaries
For Thiery and Van Schoubroeck , lawyers and actuaries have fundamentally different conceptions of discrimination and of the concept of “fairness”. Segmentation in insurance will be individual for some, and collective for others, as shown in the Manhart and Norris cases in the United States. In the Manhart case, in 1978, the Court ruled illegal an annuity plan in which men and women received equal benefits at retirement, and women made higher contributions. In 1983, the Supreme Court ruled in the Norris case that the use of gender-differentiated actuarial factors in pension plans was illegal because it fell within the prohibition against discrimination. Legally, the right to equal treatment is granted to a person as an individual, not as a member of a racial, sexual, religious or ethnic group. Thus, an individual cannot be treated differently because of his or her membership in such a group, particularly one to which he or she has not chosen to belong. These orders emphasize that individuals cannot be treated as mere components of a racial, religious or sexual class, asserting that fairness to individuals trumps fairness to classes. But this view is fundamentally opposed to the actuarial approach, which historically analyzes risks and calculates premiums in terms of groups: until recently, actuaries considered individuals only as members of a group [i].
An individual in a group with a higher statistical risk of survival, or death, must pay a higher premium or receive fewer benefits. In automobile insurance, an individual belonging to a group with a higher statistical risk of accident must pay higher premiums. Brilmayer et al  pointed out that it is the gender differences in accident probabilities (and not individual differences) that are taken into account to justify the difference in premiums, to explain the difference in benefits, or to provide a basis for a selection mechanism. Insurance classification systems are based on the assumption that individuals meet the average characteristics, stereotyped to use Schauer’s (2006) term, of a group to which they belong. Indeed, insurers argue that current statistics indicate that, on average, more women than men drive without an accident and that, therefore, the average woman has a lower probability of having a claim than the average man. Based on this data, women must pay a lower premium than men. Insurance companies aim to preserve equality between groups, not individuals. An essential foundation of insurance is the idea of “mutualization” of risk, that is, the constitution of supposedly homogeneous groups. Risk in insurance cannot be considered without this notion of mutualization, and this is the major difference with financial mathematics, where there is a fundamental value of a risk (in a market). Mutualization is intrinsic to the segmentation of insurance risks, and imposes a form of solidarity within the group; the totality of the premiums of a group must be statistically entirely compensated by the totality of the reimbursements of this same group. The insurer then imposes solidarity between policyholders who have the same risk profile (with a comparable probability of loss and size of loss). Without segmentation, or if the groups are not composed of members with a comparable risk profile, we will observe a phenomenon of “subsidizing” solidarity, in the sense that a person with a certain risk profile pays for the amount of the loss of persons with a higher loss expectancy.
Glenn  took up these two approaches to discrimination, statistical and legal, explaining that, like the Roman god Janus, an insurer’s risk selection process has two faces: the one presented to regulators and policyholders, and the other presented to underwriters. On the one hand, there is the face of numbers, statistics and objectivity. On the other, there is the face of stories, character and subjective judgment. The rhetoric of insurance exclusion (based on statistics) forms what Brian Glenn calls “the myth of the actuary, a powerful rhetorical situation in which decisions appear to be based on objectively determined criteria when they are also largely based on subjective criteria,” corresponding to the subjective nature of a seemingly objective process, as Desrosières  has shown perfectly.
When actuaries make a rate, they do not just look for correlations, they ideally look for possible causal variables, by telling themselves stories. The narrative of the model, its story, is almost as important as the statistical analysis. Glenn  pointed out, “There are many ways to score risks accurately, and that’s my point. Insurers can rate risks in many different ways based on the stories they tell about which characteristics are important and which are not […] Almost every aspect of the insurance industry is based on stories first and numbers second.” And the stories are often built on stereotypes. Indeed, according to Schauer  “to be an actuary is to be a generalization specialist, and actuaries engage in a form of decision making that is sometimes called actuarial.” Hence the importance of stereotypes, which consist in generalizing individual behaviors to a whole class of insureds.
Discrimination by proxy
Petauton  and Pradier  discuss discrimination in insurance at length, discussing the gender directive, which prohibited, in Europe, segmenting according to the gender of the insured. The idea of statistical discrimination raises many questions closely linked to the concept of “predictive variable”. Espeland and Stevens  mention the idea of “comeasures”, in the sense that a variable is used for purposes other than that for which it was created. This is the debate that we find, for example, on the use of the credit score in the United States, which is supposed to be an important predictive variable of an insured’s loss experience. But as Morris et al  noted, this may simply be because a low-income person may claim for a claim that slightly exceeds the deductible, while a person without financial difficulties will not engage in a time-consuming claim (thus giving the illusion that fewer claims have been observed for people with high credit scores).
Similarly, as Antonio and Charpentier  showed, gender, in car insurance, was a proxy for other information, which can be obtained by the connected boxes. Prince and Schwarcz  spoke of “proxy discrimination” (which could be translated “discrimination by proxy”), to describe this incidental impact. Proxy discrimination occurs when a “neutral” variable is used as a substitute – or proxy – for a prohibited variable. Austin  asserted that “the invitations to underwriters to introduce prejudgments and biases and to indulge amateur psychological stereotypes are apparent. Even generalized underwriting texts include occupational, ethnic, racial, geographic, and cultural characterizations certain to give offence if publicly stated.”
And this proxy discrimination, often unintentional, becomes a complicated challenge when dealing with massive data and black box algorithms that are difficult to interpret and explain. As Gillis and Spiess  pointed out, prohibiting the use of a protected variable is not enough to prevent discrimination, “the mere exclusion of a prohibited variable may be insufficient when other characteristics are correlated with that variable – a problem that is exacerbated in the context of big data. Not to mention that artificial intelligence (AI) and machine learning pose additional challenges. As Epstein and King  reminded us, unlike traditional statistical models, machine learning does not rely on a human’s initial intuition about the causal explanations for the statistical relationships between the input data and the target variable. Instead, the algorithm uses training data to discover for itself which features can be used to predict the target variable. Although this process completely ignores causality, it inevitably leads algorithms to “search” for proxies for directly predictive features when data on those features are not made available to the AI due to legal prohibitions.
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[i] In a sense, the notion of a “personalized premium” would almost be easier to justify under this legal view.