My wife and I have started attending a small church named Grace International Church here in Baltimore. We are pleased with the opportunity to transition from a much larger fellowship to a smaller community of believers with whom we might share more responsibility now that we know we will be in the area a bit longer than we’d thought. I’ve especially enjoyed Bible study with Pastor Ken Patterson. We’ve been studying the book of Romans, and I’ve been studying cognitive heuristics in decision making at work. I always like to combine the two where possible, and I was amused to hear an interesting example of the representativeness heuristic come up this week.
First, I’ll assume fewer people have heard of the representative heuristic than the role of circumcision in Jewish/Christian belief, so I’ll start with representativeness. Introduced by Amos Tversky and Daniel Kahneman as one of three heuristics employed in decision making in a seminal Science paper, representativeness is described (on Wikipedia) as:
“a psychological term wherein people judge the probability or frequency of a hypothesis by considering how much the hypothesis resembles available data as opposed to using a Bayesian calculation…”
In other words, representativeness describes the types of judgments people make when presented information that is irrelevant to the decision or classification problem they have at hand, but process that information by evaluating its similarity to their own pre-conceived stereotypes. A popular example [also reproduced on Wikipedia] frequently used when teaching cognitive heuristics , is the following classification task:
In a study done in 1973, Kahneman and Tversky gave their subjects the following information:
- “Tom W. is of high intelligence, although lacking in true creativity. He has a need for order and clarity, and for neat and tidy systems in which every detail finds its appropriate place. His writing is rather dull and mechanical, occasionally enlivened by somewhat corny puns and by flashes of imagination of the sci-fi type. He has a strong drive for competence. He seems to feel little sympathy for other people and does not enjoy interacting with others. Self-centered, he nonetheless has a deep moral sense.”
The next task the subjects are asked to do is choose among 9 graduate school majors Tom W’s most likely course of study. Of course, since the above description does not give any information relevant to determining Tom W’s major, the subjects will probably rely on their stereotypes for each of the 9 major choices. This is precisely what Tversky and Kahneman found:
The subjects were then divided into three groups who were given different decision tasks:
- One group of subjects was asked how similar Tom W. was to a student in one of nine types of college graduate majors (business administration, computer science, engineering, humanities/education, law, library science, medicine, physical/life sciences, or social science/social work). Most subjects associated Tom W. with an engineering student, and thought he was least like a student of social science/social work.
- A second group of subjects was asked instead to estimate the probability that Tom W. was a grad student in each of the nine majors. The probabilities were in line with the judgments from the previous group.
- A third group of subjects was asked to estimate the proportion of first-year grad students there were in each of the nine majors.
The key thing to note here is that the estimated probability and the frequency of similarity judgments are correlated with each other, indicating that the subjects use the similarity of the description to their stereotypes to make judgments about Tom W. instead of thinking mathematically about the characteristics of the underlying process. Ultimately, they should have determined that not enough information was present within the description to distinguish among the nine majors presented, and used the estimated proportion of first-year grad students in each of nine majors to make their decision.
Now this is interesting because the apostle Paul accuses first-century Jewish Christians of using representativeness to ascertain status among the believers. In Romans, Paul constructs what many Christians now understand as the “sola gratia, sola fide, soli Deo gloria” doctrines of salvation, justification, and sanctification. I am not going to provide a detailed discussion of these doctrines here. Suffice it to say that we believe men (and women) are saved from the wrath of God by faith, are justified (that is, we have Christ’s righteousness imputed to us, although there is an interesting technical discussion of this important doctrine ongoing) by grace through faith in Christ alone, and are sanctified by and through the glory of God. In particular, these doctrines are concisely set forth in Romans 3:21-26 (ESV):
But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it—the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: for all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith. This was to show God’s righteousness, because in his divine forbearance he had passed over former sins. It was to show his righteousness at the present time, so that he might be just and the justifier of the one who has faith in Jesus.
The remainder of the book of Romans is devoted to defending this argument. But why does this argument not start the book? Why does Paul wait until a third of the book is composed before asserting these most unifying of Christian beliefs? I think that Romans 3:27-30 (ESV) points us in the right direction:
Then what becomes of our boasting? It is excluded. By what kind of law? By a law of works? No, but by the law of faith. For we hold that one is justified by faith apart from works of the law. Or is God the God of Jews only? Is he not the God of Gentiles also? Yes, of Gentiles also, since God is one—who will justify the circumcised by faith and the uncircumcised through faith.
Here, Paul is indicating to his Jewish believers that the outward sign of circumcision is not a sufficient criterion for judging whether one is authentically a member of the community of faith or not. Paul had spent the first third of Romans to explain to his fellow Jewish believers that they were employing representativeness to determine whether the underlying process of spiritual regeneration had taken place. Because there was no precedent for the inclusion of non-Jews into the faith community initiated by Abraham and his descendants, it was far easier to compare individual believers to Jewish images of “religious,” authentically pious, circumcised Jews. To supplant the representative heuristic in building up the Christian diaspora, Paul had to first show that outward religious expressions are irrelevant to the process of spiritual regeneration. By irrelevant, I am talking about probabilistic irrelevance: Pr[X|Y]=Pr[X]. In the first third of his discourse, Paul demonstrates not only that the distribution of spiritual darkness is the same among Jews and non-Jews, but also that adherence to the Law does not imply any difference in the distribution of reprobation.
I am tickled that the same math we use today to address overconfidence in risk assessment was also used in the first-Century to protect the spiritual and intellectual integrity of the Christian diaspora. soli Deo gloria…