Macro-scale demonstration of the Conjunction Fallacy

Following the death of the great Daniel Kahneman.

In 2010 I reached out to Daniel Kahneman — my only personal interaction with him — for his opinion on the peculiar macro-scale demonstration of the Conjunction Fallacy or CF (sometimes known also as the Linda Problem), which I noticed to have taken place in Israel in the debate about a proposal to amend Israel’s naturalization oath. 


Conceptually and experimentally, the CF refers to individual decision-making. 

How to meaningfully extend it to a group, as a manifestation of collective decision-making or individual decision-making in a group context? 

Instead of a direct answer, consider not an experiment but an actual event taking place over a decade ago that exhibited a CF pattern: the controversy over a bill purporting to amend Israel’s naturalization oath.  

Israel’s original 1952 naturalization law prescribes an oath to be taken by the prospective citizen: “I declare that I shall be a faithful citizen to the State of Israel.” 

In 2010, a member of parliament attempted to amend that law by appending to the prescribed oath, “…as a Jewish and democratic state.”  

The question divided opinions neatly: the proposal (which did not become law) was supported by right-wingers, opposed by left-wingers, and started a national drama that did not fail to attract considerable international attention. 

The political sentiments, however, would seem misplaced considering that the proposed qualifiers “Jewish” and “democratic” are conditions to be met for the loyalty to be in force. Should Israel not be democratic (or Jewish), the oath taker is to be relieved from the obligation. The more conditions set out, the less restrictive the oath is— the more liberal it is.  To see that the rationale holds, think how awkward a wedding pledge to be “faithful to you as lovely and beautiful” sounds. (The formulation “You are x and y. I will be faithful to you” would be better, but the uneasy undertone of conditional still lingers.)

Contrary to their intentions, the right-favored amended oath is in fact more progressive than the original formulation (which is still law), which speaks of loyalty to the state without reservation, an uneasy formula for liberal democracies, in which allegiance is routinely made to the constitution, as is the case in the U.S., or to the sovereign, as in the U.K.  The liberal democratic formula is loyalty to the spring of government’s authority rather than to the state, which the government serves.

Practically no one who publicly identified with either of the sides on the question (liberal-minded experts in statistics and in decision-theory were among the opponents) seemed to form their opinion in accordance with the logical constraints. 

Kahneman replied

(I think it’s fine now to publish this private correspondence)

I have not monitored the debate – it makes me sick.  And I don’t want to weigh in on it.  If the wording says Ki-medina Yehudit (I translate from your translation) then you are certainly right, but this is linguistics and I have no special expertise on it.

What to make of it? 

We can explain the macro-scale rationality failure with the simple observation that the oath text was not interpreted as an oath, but as an expression of personal opinion, the answer to the question, “what would you like the object of your loyalty to be?”

This guarantees internal consistency: in the political theater that ensued, both sides played their roles with remarkable consistency and without consequence.  The debate died down; the bill had not become law; no one seemed to care whether the bill would become actual policy; no one seemed to care that Israel lacked a naturalization policy and that the naturalization oath — in whatever form — was not —and was not expected to be —administered. 

If the oath brouhaha obviously lacks the refinement of a controlled experiment, it suggests that a group setting under certain conditions may enhance the CF effect (irrationality crowds out rationality).  

What do we learn from the Conjunction Fallacy?

I propose next a possible lesson to draw from the robustness of the CF effect as demonstrated by the growing and sophisticated body of research since Tversky and Kahneman first reported their findings: in the tradeoff between accuracy and precision, people tend to the latter.  

In more detail:

  1. Statements are assumed heuristically to be accurate, i.e, assumed to be hypothetically and tentatively true as a prerequisite for meaningfulness. They are even mentally edited to support accuracy; no decision or judgment of accuracy is usually needed but a statement would be judged inaccurate only given a compelling reason to do so (asymmetry).
  2. Accuracy is hypothetical, theoretical or tentative: language conjures a reality. Linda never existed, and it never mattered.
  3. The CF arises because the comparison of different statements in a given context according to their accuracy (which is assumed) is awkward. Moreover, a good experiment design takes pains to place competing statements on a similar footing as to minimize variance beyond the detail of interest, and thus unwittingly exacerbates the problem by suggesting a shared context (it is like reading one uneven article vs two different articles: comparison of standards is easier in the latter).
  4. The first moment of meaningfulness is precision.  Accuracy is but a precondition for meaningfulness. In other words: we assume language to be accurate enough, and use it to convey information.