Half of declared friendships are not reciprocal

Reciprocal nomination surveys, which question every member of a group, make it possible to check whether a friendship declared by one person is also declared by the other. Reciprocity is far from systematic. The method goes back to Jacob Moreno's sociometry, which he set out in 1934 in Who Shall Survive?

A study published in 2016 by Abdullah Almaatouq and colleagues, on student groups, finds reciprocity close to one friendship in two, while participants expected near-total reciprocity.

The most interesting result of this work is not the measured rate but the gap with stated expectation: respondents strongly overestimate the probability that their declaration is shared.

That gap is stable and does not depend on the number of friends named, which rules out an explanation by mere generosity of the list. It stems rather from a conviction: a relationship experienced as reciprocal seems so by nature, and nothing in ordinary experience comes to contradict it.

The first is definitional: the word does not mean the same thing to everyone, and a relationship may occupy different ranks in two personal hierarchies.

The second is structural: a much-sought person is named by many without being able to name everyone back, a mechanism linking this finding to the friendship paradox.

A third concerns the moment of the question. A list drawn up from memory retains the relationships most present in mind that day, and two people are never questioned in the same frame of mind.

Analyses resting on unilaterally declared ties describe a different structure from those requiring reciprocity. The two types of graph give distinct results on centrality and on diffusion. A directed graph keeps the information on who names whom; a reciprocal graph retains only ties confirmed on both sides and so loses a large part of it.

Serious work therefore states which of the two is used, information that changes the interpretation of every indicator computed afterwards. In the 2016 study, influence between participants depended, moreover, on the direction of the declared tie, which shows that the distinction is not merely a matter of coding.

Non-reciprocity is neither an error nor a deception. It measures the gap between two personal hierarchies, and a relationship may be real on both sides while not occupying the same place. The finding describes how hierarchies specific to each person overlap imperfectly, and nothing more.

Studies measuring reported closeness rather than the category do find far more continuous gaps, which suggests that the threshold of the word produces part of the observed asymmetry.