The piranha principle: What does it mean, exactly?

Barnabas Szaszi writes:

I’m contacting you now to get your advice/interpretation on the piranha theorems regarding a paper I’m writing about the generalizability of behavioral interventions. Here, I use the Piranha theorem to back my claim that average affect of nudges are small:

First, there are theoretical reasons to assume that the average effect of choice architecture interventions is modest. It has been widely argued that in systems such as human behavior – and more broadly in social and behavioral sciences – phenomena are causally dense (Meehl, 1967, Gelman, 2011, Almaatouqa et al. 2022). The Piranha theorem (Gelman 2017 blogpost, Tosh et al. 2025) suggests that in such systems, many influencing factors operate concurrently, the interaction and interference of these factors would overwhelm most main effects leading to predominantly small effects.

I was wondering if you could help to clarify whether my interpretation is correct, these effects remain usually individually small because they overwhelm each other, or they are rather unlikely to remain individually small because of their cumulative impact?

My reply:

The basic piranha paradox is that there are subfields where many papers claim to find large and general effects, but of different factors. In the wild, where all these factors are operating in an uncontrolled fashion, the result of adding all these large effects, if these effects are independent, is that outcomes will be extremely variable. Given that real-world behavior is not so unpredictable, this implies that, either there are not a large number of large effects, or that the large effects happen to have large negative interactions that cause them to cancel out. But in that latter case the original claim (that effects are general) is false.

It’s also correct to say that many small effects won’t remain small, in the sense that, even when researchers talk about small effects, these effects are not so small. For example, an intervention that is claimed to increase some desirable behavior by 10%. That sounds small, but given that any intervention won’t work on most people, an average treatment effect of 0.1 is still large; see here. If you have many different treatments, each with an average effect of 0.1, then the piranha issue still arises: in the wild, with these treatments operating in an uncontrolled way, all these effects will add up in unexpected ways, leading to complete chaos–unless the effects interact in a way to mostly cancel each other out, in which case the effects of each treatment are highly context-dependent, in a way that would cast doubt on the original claims of universality.