Groupthink and the wisdom of crowds

1 Diversity dividends

Maybe diversity and tolerance aren’t just intrinsic moral goods, but they might also pay literal dividends in terms of avoiding groupthink and being more effective. What are the conditions for this happy state?

Does diversity help attain wisdom? Sometimes, it seems. Scott Page calls this the diversity dividend. Quantifying when and how it works interests me.

Practically, see cultivating diversity.

McKinsey report, Vivian Hunt, Dennis Layton, and Sara Prince: Why diversity matters:

While correlation does not equal causation (greater gender and ethnic diversity in corporate leadership doesn’t automatically translate into more profit), the correlation does indicate that when companies commit themselves to diverse leadership, they are more successful.

(They could’ve done better than that mealy-mouthed correlation phrasing, using causal analysis.)

Other random readings: Chris Dillow, diversity trumps ability.

The new Matthew Syed book (Syed 2020) (titled Rebel Ideas or Superteams depending on where you are) apparently covers some of this material.

2 Social structure of knowledge

Vested interests, contrarians, consensus. These generate some stylised dynamics in the social structure of knowledge which I would like to explore with mathematical models and simulations.

Scott Aaronson on “armchair epidemiology” uses the COVID-19 public communication fiasco as a lens on societal collective knowledge and science and the role of contrarians. Connection to red queen signal dynamics should be apparent. The comment threads in that post meander around this topic at length.

This resembles another pyramid of fashionable disagreement that he mentions, the Intellectual Hipsters and Meta-Contrarianism pyramid.

3 Crowdsourcing models

Due to Dawid and Skene (1979) and descendants.

In the classical setup, there is a latent ground truth label, and \(n\) noisy annotators each report with an unknown confusion matrix. There exist methods (expectation-maximisation) to estimate these matrices; spectral methods (Zhang et al. 2016) can identify annotator quality without ground truth. The limitation for our purposes is that Dawid-Skene-type methods assume all annotators label the same items. Internet authors write about different things. Still, the mathematical machinery — latent truth, heterogeneous noise, identification via redundancy — might be useful.

4 Crowd meta-knowledge

We can hope to extract truth from crowds by thinking about incentives, Bayes, and meta-knowledge. Key works here are Prelec (2004) and descendants (Witkowski and Parkes 2012; Miller, Resnick, and Zeckhauser 2005). The “surprisingly popular” (SP) algorithm (Prelec 2004; Prelec, Seung, and McCoy 2017) seems like a good start: it extracts truth from crowds by finding answers that are more popular than predicted. Concretely: people who hold the correct-but-minority view often know their view is rare, so they predict lower support for it from everyone else. The SP algorithm uses this gap between actual and predicted popularity as a signal — the gap between first-order beliefs (what I think) and second-order beliefs (what I think others think). Does the structure of the internet corpus contain enough second-order information to support something like this? Blog posts often respond to other positions, explicitly modelling what “they” believe. This meta-discursive structure might be informative in the SP sense — the internet running a massively distributed, ramshackle version of the same trick, finding coherent patterns that show up more than we’d expect if the corpus were just noise (cf. Collina et al. (2025) on collaborative prediction by sharing predictions, not data).

5 Robust statistics

We can estimate the mean of a distribution even when an \(\varepsilon\)-fraction of samples are adversarially corrupted, as long as the clean distribution has bounded moments. This is because, in high dimensions, adversarial corruption distorts the covariance in detectable ways. Specifically, it introduces “spurious” eigenvalues, which we can then filter out. By analogy we might hope that even if \(\varepsilon\) of the internet is adversarially generated, if the “clean” distribution over text had enough structure, we could learn through the noise. The book to read on this is Diakonikolas and Kane (2023).

This is an analogy; making it do real work needs more. What are the “bounded moments” assumptions in the text setting? What does “adversarial corruption” even mean when the data has sequential structure? 🏗

6 Incoming

• Tim Harford, How not to Groupthink
• Information Cascades

7 References