Barucca, Rocchi, Marinari, Parisi and Ricci-Tersenghi (PNAS 2015) showed that yearly Pearson correlations between the name distributions of the 50 US states plus Washington, DC (Social Security Administration data, 1910-2012) organize the states into stable clusters that persist for many decades and then abruptly reorganize in the late 20th century. The authors deliberately left the causal layer of this descriptive finding open: they did not identify the mechanisms that generate the inter-state correlations, did not determine why the clusters reorganized, and did not extract the directed (who-influences-whom) structure, noting only that their analysis could be adapted to do so. The open problem is to give a quantitative, causal-mechanistic account of this correlation structure: identify which transmission mechanisms (conformist social influence, anti-conformity and increased innovation, neutral drift, mass-media versus interpersonal transmission, changing social connectivity and migration) generate the correlations; explain the timing and drivers of the late-20th-century reorganization; and extract the directed, time-lagged network of cultural influence between states, disentangling increased name innovation from weakening social influence within the same dataset. A later literature (2016-2025) has replicated and generalized the descriptive clustering approach and quantified conformity and anti-conformity forces in national-level name time series, but the spatially resolved causal questions remain open.

Background

Quantitative cultural evolution studies how behavioral patterns shared by members of a community — cultural traits such as given names, dog-breed choices, pottery decorations or pop songs — change over time. Baby names are a canonical testbed because a name is a nearly 'neutral' cultural trait: its adoption is shaped mostly by the surrounding culture rather than by functional costs, and the US Social Security Administration (SSA) publishes, for each state and year from 1910 onward, the counts of names given to newborns (with a reporting floor of five occurrences per state-year). Several mechanistic accounts of name popularity had been proposed before 2015: random copying analogous to neutral genetic drift (Hahn and Bentley 2003), status-based copying in the sense of Simmel, in which lower-status individuals copy perceived higher-status ones, producing the 'Simmel effect' of successive fashion waves (Krawczyk, Dydejczyk and Kulakowski 2014), a model mixing individual preferences with social influence that also detected irregularities in time-lagged (retarded) cross-correlations of the aggregated US name distribution appearing in the 1970s, which its authors attributed to the post-Vietnam-War cultural transformation (Xi et al. 2014), and evidence for accelerated innovation of new names together with increased spatial diversity of US popular culture (Bentley and Ormerod 2012).

Barucca, Rocchi, Marinari, Parisi and Ricci-Tersenghi (2015) asked what the relations between the local, state-level distributions of names — rather than the national aggregate — reveal about cultural influences between US communities. For each year, they computed the Pearson correlation, across all names, between each pair of states' name-frequency vectors after subtracting the national average frequency, producing a 51-by-51 correlation matrix per year (the same conclusions held for boys' and girls' names). They analyzed these matrices with principal component analysis (PCA, the standard linear-algebra decomposition of correlation matrices into dominant eigenvectors) and hierarchical clustering (agglomerative merging of states into groups by correlation-defined distances), validating against random-matrix null models to separate genuine correlation from noise. The result: groups of correlated states emerge naturally, remain stable across many decades, and undergo a sudden reorganization in the last part of the 20th century, after which, for example, Atlantic and Pacific coastal states cluster together apart from many central states.

The paper is explicitly descriptive about this structure. Its Discussion states that the authors do not discuss the origin of these correlations or the mechanisms by which names are given to newborns, that they do not study why the reorganization of clusters happened in the last decades of the 20th century — calling these 'two very interesting issues' deserving a more specific study — and that their analysis 'can be adapted to capture which states influence a given state and which ones are influenced by the same state', which amounts to identifying a directed network relevant to studying time correlations and culture propagation. It also notes that the observed diversity increase is variously attributed to shorter name lifetimes, weakening social influence, or increased innovation, and that 'much more should be said on this', and it proposes extending the approach to other cultural traits and to the abundant digital-era records of human behavior.

Subsequent work has deepened the national-level and methodological picture but not the causal, spatial one. Newberry and Plotkin (2022) developed a maximum-likelihood method to infer frequency-dependent selection (whether a trait's copying probability depends on its current popularity) from time series of trait abundance, and found strong negative frequency-dependent selection — anti-conformity, a systematic dispreference for whatever is currently most common — in US baby names: the most common names decline on average 2-6 percent per year while rare names gain 1-3 percent per year, replicating across the US, France, Norway and the Netherlands, with different implied innovation rates for male and female names. O'Dwyer and Kandler (2017) showed how progeny distributions can distinguish neutral evolution from novelty biases, finding that neutral evolution plausibly describes abundant variants of Australian baby names while rare variants deviate and an anti-novelty bias reproduces the full distribution. Pomorski, Krawczyk, Kulakowski, Kwapień and Ausloos (2016) replicated the inter-state correlation-network approach using correlations restricted to each year's 100 most frequent names, finding communities stable until about 1980 that broadly match geopolitical regions, with a Belgium comparison. Bush, Powell-Smith and Freeman (2018) analyzed name-choice networks in the UK over 1838-2016, describing a self-correcting rarity-preference feedback, and Liu, Rosenberg and Greenbaum (2022) generalized network-based hierarchical clustering to cultural variation including US first-name data. None of these identifies what generates the inter-state correlations, why the clusters reorganized, or the direction of influence between states.

Problem Statement

Provide a quantitative, causal-mechanistic account of the inter-state correlation structure that Barucca et al. (2015) documented in the US state-level baby-name data (SSA, 1910-2012, names with at least five occurrences per state-year). The account must address the following three subgoals:

  1. Mechanism identification: determine which transmission mechanisms generate and maintain the observed yearly correlations between state-level name distributions, quantitatively discriminating on this dataset among conformist social influence, anti-conformity and increased innovation, neutral drift, and the contributions of mass-media versus interpersonal transmission and of changing social connectivity and migration. This includes the explicit disentanglement of increased name innovation and diversity from weakening social influence as contributors to the reported patterns.

  2. Explanation of the reorganization: account for the abrupt reorganization of the state clusters in the late part of the 20th century — its precise timing, the sociocultural and demographic processes driving it, and whether it was gradual or punctuated by specific events — including which candidate explanations (for example the post-Vietnam-War cultural transformation hypothesized by Xi et al. 2014, media expansion, or migration) the data support.

  3. Directed influence network: extract the time-lagged, directed network of cultural influence between states — which states lead changes in name popularity and which follow — and characterize how this directed propagation structure evolves over the century.

All claims must be validated against the SSA state-level data: a mechanistic model must reproduce the observed correlation matrices, the cluster structure, its decades-long stability and its late-20th-century reorganization, and any directed-network claim must be supported by appropriate statistical nulls. The source also proposes extending the correlation-and-clustering framework to other cultural traits and to digitally recorded behaviors.

References

  1. Barucca P., Rocchi J., Marinari E., Parisi G., Ricci-Tersenghi F. (2015). Cross-correlations of American baby names. Proceedings of the National Academy of Sciences USA 112(26):7943-7947. DOI: 10.1073/pnas.1507143112, https://doi.org/10.1073/pnas.1507143112 (preprint: arXiv:1410.2771, https://arxiv.org/abs/1410.2771)
  2. Hahn M. W., Bentley R. A. (2003). Drift as a mechanism for cultural change: an example from baby names. Proceedings of the Royal Society of London B (Biology Letters) 270 Suppl:S120-S123. DOI: 10.1098/rsbl.2003.0045, https://doi.org/10.1098/rsbl.2003.0045
  3. Krawczyk M. J., Dydejczyk A., Kulakowski K. (2014). The Simmel effect and babies' names. Physica A 395:384-391. DOI: 10.1016/j.physa.2013.10.018, https://doi.org/10.1016/j.physa.2013.10.018
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  7. Bush S. J., Powell-Smith A., Freeman T. C. (2018). Network analysis of the social and demographic influences on name choice within the UK (1838-2016). PLOS ONE 13(10):e0205759. DOI: 10.1371/journal.pone.0205759, https://doi.org/10.1371/journal.pone.0205759
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