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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.10726 |
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| _version_ | 1866911671757307904 |
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| author | Camargo, Chico Q. |
| author_facet | Camargo, Chico Q. |
| contents | Most mathematical models of opinion dynamics treat attitudes as scalar quantities or positions on a low-dimensional ideological axis. Empirical attitudes, however, are bundles of positions across many policy issues, and the geometry of the resulting high-dimensional belief space is non-trivial. This paper develops a network-theoretic framework for analysing how individuals move through such a space between two measurement waves. Continuous attitude profiles in $[0,1]^n$ are discretised onto regular grids of resolution $k$, occupied positions form a network whose adjacency is defined by single-issue unit moves, and densely populated regions are interpreted as network-normative: empirically common configurations of attitudes in the population.
We introduce a hierarchy of null models against which observed movement can be benchmarked: a closed-form coverage baseline requiring no behavioural parameters; a local random-walk that retains each respondent's baseline position and asks whether destinations are over-represented in occupied regions relative to a uniform 1- or 2-step move; and a marginal permutation null model that preserves per-issue change distributions while disrupting within-respondent cross-issue coupling. Applying the framework to a two-wave panel of $N=1194$ respondents on $n=10$ issues, we find that the observed inside rate exceeds the coverage baseline by a factor of 36 at the focal resolution $k=3$, exceeds the two-hop random-walk null model by $\sim 0.30$, and exceeds the perturbation null model by $\sim 0.04$; only the one-hop random walk is competitive. The perturbation gap grows from near zero at $k=2$ to $\sim 0.14$ at $k=5$, indicating that coupled cross-issue updating is detectable only at fine resolutions. Network-normative attraction is therefore real but representation-contingent: which null model is exceeded, and by how much, changes systematically with $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10726 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Network-Normative Belief Updating in High-Dimensional Ideological Space Camargo, Chico Q. Physics and Society Social and Information Networks Most mathematical models of opinion dynamics treat attitudes as scalar quantities or positions on a low-dimensional ideological axis. Empirical attitudes, however, are bundles of positions across many policy issues, and the geometry of the resulting high-dimensional belief space is non-trivial. This paper develops a network-theoretic framework for analysing how individuals move through such a space between two measurement waves. Continuous attitude profiles in $[0,1]^n$ are discretised onto regular grids of resolution $k$, occupied positions form a network whose adjacency is defined by single-issue unit moves, and densely populated regions are interpreted as network-normative: empirically common configurations of attitudes in the population. We introduce a hierarchy of null models against which observed movement can be benchmarked: a closed-form coverage baseline requiring no behavioural parameters; a local random-walk that retains each respondent's baseline position and asks whether destinations are over-represented in occupied regions relative to a uniform 1- or 2-step move; and a marginal permutation null model that preserves per-issue change distributions while disrupting within-respondent cross-issue coupling. Applying the framework to a two-wave panel of $N=1194$ respondents on $n=10$ issues, we find that the observed inside rate exceeds the coverage baseline by a factor of 36 at the focal resolution $k=3$, exceeds the two-hop random-walk null model by $\sim 0.30$, and exceeds the perturbation null model by $\sim 0.04$; only the one-hop random walk is competitive. The perturbation gap grows from near zero at $k=2$ to $\sim 0.14$ at $k=5$, indicating that coupled cross-issue updating is detectable only at fine resolutions. Network-normative attraction is therefore real but representation-contingent: which null model is exceeded, and by how much, changes systematically with $k$. |
| title | Network-Normative Belief Updating in High-Dimensional Ideological Space |
| topic | Physics and Society Social and Information Networks |
| url | https://arxiv.org/abs/2605.10726 |