Borda Aggregation Dynamics of Preference Orderings on Networks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910105305350144 |
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| author | Boudourides, Moses |
| author_facet | Boudourides, Moses |
| contents | We introduce and analyze a discrete-time network process in which each node holds a (weak) preference ordering over a finite set of alternatives and updates by local Borda aggregation. At each step, a node forms a weighted average (row-stochastic random-walk normalization) of its neighbors' Borda score vectors and projects the aggregated score back to a weak order. Updates are bounded: in each round, a node advances by at most one step along a shortest path in the fixed graph of preference orderings, following the direction prescribed by its neighbors' Borda-aggregated preferences. Our emphasis is dynamical: we develop sufficient conditions, stated directly in terms of graph topology, weights, and the bounded step rule, for (i) self-sustained oscillations in the absence of persistent sources, and (ii) forced oscillations under contrarian persistent camps. We also record robustness (structural stability) away from score-tie hyperplanes and contrast synchronous (Variant S) and asynchronous (Variant A) updating. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_04209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Borda Aggregation Dynamics of Preference Orderings on Networks Boudourides, Moses Social and Information Networks We introduce and analyze a discrete-time network process in which each node holds a (weak) preference ordering over a finite set of alternatives and updates by local Borda aggregation. At each step, a node forms a weighted average (row-stochastic random-walk normalization) of its neighbors' Borda score vectors and projects the aggregated score back to a weak order. Updates are bounded: in each round, a node advances by at most one step along a shortest path in the fixed graph of preference orderings, following the direction prescribed by its neighbors' Borda-aggregated preferences. Our emphasis is dynamical: we develop sufficient conditions, stated directly in terms of graph topology, weights, and the bounded step rule, for (i) self-sustained oscillations in the absence of persistent sources, and (ii) forced oscillations under contrarian persistent camps. We also record robustness (structural stability) away from score-tie hyperplanes and contrast synchronous (Variant S) and asynchronous (Variant A) updating. |
| title | Borda Aggregation Dynamics of Preference Orderings on Networks |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2604.04209 |