{"ID":2880710,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.13841","arxiv_id":"2508.13841","title":"Optimal Candidate Positioning in Multi-Issue Elections","abstract":"We study strategic candidate positioning in multidimensional spatial-voting elections. Voters and candidates are represented as points in $\\mathbb{R}^d$, and each voter supports the candidate that is closest under a distance induced by an $\\ell_p$-norm. We prove that computing an optimal location for a new candidate is NP-hard already against a single opponent, whereas for a constant number of issues the problem is tractable: an $O(n^{d+1})$ hyperplane-enumeration algorithm and an $O(n \\log n)$ radial-sweep routine for $d=2$ solve the task exactly. We further derive the first approximation guarantees for the general multi-candidate case and show how our geometric approach extends seamlessly to positional-scoring rules such as $k$-approval and Borda. These results clarify the algorithmic landscape of multidimensional spatial elections and provide practically implementable tools for campaign strategy.","short_abstract":"We study strategic candidate positioning in multidimensional spatial-voting elections. Voters and candidates are represented as points in $\\mathbb{R}^d$, and each voter supports the candidate that is closest under a distance induced by an $\\ell_p$-norm. We prove that computing an optimal location for a new candidate is...","url_abs":"https://arxiv.org/abs/2508.13841","url_pdf":"https://arxiv.org/pdf/2508.13841v1","authors":"[\"Colin Cleveland\",\"Bart de Keijzer\",\"Maria Polukarov\"]","published":"2025-08-19T14:01:57Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}