{"ID":2826318,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.20686","arxiv_id":"2512.20686","title":"Sequential Apportionment from Stationary Divisor Methods","abstract":"Divisor methods are well known to satisfy house monotonicity, which allows representative seats to be allocated sequentially. We focus on stationary divisor methods defined by a rounding cutpoint $c \\in [0,1]$. For such methods with integer-valued votes, the resulting apportionment sequences are periodic. Restricting attention to two-party allocations, we characterize the set of possible sequences and establish a connection between the lexicographical ordering of these sequences and the parameter $c$. We then show how sequences for all pairs of parties can be systematically extended to the $n$-party setting. Further, we determine the number of distinct sequences in the $n$-party problem for all $c$. Our approach offers a refined perspective on size bias: rather than viewing large parties as simply receiving more seats, we show that they instead obtain their seats earlier in the apportionment sequence. Of particular interest is a new relationship we uncover between the sequences generated by the smallest divisor (Adams) and greatest divisor (D'Hondt or Jefferson) methods.","short_abstract":"Divisor methods are well known to satisfy house monotonicity, which allows representative seats to be allocated sequentially. We focus on stationary divisor methods defined by a rounding cutpoint $c \\in [0,1]$. For such methods with integer-valued votes, the resulting apportionment sequences are periodic. Restricting a...","url_abs":"https://arxiv.org/abs/2512.20686","url_pdf":"https://arxiv.org/pdf/2512.20686v2","authors":"[\"Michael A. Jones\",\"Brittany Ohlinger\",\"Jennifer Wilson\"]","published":"2025-12-22T15:43:36Z","proceeding":"math.GM","tasks":"[\"math.GM\",\"cs.CR\"]","methods":"[]","has_code":false}