2025/12/22 by Michael A. Jones, Jones, Michael A., Brittany C. Ohlinger +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #91B32 91B12 91F10 #Benford’s Law and Fraud Detection #Complexity and Algorithms in Graphs #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Voting Systems #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2512.20686
openalex publication_date 2025/12/22 · openalex created_date 2025/12/26 · openalex updated_date 2026/07/28
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 ∈ [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.