2 papers
math.PR2026
Quantifying the Balinski-Young Theorem: Structure and Probability of Quota Violations in Divisor Methods for Three States
Joseph Cutrone, Tyler C. Wunder
The apportionment problem asks how to assign representation to states based on their populations. That is, given census data and a fixed number of seats, how many seats should each…
math.PR2026
Probability of Quota Violations in Divisor Apportionment Methods with Nonzero Allocations
Tyler C. Wunder, Joseph Cutrone
Apportionment assigns indivisible items among groups. By the Balinski-Young theorem, no method can satisfy both house monotonicity and the quota rule. This paper investigates quota…