TY - JOUR
T1 - Seat biases of apportionment methods for proportional representation
AU - Schuster, Karsten
AU - Pukelsheim, Friedrich
AU - Drton, Mathias
AU - Draper, Norman R.
PY - 2003/12
Y1 - 2003/12
N2 - In proportional representation systems, an important issue is whether a given apportionment method favors larger parties at the expense of smaller parties. For an arbitrary number of parties, ordered from largest to smallest by their vote counts, we calculate (apparently for the first time) the expected differences between the seat allocation and the ideal share of seats, separately for each party, as a function of district magnitude, with a particular emphasis on three traditional apportionment methods. These are (i) the quota method with residual fit by greatest remainders, associated with the names of Hamilton and Hare, (ii) the divisor method with standard rounding (Webster, Sainte-Laguë), and (iii) the divisor method with rounding down (Jefferson, Hondt). For the first two methods the seat bias of each party turns out to be practically zero, whence on average no party is advantaged or disadvantaged. On the contrary, the third method exhibits noticeable seat biases in favor of larger parties. The theoretical findings are confirmed via empirical data from the German State of Bavaria, the Swiss Canton Solothurn, and the US House of Representatives.
AB - In proportional representation systems, an important issue is whether a given apportionment method favors larger parties at the expense of smaller parties. For an arbitrary number of parties, ordered from largest to smallest by their vote counts, we calculate (apparently for the first time) the expected differences between the seat allocation and the ideal share of seats, separately for each party, as a function of district magnitude, with a particular emphasis on three traditional apportionment methods. These are (i) the quota method with residual fit by greatest remainders, associated with the names of Hamilton and Hare, (ii) the divisor method with standard rounding (Webster, Sainte-Laguë), and (iii) the divisor method with rounding down (Jefferson, Hondt). For the first two methods the seat bias of each party turns out to be practically zero, whence on average no party is advantaged or disadvantaged. On the contrary, the third method exhibits noticeable seat biases in favor of larger parties. The theoretical findings are confirmed via empirical data from the German State of Bavaria, the Swiss Canton Solothurn, and the US House of Representatives.
KW - Hamilton
KW - Hare
KW - Hondt
KW - Jefferson
KW - Sainte-Laguë
KW - Webster
UR - http://www.scopus.com/inward/record.url?scp=0141976818&partnerID=8YFLogxK
U2 - 10.1016/S0261-3794(02)00027-6
DO - 10.1016/S0261-3794(02)00027-6
M3 - Article
AN - SCOPUS:0141976818
SN - 0261-3794
VL - 22
SP - 651
EP - 676
JO - Electoral Studies
JF - Electoral Studies
IS - 4
ER -