TY - JOUR
T1 - Find the Threshold of Exclusion for all single seat and multi-seat scoring rules: Illustrated by results for the Borda and Dowdall rules
AU - Fraenkel, Jon
AU - Bernard Grofman, Bernard Grofman
AU - Feld, Scott
PY - 2017
Y1 - 2017
N2 - We provide a general analytic approach for calculating the Threshold of Exclusion (TE) for the singleseat
and the multi-seat versions of all scoring rules, an infinitely large class of voting systems (Fishburn,
1973; Young, 1975; Saari, 1994, 1995). We offer specific results for two rules used for parliamentary
elections at the national level: Borda (Black, 1958), used for national elections to special reserved seats
for Hungarian and Italian ethnic minorities in Slovenia, and the unique and little known electoral system
used for legislative elections on the Pacific Island state of Nauru, the Dowdall rule. When voters are
required to provide a complete ranking of all candidates, we find that Borda does not, in general, operate
as a majoritarian system in that a supermajority of roughly 2/3rd is required to guarantee electing a
candidate of choice. In contrast, we find that, as district magnitude increases, the Threshold of Exclusion
for the Dowdall rule tends to zero, in the same way as do list systems of proportional representation (PR).
However, in contrast to the case for list PR rules, TE for Dowdall can still be relatively close to 1/2 for small
district magnitudes
AB - We provide a general analytic approach for calculating the Threshold of Exclusion (TE) for the singleseat
and the multi-seat versions of all scoring rules, an infinitely large class of voting systems (Fishburn,
1973; Young, 1975; Saari, 1994, 1995). We offer specific results for two rules used for parliamentary
elections at the national level: Borda (Black, 1958), used for national elections to special reserved seats
for Hungarian and Italian ethnic minorities in Slovenia, and the unique and little known electoral system
used for legislative elections on the Pacific Island state of Nauru, the Dowdall rule. When voters are
required to provide a complete ranking of all candidates, we find that Borda does not, in general, operate
as a majoritarian system in that a supermajority of roughly 2/3rd is required to guarantee electing a
candidate of choice. In contrast, we find that, as district magnitude increases, the Threshold of Exclusion
for the Dowdall rule tends to zero, in the same way as do list systems of proportional representation (PR).
However, in contrast to the case for list PR rules, TE for Dowdall can still be relatively close to 1/2 for small
district magnitudes
U2 - 10.1016/j.mathsocsci.2016.11.004
DO - 10.1016/j.mathsocsci.2016.11.004
M3 - Article
SN - 0165-4896
VL - 85
SP - 52
EP - 56
JO - Mathematical Social Sciences
JF - Mathematical Social Sciences
IS - 1
ER -