Geometric Voting and Consecutively Halved Positional Voting

Evaluations: CHPV Maps 2

Three-Party Multiple-Winner CHPV Elections

Three-party maps that contain all the possible election outcomes for a given number of winners are introduced in the previous section. The maps for three parties A, B and C contesting up to three vacancies in party-list CHPV elections are shown on this page and those for four to six vacancies are shown on the next one. Recall that the actual per-unit tally shares for A, B and C are represented by the appropriate point on the triangular map where each share is measured at right-angles from the base (or map edge) towards its opposing apex.

The boundaries of the OPV domains are hexagonal (or part thereof) and are indicated by the dotted lines on the map. Any point within an OPV domain is closer to the central dot in that domain than to a dot in any another domain. The stated seat share for the domain is therefore the optimal outcome for any such point (tally share) within that domain.

The boundaries for the CHPV domains are determined by the numerous two-way and three-way critical ties that may occur in elections with W winners. For the specific details of how party stick diagrams are used to deduce the position of these boundaries, please refer to the Three-Party CHPV Maps page in the Map Construction appendix.

For all points on a map that are in the same CHPV and OPV domains the outcome is optimally proportional. For all points in dissimilar domains the outcome is not optimal.