Contents

Description of CHPV and GV

Introduction
Analogy
Weightings
Voting
Counting
Outcomes
Party-List
Summary

Evaluations of CHPV and GV

Ranked Ballot

Introduction (RB)
General Criteria
Majority Criteria
Clones & Teaming
Teaming Thresholds
Summary (RB)

Party-List

Introduction (PL)
Diagrams & Maps
CHPV Maps
Optimality
Party Cloning
Proportionality
Summary (PL)

Comparisons of CHPV with other voting systems

Single-Winner

Introduction (SW)
Plurality (FPTP)
Borda Count
Geometric Voting
Positional Voting
Condorcet Methods
AV (IRV)
Plur. Rule Methods
Summary (SW)

Multiple-Winner

Introduction (MW)
STV
Party-List
PL ~ Hare
PL ~ Droop
~ Maps Opt PC Pro
PL ~ D'Hondt
~ Maps Opt PC Pro
PL ~ Sainte-Laguë
~ Maps Opt PC Pro
Mixed Member Sys
Summary (MW)

Conclusions

Ranked Ballot CHPV
Party-List CHPV

General

Table of Contents

Map Construction

Table of Contents

Mathematical Proofs

Table of Contents
Notation & Formats

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Home > Evaluations > CHPV Maps > Page 3 of 3
Last Revision: New on 25 Aug 2012

Evaluations: CHPV Maps 3

Three-Party Multiple-Winner CHPV Elections (continued)

Consider what happens when extra winners are increasingly added. For the OPV domains, they get smaller in size but they remain as regular hexagons of equal area (albeit that peripheral ones are truncated) and are still evenly distributed across the map. However, for the CHPV domains, they differ is shape and area as extra winners are added. Domains shrink in size depending upon how close they are to the centre of the triangular map. Those near the centre are the largest and those furthest away are the smallest.

CHPV three-party four-winner map

The large central domain for three, six, nine and other integer multiples of three winners is the same size and shape on each map. However, the domains in the three corners rapidly become tiny as further winners are included. It is therefore clear that when large numbers of winners are required from three-party contests an increasing number of outcomes are not optimally proportional.

Indeed, even perfect proportionality between party tally share and party seat share may not be achievable when there are a large number of winners. Consider the case where there are six winners (W = 6) and the tally share is exactly 5:1:0. The ideal seat share is clearly also 5:1:0. However, the 5:1:0 dot on the map is in the 4:2:0 CHPV domain and the outcome is hence neither perfect nor optimal.

For less than five winners, all dots are within their appropriate CHPV domains. For five winners, six dots (4:1:0, 1:4:0, 4:0:1, 1:0:4, 0:4:1 and 0:1:4) coincide with a CHPV domain boundary and a perfect outcome is dependent on a random tie-break. Increasingly, for more than five winners, some dots appear in an inappropriate CHPV domain.

This threshold of five winners is the same as that for the two-party maps. This is to be expected since each edge of the map is equivalent to a two-party map; as along each edge one party has a zero share of the vote.

CHPV three-party six-winner map
CHPV three-party five-winner map


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