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

Valid XHTML 1.0 Strict

Valid CSS

Home About Description Evaluations(RB) Evaluations(PL) Comparisons(SW) Comparisons(MW) Conclusions General Maps Proofs
Home About Description Evaluations(RB) Evaluations(PL) Comparisons(SW) Comparisons(MW) Conclusions General Maps Proofs
Home > Evaluations > Majority Criteria > Page 3 of 4
Last Revision: 25 Apr 2021

Evaluations: Majority and Related Criteria 3

Consensus versus Polarized Candidates

Apart from one special case, GV does not satisfy the majority criterion. This raises the prospect of a consensus candidate C 'coming through the middle' to beat two polarized candidates A and B. Let m remain the proportion of voters casting a first preference (P1) for A while the remaining proportion of 1 - m cast a first preference for B. If C receives a second preference from every voter, can C win despite having no first preferences at all? Following a pairwise comparison of the GV tally (T) for every pair of candidates, the answer is yes! The ranking thresholds for such an election are given below.

Proportion supporting A versus Common Ratio

The above three threshold conditions are each represented on the graph opposite by a straight line. The solid half of each line is the threshold between the first- and second-ranked candidates exchanging places and the dashed half is between the second- and third-ranked candidates swapping places. Each threshold line represents a tie between two candidates and the single point at which all three lines cross represents the only three-way tie between A, B and C. This three-way tie only occurs when using CHPV (r = 1/2).

The white region of the graph is where the tally for C is greater than for either A or B and hence where C wins. It is clear from this graph that for common ratios less than one half (r < 1/2), C can never win. However, for common ratios greater than one half (r > 1/2), C might easily win. The chances of C winning are best when the polarization between A and B is well balanced and they improve steadily as the common ratio is increased. A common ratio of one half is therefore the threshold below which a consensus candidate with unanimous second preference support cannot beat the leading candidate of two who share all the first preferences between them.

CHPV is therefore the boundary GV variant for a consensus candidate with no first preference support to be able to 'come through the middle' and beat two polarized candidates sharing such support. Using CHPV in practice, a candidate with almost universal second preference support must have at least one first preference to stand any chance of being elected (without winning a tie-break). This chance improves as more first preferences are accumulated and when the polarization between the other two candidates becomes more evenly balanced.


Proceed to next page > Evaluations: Majority Criteria 4

Return to previous page > Evaluations: Majority Criteria 2