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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Last Revision: New on 25 Aug 2012

Comparisons: Droop Quota ~ Optimality 2

Comparative Optimality in Two- and Three-Party CHPV and Droop Quota Party-List Elections

In the earlier Evaluations: Optimality of CHPV section, the proportion of CHPV outcomes with optimum proportionality in two-party and three-party elections is already established. These results can now be compared directly with those for Droop Quota optimality; see previous page. The bar chart below left presents a comparison between Droop Quota and CHPV for two-party elections and the one below right is for three-party elections.

Three-Party Optimality
Two-Party Optimality

For two-party contests, both Droop Quota and CHPV produce optimally proportional outcomes in 83% or five out of every six possible election input profiles with two seats (W = 2). As extra seats are added, Droop Quota optimality declines slowly but for CHPV it rises initially before then dropping quickly. For three or four winners, CHPV performs better than the Droop Quota. However, for five or more winners, the reverse is true.

For three-party contests, Droop Quota optimality is better than CHPV with just two winners. Again, as extra seats are added, Droop Quota optimality declines slowly while for CHPV it drops quickly after initially rising. Here again, for three or four winners only, CHPV performs better than the Droop Quota. For five winners, both perform about the same but the Droop Quota outperforms CHPV thereafter.

For the Droop Quota, its optimality is lower for three parties than for two. Optimality is always at a maximum with just two seats (W = 2). It declines somewhat more quickly for three parties as extra winners are added. For three parties in comparison to only two, CHPV optimality is initially lower but beyond five winners it becomes higher. Peak optimality occurs with three seats (W = 3) for two-party CHPV elections but at four seats (W = 4) for three-party ones. It is only at and around these peaks that CHPV outperforms the Droop Quota.

For up to five winners in two- or three-party contests, both Droop Quota and CHPV elections generate optimally proportional outcomes in over 70% of all possible cases. For few winners and few parties, these two voting systems are therefore comparable methods.


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