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: Mixed Member Systems

Description of Mixed Member Systems

In elections using the Mixed Member Proportional (MMP) voting system or the Additional Member System (AMS) more than one type of member is elected. In fact, there are usually just two types. One member type is chosen by a local electorate and the other is elected at a wide-area level; usually at a regional or national one. The Alternative Vote Plus (AV+) is another mixed member system that elects these two types of member.

Local-area members are simultaneously elected in numerous multiple-candidate single-seat constituencies. The single-winner voting system is only required to be simple and straightforward as overall party proportionality is neither achievable or needed here. Hence, First-Past-The-Post (FPTP) is frequently adopted for these local elections. However, other single-winner systems such as the Alternative Vote (that is used within AV+) may also be employed.

Wide-area members are elected concurrently with their local counterparts but in a manner that maximises (or at least significantly improves) the proportionality between the competing parties in terms of the overall tally and seat shares. A closed party-list method is generally adopted for this purpose. Usually, there will be enough seats at the wide-area level to ensure overall proportionality. Where this is the case, a party that wins X seats overall but only Y seats at the local level will then be awarded the remaining X - Y seats at the wide-area level. The 'additional' or 'top-up' members are those top-ranked X - Y candidates on the relevant closed party list.

For a more detailed and comprehensive description of mixed member systems, please visit the voting system section of Wikipedia or another reference source.

Mixed Member Proportional Voting System Example

Consider the following MMP election as an example. Fifty local seats are to be filled using the FPTP voting system and another fifty at the regional level using the optimally proportional Hare Quota Party-List method. Based on voting at the local level, parties A, B, C and D gain 20, 15, 10 and 5 seats respectively. At the regional level, they gain the support of 32.8%, 29.0%, 16.2% and 22.0% of the voters respectively.

With one hundred members to be elected in total, the Hare Quota tally share is 1/W, 1/100 or 1%. Hence, by reaching integer multiples of this quota, parties A, B, C and D are awarded 32, 29, 16 and 22 seats respectively. As party A has the largest remainder (at 0.8%), then it gains the final seat and so its total rises to 33 seats. Party A already has 20 elected local members, so it gains another 13 additional members from the closed party list at the regional level. Likewise, the other parties B, C and D win an extra 14, 6 and 17 top-up members respectively.

Properties of Mixed Member Systems

The properties of any mixed member system are essentially the ones associated with the local-area and wide-area voting systems employed. These have already been covered in the preceding single-winner chapter and this multiple-winner one. Nevertheless, there are some unique distinguishing features.

With two types of member, each type has a different status and set of responsibilities within the elected body. Local members are accountable to their local electorates while additional members are solely dependent upon their own parties for their success. For some individual party candidates, whether to aim for a local-area or a wide-area seat is difficult to analyse. Where candidates cannot be nominated at both levels, it can be a risky decision.

In some elections, there may be more local members for a particular party than its overall seat entitlement. Unless other parties are also given extra 'overhang' seats to compensate the outcome will not be optimally proportional. Some mixed member systems deliberately allocate relatively few wide-area seats so that outcomes are semi-proportional at best rather than fully proportional. Some variants also impose a minimum threshold below which a party receives no seats at all.

With some electorates, parties may attempt to gain unfair advantage by cloning itself into two parties. Here, only one of the two clone parties nominates candidates at the local level while only the other one issues a party list (known as a decoy list) at the wide-area level. As any local-area seats it may gain are in addition to its proportional wide-area share of seats, the two clone parties have a larger total than would be the case with just the one original non-cloned party.

Comparison with Party-List CHPV

Ranked ballot CHPV can readily be used for the single-winner local elections in a mixed member system. However, with the large number of wide-area seats usually employed in fully proportional mixed member systems, party-list CHPV would be inappropriate for electing the additional members as the outcome would not be party proportional. Like the Single Transferable Vote (STV), party-list CHPV is only employed in one or more few-winner constituencies. Both STV and party-list CHPV achieve a high degree of local optimality and overall proportionality at the wide-area level without the need for any additional adjustment or top-up mechanism.

Unlike mixed member systems, party-list CHPV and STV also accord the same status and set of local responsibilities to each and every winning candidate without discrimination. Members elected using closed party-list CHPV will remain accountable to their local electorates where supporters are additionally allowed to rank the candidates on their own free party list.


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