Geometric Voting and Consecutively Halved Positional Voting - Comparisons: Summary (Multiple-Winner) 2

Comparisons: Summary (Multiple-Winner) 2

Both systems use the highest averages approach to the party-list method.
The D'Hondt method uses the divisors 1, 2, 3, 4 and so on while CHPV uses 1, 2, 4, 8 and so on as divisors.
For up to five winners in two- and three-party contests, the optimality of the D'Hondt method is over 60% but it is over 70% for CHPV.
The optimality of CHPV exceeds that for the D'Hondt method for three and four winners in two-party elections and for three, four and five winners in three-party ones.
The D'Hondt method is not as susceptible to party cloning as is CHPV.
However, for up to five winners, cloning attempts by the minority party in CHPV will fail.
In terms of party proportionality, CHPV outperforms the D'Hondt method when there are less than 5, 6, 7, 7 and 8 winners in elections with 2, 3, 4, 5 and 6 parties respectively.
As party-list CHPV is designed for use in few-winner constituencies, it is a more party-proportional system than the D'Hondt method for concurrent elections in numerous such constituencies.

Both systems use the highest averages approach to the party-list method.
The Sainte-Laguë method uses the divisors 1, 3, 5, 7 and so on while CHPV uses 1, 2, 4, 8 and so on as divisors.
The optimality of the Sainte-Laguë method is 100% for two-party elections and over 90% for three-party ones with up to six winners; while for CHPV it is always somewhat lower.
Any disproportionality associated with the Sainte-Laguë method is largely due to seat resolution whereas with CHPV the system itself also introduces significantly more disproportionality.
However, the Sainte-Laguë method is readily susceptible to parties seeking to gain an unfair advantage through cloning.
In contrast, party cloning in few-winner CHPV elections is most likely to be counterproductive.
The Sainte-Laguë method is generally used in a multiple-winner constituency but CHPV is instead used in numerous few-winner ones.

Unlike CHPV, mixed member systems [such as Mixed Member Proportional (MMP), Additional Member System (AMS) or the Alternative Vote Plus (AV+)] elect two different types of member (one local-area and the other wide-area) with each having a different status and set of responsibilities to the other.
Depending upon the proportion of local-area and wider-area seats within their total number, mixed member systems may or may not produce reasonably proportional outcomes overall.
When the number of local-area seats for a party exceeds its proportional overall share, the election outcome in a mixed member system is either somewhat disproportionate or extra 'overhang' seats must be awarded in compensation to other parties.
In mixed member systems, parties may clone themselves into one party for the local-area elections and another 'decoy' party for the wide-area one in order to gain an unfair advantage in seats; the local-area seats then being additional to - and not just part of - their proportional share of seats.
Party-list CHPV is designed for use in concurrent elections across multiple few-winner constituencies whereas mixed member systems use multiple single-seat local-area constituencies and no more than a few multiple-winner wide-area ones.

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