Conclusions: Party-List CHPV 1

CHPV is one of several party-list methods and one of even more multiple-winner voting systems. Is it capable of thwarting strategic nominations while still achieving sufficient party proportionality? In what circumstances is party-list CHPV better than any alternative approach? And why is it preferable? This concluding section aims to consolidate such matters and hence to promote party-list CHPV as a viable, robust and party-proportional voting system for certain electoral applications.

A Niche Voting System

The party-list version of Consecutively Halved Positional Voting (CHPV) adopts the highest averages method. Each voter votes solely for their preferred party and thereby its closed list of candidates. The top-ranked candidate on each party list receives a tally (T) equal to the number of votes cast for that party. Successively ranked candidates receive consecutively halved tallies (averages); namely T/2, T/4, T/8 and so on. Irrespective of party affiliation, those candidates with the highest tallies are elected to fill the vacant seats.

By consecutively halving the party vote, averages for low-ranked candidates on a party list quickly become very small. As a result, the prime candidates of parties with relatively low levels of support then too easily gain seats at the expense of the larger parties. It is therefore no surprise that the optimality and proportionality of CHPV deteriorates rapidly as the number of seats is increased beyond just a few. Party-list CHPV is simply not suited to a single-constituency multiple-winner election where there is a large number of seats as it is then too heavily biased in favour of small parties.

To retain an acceptably high degree of proportionality between party tally shares and party seat shares, party-list CHPV is necessarily restricted to few-winner (W ≤ 6) contests. Where a large number of winners is required in total, concurrent CHPV elections are conducted across multiple local few-winner constituencies. In contrast, voting in most party-list systems occurs in just one (national) or a few (regional) constituencies. As a party-list method, CHPV is essentially unique in being a local-area few-winner voting system as opposed to a wide-area multiple-winner one.

Like CHPV, many Single Transferable Vote (STV) elections are held across multiple local constituencies with a few seats in each. Mixed member systems also employ elections in local constituencies but these are single-winner ones with multiple-winner contests at a higher level compensating towards overall proportionality. Such elections (MMP, AMS, AV+) are not few-winner ones. As a niche few-winner voting system, party-list CHPV is therefore a direct rival to STV.

Balancing Party Proportionality and Susceptibility to Party Cloning

For truly proportional representation, optimality should be maximised and any disproportionality minimised. When optimality is at its peak, any systemic bias towards or against a party is necessarily minimal; regardless of its level of voter support. For a given number of competing parties, the strength of party-list CHPV is that its optimality and proportionality both peak at around the same number of vacant seats (where typically W = 5).

Optimality for the Hare Quota method is 100% and any disproportionality is due to seat resolution only. For the Sainte-Laguë method, both parameters are almost but not quite as good as the Hare Quota ones. Both these systems outperform party-list CHPV for party proportionality. However, in few-winner elections (where W ≤ 6), CHPV generally produces more optimally proportional outcomes than does the D'Hondt method. For elections with few winners and few parties, CHPV is just as likely as the Droop Quota method to generate an optimal outcome. Hence, for few-winner contests, CHPV is comparable to the Droop Quota method, significantly ahead of the D'Hondt method but invariably lagging the Hare Quota and Sainte-Laguë methods in terms of proportionality.

Notice that, comparing the Sainte-Laguë method against the Hare Quota one and the D'Hondt method against the Droop Quota one, the highest averages method is slightly less party proportional than its largest remainder equivalent. This slight difference results from the quota methods satisfying the quota rule. In compensation, all highest averages methods including CHPV are monotonic and so do not suffer from the voting paradoxes experienced by the largest remainder ones.

However, there is an inherent trade-off between party proportionality and susceptibility to party cloning for party-list systems. The Hare Quota and Sainte-Laguë methods are highly party proportional with minimal systemic bias. Conversely, the Droop Quota and D'Hondt methods both exhibit a somewhat reduced optimality with the consequent marginal bias favouring larger parties. However, in compensation, the Droop Quota and D'Hondt methods are much less vulnerable to attempts to gain seats unfairly through party cloning than the other two methods. The Sainte-Laguë method is only slightly more susceptible than the Hare Quota one.

Given this trade-off and that CHPV is intermediate between the two other highest averages methods for proportionality, it is again no surprise that it is intermediate for susceptibility to party cloning too. CHPV is significantly less vulnerable to party cloning than is the Sainte-Laguë method; although it is not as good as the D'Hondt one. Nevertheless, cloning by small parties seeking to gain their first seat is more likely to be harmful than helpful with few-winner party-list CHPV.

Clearly, CHPV balances the trade-off between the two inherently conflicting parameters. It maintains a considerably high degree of party proportionality and so lacks a significant bias towards any party while at the same time it prevents small parties benefiting from strategic nominations. It must be emphasised however that party-list CHPV only achieves this balance at or around the few number of seats needed for peak optimality. This number varies slightly according to the number of parties in an election but is typically four seats for up to five parties and five seats for six or more parties. In practice, it is unlikely ever to exceed six seats even when a large number of parties compete in a party-list CHPV election.

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