Comparisons: D'Hondt ~ Proportionality 3

Comparison between the D'Hondt and CHPV Voting System LSIs

The preceding bar chart for the D'Hondt method can now be compared directly to the corresponding one for CHPV; see the relevant Evaluations: Proportionality of CHPV page. The bar chart below displays the various LSI_VS for CHPV and D'Hondt side-by-side. For each corresponding pair, the left bar for CHPV is highlighted in green and the right bar for D'Hondt is coloured blue.

It is clear from this comparison that CHPV is generally more proportional than the D'Hondt method when there are few winners. The reverse is true when there are numerous winners. 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.

Party Proportionality of D'Hondt and CHPV

Party-list CHPV can now be compared to the D'Hondt method in terms of both disproportionality and optimality (see earlier section). For the D'Hondt method, the proportion of all possible outcomes that generate an optimally proportional election result (optimality) declines with each extra seat added. Yet minimising the discrepancies between tally and seat shares (proportionality) for the D'Hondt method improves with each extra seat added. Where a large number of winners is required, a party-list D'Hondt election can be held in either one constituency (for maximum proportionality) or across numerous smaller ones (for a geographically distributed representation).

In contrast, for CHPV, both optimality and proportionality peak around a narrow range of a few winners. It is for this reason that party-list CHPV is only conducted concurrently across multiple few-winner constituencies. For more than a few winners, CHPV does not outperform the D'Hondt method. For two winners, the two systems produce identical election outcomes as they use the same two divisors (1 and 2) for the two averages. However, for three to five winners with two or three parties, the optimality of CHPV is better than that for the D'Hondt method; with the sole exception of two parties competing for five seats.

As observed above, the proportionality of CHPV exceeds that of the D'Hondt method for two parties competing for up to four seats and for three parties contesting up to five seats. This proportionality performance therefore closely matches that for optimality. For more competing parties, the number of seats has to rise steadily for the D'Hondt method to better CHPV in relation to minimising disproportionality.

In conclusion, CHPV significantly outperforms the D'Hondt method in terms of party proportionality when multiple-party few-winner (W ≤ 6) elections are conducted and it is precisely these elections that the party-list CHPV voting system is designed to suit.

Proceed to next section > Comparisons: Party-List ~ Sainte-Laguë

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