Under New Zealand’s Mixed Member Proportional (MMP) system, a voter has two votes: one for a local constituency (riding) contest run using First Past the Post, and one for a national party list. The local riding results are determined first, and then seats are assigned to parties off the national list in a compensatory manner such that the total number of seats won by each party is proportional to the number of votes it received on the second ballot.
We calculate the Legislative Power Share scores for New Zealand voters in a two-stage process similar to what we did for Norwegian voters. As with Norway’s List PR system, we consider a voter to receive a share of legislative power if they either voted for a candidate elected in the local riding or voted for a party that received a compensatory (list) seat.
For a voter who voted for an elected candidate in their local riding, we compute their Legislative Power Score the same way as we do with FPTP, except that we use the total number of seats in the country1 (120) when computing the quota (i.e., the average votes per seat, Q = V/S, where S = 120). For example, in the 2020 New Zealand election, 2.82 million voters cast votes in the constituency elections, which gives an average quota, Q, of 23,535 votes per seat for the 120 total seats. In Auckland Central, the winning candidate won the seat with 12,631 votes (35.5% of the constituency vote), so the Legislative Power Share score for the voters who supported this candidate is calculated to be 23,535/12,631 = 186.3%.
Under New Zealand’s voting rules, a voter is not required to cast a vote on the list ballot that matches their vote on the riding ballot. That is, a voter who supports a Labour candidate in the local riding may opt to cast a vote for the Green Party on the list ballot. Thus, in principle, a voter could potentially obtain legislative representation independently via both the riding and list sides of the ballot, and we should ideally calculate the two contributions to an individual voter’s Legislative Power Share score separately and add them together to accurately determine the distribution of LPS scores.
While the data necessary for such an analysis is technically available, it is challenging to process in a time-efficient manner as it is distributed across 72 individual data files for the 2020 election (one for each riding), and for each one of these the full set of intra-riding transfer possibilities would need to be considered (since there were five or six parties contesting each riding, there would typically be 55=25 or 66=36 transfer possibilities to consider for each riding). We therefore adopted a modest simplifying assumption to facilitate making estimates of the LPS score distribution: we restricted our analysis to the votes indicated on the first ballot only (i.e. the vote cast for their local constituency MP), and treated voters who did not see their preferred candidate elected in the riding as receiving representation through the compensatory lists only. Such a single-ballot MMP system is used in the state of Baden-Württemberg in Germany.2 Applying this simplifying assumption does introduce some small distortions into our calculations, but we believe the overall effects are likely to be relatively small and will only modestly affect our overall conclusions.3
Using this assumption, we therefore compute the LPS score for voters who voted for a losing candidate from party j in the local riding by calculating LPSj = Q/(Vj/Sj), where Q is the national quota (=V/S, where V = total votes cast in all ridings and S is the total number of seats in the legislature), Vj is the total number of votes cast for losing candidates of party j across all ridings, and Sj is the total number of compensatory seats awarded to party j.
As a specific example from the 2020 New Zealand election, the Labour Party was entitled to 65 seats based on their share of the party vote, but won only 46 constituency seats, so was awarded another 19 compensatory seats from the party lists. There were 387,186 voters across the country who voted for Labour Party candidates locally who did not see their local candidate elected, so we consider these voters to take equal shares in the list MPs (387,186/19 = 20,378 voters/seat). Their Legislative Power Share score is then calculated as 23,535/20,378 = 115.5%. We note that such voters can be said to receive their legislative influence indirectly - that is to say, not by voting directly for the compensatory candidates, but by voting for the party list to which these candidates belong.
For New Zealand we treat the entire country the same way we treat a single Canadian province because, in contrast to Canada, New Zealand uses a compensatory list mechanism to equalize Legislative Power Shares across regions of the country. ↩︎
http://www.landtag-bw.de/files/live/sites/LTBW/files/dokumente/fremdsprachen/Willkommen-E.pdf ↩︎
The main distortions arise from two effects: (1) the number of compensatory seats assigned would be different had they been assigned based on the party distributions on the first ballot rather than the second, and (2) those voters who switched their votes between the two ballots (meaning that the party affiliation of their choice on the first ballot does not match the party they chose on the second) may have received either a higher or lower LPS score in real life than we compute for them here.
With respect to the first issue, we can compare the vote share by party on the riding and list ballots. In the 2017 election, there was very little difference - the largest difference was that New Zealand First (one of the smaller parties) received 5.4% of the riding votes and 7.2% of the list votes, which means that they received two seats more in the real election than they would have under a single-ballot system. There was a larger discrepancy in the 2020 election, in which the National Party received 34% of the riding votes, but only 26% of the list vote, and so received 10 fewer seats than if the compensatory seats had been awarded based on the first vote alone. This discrepancy appears to be attributable to the emergence of the ACT Party, which is a social liberal party that is likely more closely aligned in philosophy to the National Party than to any other party. Since it is a smaller party, it is less likely to win riding seats, and the results show that indeed ACT received only 3.5% of the vote in the riding elections, but 7.6% in the list vote. Therefore, it appears likely that ACT supporters frequently voted strategically for National Party candidates in the riding elections and for ACT on the list. In our calculations, this will have the effect of overstating the LPS scores for ACT voters (because they apparently share more compensatory MPs than their first ballot support would otherwise warrant) and understating the LPS scores for National Party voters (because they apparently share fewer compensatory MPs than their first ballot support would otherwise warrant). The net effect of our simplifying assumption is that the Legislative Power Disparity Index we calculate for the 2020 election will likely overstate the actual disparity in that election, while there would likely be no significant overstatement of disparity in the 2017 election.
With respect to the second issue (not fully accounting for vote switchers), we anticipate that the effect on the LDPI will be modest. There will be no effect on the calculations for voters who voted for the local winning candidate and did not switch, or for voters who voted for a local losing candidate and switched to another party that did not win locally. Voters who voted for the winning local candidate and switched their vote on the list side should, in principle, also receive some additional contribution to their LPS score from the compensatory seats awarded to the party they voted for on the list side, but this would come at the expense of decreasing the LPS scores of all voters who received representation via the compensatory lists, so there would be a small increase in disparity from this effect. In contrast, voters who voted for a local losing candidate and switched their list vote to the party that won locally should in principle only receive a contribution to their LPS score from the compensatory seats for the party that won locally, even though they would presumably also be satisfied with the local winner since that candidate comes from their preferred party. Under our calculations, they will instead receive a contribution from the party for which they voted locally. However, there should be relatively few such voters since a voter who prefers a particular party will presumably vote for the local candidate from that party if they feel that that candidate has a good chance of winning. Overall, we know that the fraction of voters who switch votes is moderate (about 30% - 27% in 2017 and 32% in 2020; see https://www.electionresults.govt.nz/electionresults_2020/statistics/split-votes-index.html), and that there will be a modest effect for only some of these voters (primarily those who voted strategically - i.e., not for their most preferred party - in order to elect a ‘lesser of two evils’ candidate locally). The net effect of our simplifying assumption should be a slight increase in apparent disparity as measured by the LPDI. ↩︎