Thinking about overhangs

The concept of the second choice of party vote should work regardless of overhang rules. But if the coat-tails rule is abolished, there is an increased risk of overhangs. The method chosen to handle overhangs can disrupt the proportionality of the result.

In general, overhangs arise when a party or independent candidate win electorate seats, but the St Lague system allocates them fewer seats.

There are several main ways this can happen:

  • A dominant party overhang occurs when a large and dominant party wins more seats than its party votes justify. This happens frequently in other countries, but is very unlikely in New Zealand. Conceptually this type of overhang could occur where a party is very dominant only within a small region, but such situations have not yet occurred in New Zealand.
  • A vote-splitting overhang occurs when voters vote for a candidate for one party and give their party vote to another party. This has occurred in NZ when voters have voted for Maori party electorate candidates and given their party vote to the Labour Party. This practice could theoretically be practised widely, so gaming the system and greatly distorting proportionality,
  • A threshold-driven overhang occurs only in the absence of the present coat-tails rule. It occurs when a party wins an electorate seat, but not enough votes to pass the 5% threshold.

In reality there are overlaps between these types of overhangs, so that rules are needed that work in a wide variety of circumstances.

The threshold driven overhang occurs only if the present coat-tails rule is abolished. In New Zealand there have been several situations where MPs have resigned from major parties and created their own party. This type of situation demonstrates an inconsistency between handling of elecorate and party votes. Independents can be lone voices in parliament, while parties are allowed only if they can get to six seats (5% of 120).

At present when an overhang occurs the party or candidate is allocated a seat over and above the normal 120 seats in parliament, and the proportionality of parliament is disturbed.

Another method of handling overhangs is to take the overhang seats from the seats otherwise allocated to list votes, so avoiding extra seats in parliament. Proportionality is disturbed, but often not greatly in NZ, as the overhang seats are taken from parties approximately in turn, and in proportion to their party votes.

This method is used in a similar electoral system in Scotland. There the overhangs are mostly of the dominant party type. As a result the overhang seats are effectively taken from other parties to give to the dominant party, so substantially disturbing proportionality.

The use of a second choice of party vote does not alter the overhang problems outlined above. Dominant party overhangs are unlikely in NZ and not serious, so can be safely disregarded.

A better treatment is needed of overhangs resulting from independents without supporting party votes. It is complicated by the ideal of representation i proportional to party votes whereas an independent has not party votes.

And the solution needs to work around the inconsistency between allowing single seats for independents, but refusing representation for parties with less than 5% of the national party vote.

Here is a sugestion that could largely eliminate the overhang problem. But I need to look more closely to be sure.:

  1. in electorate contests, there will be one winner. typically in NZ with 12-20k votes.
  2. All voters who gave their electorate vote to this winner , will have their party vote redirected to that winner s party. For an independent, the party is just the candidate them selves. The winner will receive one seat from their party s allocation, irrespective of the quotient.

This method should ensures that an electorate winner receives approximately the normal quota of party votes for their seat, and uses them to gain a seat.

In this way every seat requires a quota of party votes. And there is only a limited total quantity in the election.

This system makes vote counting more complex, because it is necessary to keep a total for every combination of party vote and candidate vote.

So there are things to check here. Does this work in every likely circumstance? How would you organise vote counting?

Based on a small sample, when there are about 40 000 votes, with two major candidates, the winner gains at least about 19 000 votes. With three major candidates, the winner often received about 13 000 votes. A typicalNZ general election has 72 electorates each with 40 000 votes on average. That means 40 000 electorate votes and 40 000 party votes. This corresponds to 2.88 million votes. If a candidate wins on 13 000, there will normally be two others at about 12 000 each , and about 3 000 among other parties.

More information to come

German lessons

It is commonly said that the New Zealand MMP system was modelled on the German PPR (personalized proportional representation). There may be lessons for New Zealand here. The language difference makes it more difficult to fully understand the diferences.

Here I will endeavour to explain the German system using terms familiar to those who know the New Zealand system.

My sources of information were:

The youtube video is easy to follow, but light on detail. The wikipedia page seems to use complex language, so is more difficult to follow, and uses many unfamilar terms. The Spiegel page is easier to understand but with less detail. And it is not clear just how accurate is the information provided in any of these. So this post should be read on the understanding that I have limited confidence in the details.

To improve clarity, I will refer to :

  • An assembly ( for NZ: parliament, Germany: Bundestag)
  • A mandate (for NZ: a (voting) seat in parliament, or MP, Germany: a voting seat in Bundestag)
  • Mandates can be district mandates or list mandates.
  • A district (for NZ: electorate, and <electorate MP>, Germany: district, elects a <direct mandate>, UK: constituency)

NZ and Germany both offer two votes, one for a district mandate, one for a list mandate. (German: direct mandate, <second vote>). NZ has 120 mandate assembly with 72 districts (72/120 = 60%), Germany a 598 mandate Bundestag with 299 districts (299/598 = 50%). Both systems allow overhangs to arise (a party wins more direct mandates than its party votes justify). This has happened a few times in NZ, with up to 2 additional overhang mandates. Overhangs seem more common in Germany. Germany has a complex system of <levelling mandates> to rebalance the assembly.

The German system has rules to deal with the numerous overhangs that appear there. New Zealand has had few overhangs, and so few special rules to govern them. New Zealand seems exposed to the misuse of overhangs to distort the proportionality of results

Germany has a provision that, where an independent is elected to a direct mandate, that party votes from the independent s voters are disregarded. This is to avoid those voters having double value in the election.

Both countries suffer from the problem that many voters do not understand the importance of the party vote compared with the district vote.

Germany has regional party lists, and a 5% national threshold. It is not clear how list candidates are allocated to list mandates. From which (regional) list is each mandate recipient chosen? Germany has constituent states. Regional lists seem to be lists for each state, but I am not certain

I have identified perverse effects of the 5% threshold in New Zealand, and have suggested a second choice of party vote to avoid them. I have not seen any reference to similar issues in the German system.

This page was last updated 23/10/21. Beware this post may not be accurate!

In the meantime, a two-choice NZ voting paper may look like this:

A possible two-choice voting paper layout, based on 2020 Hutt South

Scottish MMP/AMS elections 6 May 2021

I am writing this late morning on 7 May 2021 in France. There was an MMP/AMS election yesterday in Scotland. And there are no results yet, it seems!

We are fortunate in New Zealand, that General Election results are processed quickly, and we seldom if ever need to go to bed on election night without having a very good idea of the result.

The Scottish system is very similar to the New Zealand one, but is called AMS, for A-additional M-member S-system. Named because they (like NZ) elect constituency MPs then ‘add’ list members to create a proportional result.

The Scottish system differs in that Scotland selects list MPs in eight regions, so that each region has it own more or less proportional result. There are no fixed thresholds, but because each region elects only about 16 MPs, there is an effective threshold of about 8%. Scotland also uses the d’ Hondt method for allocating seats, whidh reputedly is more favourable to larger parties that the StLague system in NZ.

It seems a problem of many description of MMP/AMS that they talk about having constituency elections then about ‘added’ list MPs to achieve proportionality.

But as we know, it is the party votes that determine in MMP/AMS the overall makeup of parliament. So it is simpler to say that we use party votes to determine the overall number of seats in parliament for each party, and THEN fill those seats beginning with electorate/constituency winners, and taking the rest from party lists. (Noting that Scotland uses open party lists so that voters have a choice of list members, but voting papers are more complex).

Once you see it this way, the party votes are what you count first, because they take you straight to the overall result. By contrast the constituency and list results are of mainly local interest.

Two conclusions:
1. Descriptions of AMS/MMP should make more clear that it is party votes that almost solely determine the numbers seats in parliament for each party.
2. Once this is understood, it seems that Scotland could determine much more quickly the overall result of its AMS elections.

Comments relating to the New Zealand MMP threshold:

The use of several regions in Scotland makes for quite high effective thresholds. Many tiny parties have no hope of representation. The system might be made more proportional by having a fixed threshold and offering a second choice of party vote. That would allow every voter to vote for a party representated in parliament. The use of open lists in Scotland makes voting papers, and hence a second choice of party vote, more complicated than is proposed for NZ.

Inquiry into 2020 election

I have just learnt from facebook that the Justice select committee of parliament is holding an inquiry into the 2020 election. This is apparently something routine after each election. Unfortunately the closing date for submissions was 6 April 2021, so I missed it by a week or so.

From what I have read, the problem of wasted votes creates a barrier to participation in the electoral process. In the 2020 election, about 8% of party votes were disregarded because the voter voted for a party that did not pass either of the thresholds, being 5% or an electorate seat.

Young voters are likely to be interested in new ideas and new parties. But we have a system that disenfranchies anybody who votes for a party that does not pass one or other threshold. This disenfranchisement of minor party voters, perhaps mostly young voters, has a discouraging effect on voter participation.

MMP aims to be a proportional system. But bizarrely we have chosen to disenfranchise a small but significant proportion of voters by discarding their votes. This is a severe deficiency in our supposedly proportional electoral system.

And the problem is not one of the size of the threshold. Reducing the threshold would indeed reduce the problem, and eliminating the threshold would eliminate the problem.

But the problem can be better eliminated by giving voters a second choice of party vote. This solution means that every voter can have a say in the makeup of parliament, as well as expressing support for a minor party.

The two-choice system for party voting effectively decouples the size of the threshold from the issue of wasted votes. We can retain MMP with the threshold at whatever level we want, and still have a highly proportional electoral system.

The size of the threshold is not the problem

Here is a comment placed after the following article:

The problem with the threshold is not so much its size, but the fact that votes, if cast for parties that do not pass one or other treshold, are wasted.

The wasting of votes in this way is widely hated, for well-known reasons.

Reducing but not eliminating the threshold reduces but does not eliminaate this vote wasting effect.

Reducing or eliminating the threshold prejudices the avowed purpose of the threshold – to discourage the proliferation of small parties in parliament.

The solution is one easily understood and widely used in many situations where we want people to make choices, and we want to ensure that almost nobody misses out. That solution is to offer each voter a second choice of party vote.

No need for a complex preferential voting system. Just a second choice eliminates the problems. Voters can vote first choice for their preferrred party, and second choice for a party which they think is certain to pass the threshold. If their first choice does not pass one or other threshold, their vote goes to their second choice.

This is easy to understand, easy to implement, and solves the problem.

More details at

More on History of MMP election results

Thank you for the comment suggesting that wasted votes might be compared the level of non-voting and informal votes.

Each of these statistics tells us something a little different.

Turnout (the inverse of non-voting) shows the level of engagement in the population. MMP elections have had turnout percentages between 74% and 88%, with the highest figure for the first such election. I’d interpret that high figure as indicating a high level of support for the new system.

The level of informal votes indicates, I understand, voters who wanted to make a protest of some kind, or who did not fill out the voting paper properly. For MMP elections that rate of informal votes ranged between 0.39% and 0.95%. The lowest figure was for the first MMP election. That suggests that voters did not have difficulty adapting the new voting paper. For later elections voters were less careful or more often wanted to make a protest.

I do not fully understand how spoiling a voting paper can be seen as a useful form of protest, but I understand that it is not uncommon.

Wasted votes for failing to meet a threshold fall into another category, one which is more directly associated with design of the voting system. These voters have gone to the trouble of voting. they had no way of knowing whether their preferred party would meet the treshold, but still their vote was disregarded. If the aim of a proportional voting system is to measure numbers of voters supporting different parties in government, then it is important that voters be able to support a party that may not pass the threshold AND have a say in the makeup of parliament.

Often, I’d suggest, people supporting minor parties are those with a strong interest in the political process, and perhaps in supporting new ideas. The threshold system without a second choice forces those people to either put aside their support for a small party OR risk taking no part in the deciding the makeup of parliament.

That is a difficult choice for someone with a strong interest in the political process.

Reducing the threshold only reduces the problem, it does not eliminate it, whereas the second choice eliminates the problem.

Here are the turnout and informal vote stats, transcribed from the election results website.

ElectionTurnout %Informal %
Turnnout and informal vote stats for MMP elections. Manually transcribed from results site.

Small aside. We are very fortunate in New Zealand to have such easy access to stats like this. Reseaching other countries, it is often very difficult to find similar information.