Only one day left to put in your MMP Review submissions. Here is one I prepared just now.

In the spirit of earlier large-scale nerdery by electoral system-enamoured-online-commentator-folk, here is my submission to the MMP Review. "Enjoy."


1          Introduction

1.1           This submission is from Rob Salmond. I am an Assistant Professor of political science at the University of Michigan, and have authored multiple academic articles on New Zealand elections and on the impact of electoral systems on politics.

1.2           Because I am currently based in the US, I am not available to speak personally to this submission.

1.3           This submission addresses the matter of the thresholds for allocation of seats.


2               The party vote threshold

2.1           As a matter of principle, I favour the lowest possible threshold consistent with good government in New Zealand, because proportional elections should lead to proportional outcomes unless there is very good reason to do otherwise.

2.2           I note that a number of other submitters have expressed concern that if the party vote threshold drops below either 5% or 4%, then the result could be fragmentation of the New Zealand party system leading to increased political instability that ultimately stands in the way of effective government. In almost all cases, this claim is made as an assertion, without much evidence. When evidence is produced, it is often in the form of a supposedly exemplary case, such as Israel or Italy.

2.3           There is not rigorous evidence to support the claim that a lower threshold is likely to lead to instability in New Zealand.

2.4           To look for such a relationship, I used data from the University of Berne on the number of changes in the makeup of a government that happen each year in the OECD, a good measure of government instability. I combined these data with Arend Lijphart’s data about the national-level legal thresholds and effective thresholds for party representation. The total number of countries under examination is 23 and the total number of country years is 826. The chart below shows that there is no obvious relationship between the threshold for party representation and instability in government, either in all years or in non-election years.

2.5           Further analyses show there is not a statistically significant relationship between the threshold for party representation and the level of government instability, measured using annual changes in government composition. For the technically-minded: simple bivariate correlations between thresholds and instability in PR countries were only significant at 0.514, and this significance drops further to 0.952 if election years are discarded from the analysis to give an estimate of between-election instability. In non-technical terms: for every unstable low-threshold country like Israel, there is a stable low-threshold country like the Netherlands (where there were only thee between election changes in government composition over almost forty years).

2.6           The data do show, however, true that as the number of political parties goes up, instability also tends to rise. And it is also true that decreases in the threshold tend to increase the number of parties. What, then, explains the lack of a relationship between the threshold and instability?

2.7           The answer is that many things other than the electoral system threshold cause the number of parties to rise and fall, and some of those other reasons are also causal of government instability. Religious fragmentation, for example, frequently causes the number of political parties to rise and is also an indication of a divided society, often linked to government instability. Multi-ethnic societies have the same issue.

2.8           These relationships can jointly give the misleading impression that the number of parties is a prime cause of instability, whereas in fact deeper divisions in the community are causing both more parties and more instability at the same time. The parties-instability correlation is likely spurious.

2.9           As a result, I recommend a substantial lowering of the party vote threshold, down to 2% at most.


3               Electorate seat thresholds

3.1           Like the majority of submitters, I favour abolishing the rule that allows parties full proportionality if they win one electorate seat.

3.2           These so-called “electorate lifeboat” rules are often designed to protect the interests of regional parties that have deep appeal to a small, regionally concentrated proportion of voters. In the New Zealand case, such regional parties have seldom emerged. Indeed, where parties really are successfully targeting a narrow slice of voters – for example the Maori Party and Mana – our experience is that these parties have done well enough in electorate contests not to need any list seats to achieve proportionality. Put simply, the problem that this rule was designed to solve has simply not arisen.

3.3           Instead, the rule is protecting the interests of some parties that seek broad nationwide appeal, but that fail to win more than a couple of percent support. I think it is hard to make a normative case why a party with 3.7% support including an electorate seat (ACT in 2008) should receive five seats in Parliament while a party with higher party vote total but no electorate seats (New Zealand First in 2008) should receive none. If this kind of anomaly were the cost of protecting a vibrant set of parties representing small, otherwise-easily-forgotten regions of the country, then we would have to seriously consider the appropriate tradeoffs. But at the moment we have the anomalies without the resulting benefits, which is very hard to defend.

3.4           Further, the issue of inadequate representation for a sub-5% party with an electorate seat will become less important if the 5% threshold is lowered, as I recommend.

Comments (15)

by Andre Terzaghi on May 30, 2012
Andre Terzaghi

A question for fellow enthusiasts of a low threshold for party represenatation: how do you feel about the current Saint Lague method of allocating seats?

With 120 seats, and roughly 2,400,000 voters, each seat can be roughly thought of as representing 20,000 voters. However, the St lague method allocates a party that gets more than 10,000 votes one seat, then a party that gets over 30,000 votes gets 2 seats, then 50,000 votes for three seats and so on. In other words, it's a process of rounding the vote count up or down when allocating seats. This appears to give parties with very low votes a good chance of getting one more seat than they really appear entitled to.

An alternative is the d'Hondt method, which allocates the first seat at 20,000 votes, the second at 40,000 votes, the third at 60,000 and so on. In other words, in the d'Hondt method a party has to earn the full share of votes before it gets the seat.

Personally I find any scheme that makes one person's vote more influential than most other votes to be a very undesireable distortion of democracy. For that reason I strongly oppose the electorate lifeboat option, and I'm uncomfortable about retaining the St-Lague method of allocating seats.

I'm also deeply uncomfortable about deliberately disenfranchising anyone, particularly if it's just because they hold strong opinions about issues that aren't so important to the masses, such as ACT voters or the Aotearoa Legalise Cannabis voters. So to me, lowering the threshold is important, preferably all the way down to one seat.

by Graeme Edgeler on May 30, 2012
Graeme Edgeler

In other words, in the d'Hondt method a party has to earn the full share of votes before it gets the seat.

1. No it doesn't. At the 2011 election in New Zealand, if held under d'Hondt, the first seat would be received once a party (with a seat) once it had enough votes to have earned ~0.8 seats.

2. Under d'Hondt at the 2011 election National (with 47.3% of the party vote) would have received 60 seats, and United Future wouldn't have had enough to earn one (so would have caused an overhang). Is it really fairer that a party which receives enough votes for 58.2 seats should get 60, while a party with enough votes for 0.74 seats gets none/causes overhang?

by Andrew Geddis on May 30, 2012
Andrew Geddis

Did you really just call me "earlier"? 

I'd like to see you say that to my face, buster!

by Andre Terzaghi on May 30, 2012
Andre Terzaghi

Thanks, Graeme. I appreciate your time in helping me think these things through.

For the 2011 election, by a quick check it looks to me that the anomalies you point out arise from the combined effects of the current 5% threshold creating a lot of wasted votes, and the way the current law adds more seats (and discards votes) in the event of an overhang. If the threshold was eliminated completely my assertions about d'Hondt would be more accurate, though there will be variations due to overhangs and wasted votes still remaining. Or maybe I misunderstand the d'Hondt method and there's a different system that gets closer to what looks best to me.

To your second point, we currently disenfranchise any party with less than 5% of the vote, unless that party has a sufficiently charismatic (Harawira) or entrenched (Dunne) electorate candidate or gains the connivance of a major party to pull off a deceitful manipulation of an electorate (Epsom, almost Coromandel). So historically we've shown we're generally OK with stiffing parties with low support.

I also think there is some validity to the view that smaller parties are likely to be more extreme and not play well with others, and the smaller the party the more extreme it is likely to be. At some point, the extremism will be such that we we're better off without them. In my view, that "too extreme" cut-off fits quite neatly with "one MPs worth of party votes".

With this background and my values, yes, it does seem to me that it's a less unfair outcome that larger parties are slightly disproportionately over-represented and very small parties may be significantly under-represented or miss out completely, compared to the large unfairness that results if a very small party is proportionately significantly over-represented.

There need to be lines drawn somewhere, and to me, one MP's worth of votes to get one MP, two MP's worth of votes to get two MPs and so on looks like the right place to put them.

Overhangs are a separate issue, but my imagination totally fails me in coming up with a way to deal with them that really seems completely fair given that retaining a mix of electorate and list MPs is an important ongoing feature. I don't really see the anomalies the current system creates as a major problem, unless it starts happening enough that larger parties start getting fewer seats than their absolute proportion of the party vote.

by Rob Salmond on May 30, 2012
Rob Salmond

@Andrew: Would you have preferred to have been "large-scale" or "nerdery?"

@Andre / Graeme: Andre, you don't have the mechanics of St Lague or d'Hondt quite right. Both work by dividing each party's total votes by a series of numbers (1,2,3,4 etc in d'Hondt; 1,3,5,7 etc in "pure" St Lague; 1.4,3,5,7 etc in "modified" St Lague), then you look across that huge array of numbers for the 120 biggest ones. Those indicate which parties to give seats. So there is no magic number of votes you need to guarantee a seat in either system - the number of seats you get with any particular number of votes depends also on how all the other votes are distributed among all the other parties. 

These sets of divisors can either over-represent or under-represent small parties, at the expense / benefit of large parties. Here are two toy examples:

1. Consider the (pretend) set of divisors 1, 1001, 2001, 3001, etc. If you used this system, basically all parties would end up with at least one seat. If a party has more than 1/1000th of the votes of the biggest party, it will get at least one seat - although the rest of the seats would usually go off fairly proportionately. This is some insurance for small party leaders, and bad on the margins for big parties, leading to a lot of one person parties.

2. Now consider a second (also pretend) set of divisors 1, 1.0001, 1.0002, 1.0003, etc. This has the opposite effect, giving all the seats to the largest party, almost regardless of the result. (The largest party gets the first 100 seats in this example if it gets 100 votes for each 99 won by its closest competitor). It is very hard in this system to get that initial seat. Great for one big party, bad for small ones.

Somewhere between these extremes is a sweet spot where, on average, parties get that first seat in proportion to their performance. But where is the sweet spot? Plenty of research shows that d'Hondt is mildly biased towards large parties (see Arend Lijphart's 1994 book for example), while "pure" St Lague is about as close as you can get to fair. "Modified" St Lague was specifically designed by (generally large party) incumbent politicians to make it harder for small parties to gain their first seat - this is the effect of turning the initial 1 into a 1.4. That is, it was a calculated attempt to make a fair system less fair, for the benefit of large parties at the expense of small ones.

As I said in my submission, "proportional elections should lead to proportional outcomes unless there is very good reason to do otherwise." I do not think that a desire to stick it to small parties to the tune of a marginal MP every now and then constitutes a good reason to depart from the principle of proportionality, and as a result I am pretty comfortable with keeping our pure St Lague system intact.

by Andre Terzaghi on May 30, 2012
Andre Terzaghi

Rob, thanks for that. But it doesn't help me see where I'm going wrong in my understanding of Saint Lague versus d'Hondt.

Looking at the 2011 results and asking what would the results be if electorate results are ignored and thresholds were completely removed: by St Lague, ALCP and United Future are a comfortable one seat each, Maori Party has a comfortable two seats, Mana and Act weren't far from two seats. By d'Hondt, ALCP and United Future are a bit short of one, ACT and Mana weren't far over one seat, Maori Party were a wee bit short of two seats. Either way the Conservatives would get three. To me, the d'Hondt outcome looks fairer, with only the Maori Party having reason to feel they've missed out.

It's important to me that proportional means proportional, with the proviso that selecting a small number of representatives to represent a larger population will always incur some disproportionality somewhere, until we find some way to elect a non-integer number of representatives. The effects of that disproportionality will by mathematical necessity be greatest on the small parties, unless the distribution of votes is particularly fortuitous to creating a truly proportional outcome. Whether that disproportionality tends to be favourable or disfavourable to small parties depends on the system.

Fundamentally I don't think there's a symmetry of fairness between a party being over-represented and under-represented. I think a party being granted one MP when it won a half MPs worth of votes is much more unfair than saying sorry, you missed out so now the party that won 49 1/2 MPs worth of votes gets 50 MPs.

Now to consider that difference between St-Lague and d'Hondt. In the lands of Hypothetica and Suppositia there are no voting thresholds, there are no electorates (no overhangs) so its a pure proportional system.

They both have 10,000 voters, 100 elected representatives and 10 political parties called A,B,C,D,E,F,G,H, J and K. They hold simultaneous elections, and amazingly they get the exact same results: A gets 49 votes, B gets 51 votes, C gets 97 votes, D gets 103 votes, E gets 149 votes, F gets 151 votes, G gets 199 votes, H gets 201 votes, J gets 4449 votes and K gets 4551.

Hypothetica uses pure St-Lague. A gets no MPs,(but would probably get one if there existed a lower polling party), B, C, D and E get one each, F,G,H get two each, J gets 44 and K gets 46. To me it looks like B and F are seriously over-represented, since 51 votes was enough to get a B MP elected and 151 votes was enough for 2 F MPs, and all the other parties needed just over 100 votes for each of their MPs.

Suppositia uses d'Hondt. A,and B get no MPs, C,D,E and F get one each, G and H get two, J gets 45, K gets 47. No-one looks seriously over-represented to me, but D and F may feel a wee bit under-represented. I don't think A and B can really feel aggrieved that they've missed out.

Or have I gone wrong somewhere?

So it seems to me that Saint Lague is excessively generous to low polling parties, while d'Hondt is only a bit tough on the low polling parties. I don't think I've got a hidden desire to stick it to the smaller parties, especially since it's usually one of the smaller ones that gets my vote. But given that small parties are likely to hold the balance of power, I don't think we should build in a systemic over-representation for them.

In any case, the effect is fairly small if a threshold is retained, even as low as 2%. Unless my wildest dreams come true and the thresholds are completely abolished, I guess it's pretty much a moot point.

by Rob Salmond on May 31, 2012
Rob Salmond

@Andre: First, I do not agree with your statement "I think a party being granted one MP when it won a half MPs worth of votes is much more unfair than saying sorry, you missed out so now the party that won 49 1/2 MPs worth of votes gets 50 MPs." I think saying to a political movement "sure, you earned half a seat, but we're going to round that down to nothing at all" is the bigger unfairness. The difference between "something" and "nothing" is far more qualitatively important than the difference between 49 and 50.

Second, I rechecked your hypothetical calculations, which were right, and then calculated the Index of Disproportionality for the two results. You can see a description of the two indexes I used here, and neither index makes any explicit value judgement about which form of unfairness - big or small party overpresentation - is "worse." Both indexes show that the d'Hondt result is less proportional overall than the St Lague result. (For example, the Gallagher Index - small numbers indicate a more proportional result - has St Lague at 0.85 and D'Hondt at 1.32.) The reason for this is mainly what happens with party K, which got 45.51% of the vote. Under St Lague this gets rounded up to 46. But under d'Hondt, K's seat share goes all the way up to 47 - a clear over-representation that goes beyond simply rounding error. This example backs up my earlier point that St Lague is overall fairer than d'Hondt, which tends to marginally over-represent large parties at the expense of small ones.

by Andre Terzaghi on May 31, 2012
Andre Terzaghi

Thanks again for your time. I need to look into and think a bit more about that Party K aspect. I suspect our difference in value judgements about what's fair and unfair at that 0.5 to 2% of the vote level will stay unresolved.

But I'm curious: given that a 2% threshold is much harsher to very small parties than the difference between d'Hondt and St-Lague with no threshold, why did you word your submission to appear that you advocate retaining a 2% threshold? A pragmatic judgement that a reduction to 2% might actually be politically achievable? I realise on careful reading that you advocate that threshold go as low as possible, but on my first skim read and second quick read that "2% at most" got truncated down to "2%". Or is it just confidence that Commission members are more careful readers than I am?

by Rob Salmond on May 31, 2012
Rob Salmond

@Andre: Yep, you nailed it. Prgamatically, I think 2% is about as low as it could go, so I pitched for there.

by Chuan-Zheng Lee on May 31, 2012
Chuan-Zheng Lee

Andre, I'm curious:  If your concern is very small parties winning a whole seat whey they've got only just over half of "one seat's worth" of the vote, then what's your take on the modified Sainte-Laguë method (mentioned by Rob above, where the divisors are 1.4, 3, 5, 7, …)?

I think it's possible to design the divisors to have it both ways: to insist that small parties get a full seat's worth (or close to it) before granting them a seat, and to avoid the "more than a rounding error" issue with bigger parties.  You just make the small divisors bigger, while keeping the big divisors consistent with the pure Sainte-Laguë method.

For example, the modified-to-1.4 method would require that a party get roughly (roughly!) 70 votes (as opposed to 50 votes) out of 10,000 to get one seat in 100.  If you wanted to make the "effective threshold" similar to d'Hondt, you could just increase it to 2 (so 2, 3, 5, 7, …).  If you wanted to do the same for the second seat, you could increase the first two divisors (2, 4, 5, 7, 9, 11, …).  You could probably go as far as you wanted, since the series (2, 4, 6, 8, …) and (1, 2, 3, 4, …) are equivalent, but I haven't actually tried that.

With the modified-to-1.4 method, Party B in your example would not get a seat.  Party C would, but I think that's fair, since they got really close to 1%.  The seat dropped by Party B would go to Party J, who now has 45 seats, which I don't think is unfair given that they were only just shy of 44.5%.

If it were modified to 2, then Party C's seat would go to Party E, who now has 2 seats with 1.49%.  Party K stays on 46.

Would either of those be more satisfactory?

In my submission I proposed the modified-to-1.4 method with no other threshold, for basically the same reservation that I think you (Andre) have with the pure Sainte-Laguë method.

by Andre Terzaghi on May 31, 2012
Andre Terzaghi

Chuan-Zheng, fundamentally my concern is less with small parties winning seats which they don't appear to have received enough votes to fairly win, than with avoiding situations where some votes are significantly more influential than others.  From this viewpoint, someone voting for a party that just barely gets one seat in pure St Lague has an "influence multiple" of around 2, if it just barely gets one seat in 1.4 modified St Lague the "influence multiple" is about 1.4, an Epsom ACT voter in 2008 had an "influence multiple" of about 5, which really really wound me up. In d'Hondt, the "influence multiple" can go very slightly over 1 for voters for large parties, at the cost of dropping as low as 0.5 for small party voters, or 0 for a lot of very small party voters. A very fine distinction in terms of the nerdery above, I know.

I also want to be clear that I'm unhappy denying a seat to a party with substantial support in that 0.5 to 1 "seats worth of votes" range, but it seems to me a lesser wrong than allowing any votes to be significantly over-influential. Gotta also point out if there were a lot of small parties allocated seats with less than "1 seat's worth of votes", proportionality would be distorted as well.

To directly answer the question, yes, if all thresholds were removed, I would prefer a 1.4 modified St-Lague to pure St-Lague, and I would probably still prefer d'Hondt over 1.4 modified St Lague (still need to fully think that through). I agree the early divisors could be modified to address my concerns, and I'm sure I could come up with a set of divisors I was completely happy with, probably something like 1.8, 3.5, 5.2, 7, 9 etc. I'm also sure others would be very unhappy with them for valid reasons. It appears Rob's happiest with pure St-Lague, and I respect the argument even though I don't agree with the conclusion.

And in the context of MMP in New Zealand, there's also the issue of overhangs. I've never been happy with increasing the size of Parliament to accomodate an overhang. I've always preferred the idea of the overhang party getting its electorate seats (eg 3 for the Maori Party in 2011), then discarding its party votes from further consideration, and allocating the remaining seats according to the chosen method (eg 117 seats by St Lague in 2011).

I tried various scenarios with the 2011 results, and it seemed to me the fairest proportional result came with this method of treating overhangs and d'Hondt with no thresholds. In this proposed scheme, the Maori Party and United Future both have overhangs, so they are allocated their electorates, and their party votes discarded. The remaining 116 seats get allocated by d'Hondt. ALCP missed out, but all the other parties had a seat share that was within 0.2% of their proportional vote share. By the way the numbers changed, it appeared that reducing the seats to be allocated by d'Hondt to accomodate the overhang had the effect of eliminating the over-representation of the larger parties that is apparently the usual flaw in d'Hondt. Of course, much more analysis is needed to say whether that's a general principle or just a quirk thrown up using this particular set of results. Maybe Rob already has the answer there. But even if it is generally true it doesn't seem a good idea to rely on overhangs to produce proportionality.

In the end though, I can't in my wildest fantasies imagine that a "no threshold" recommendation will come out of the Commission  and get enacted by Parliament. If there is a threshold, I'm happier with St-Lague. And should a percentage threshold be retained and the one electorate seat threshold abolished there will also be "underhangs" to deal with.

by Chuan-Zheng Lee on June 01, 2012
Chuan-Zheng Lee

Fair enough, that all makes sense.  Do you have a formal definition of "influence multiple"?  I just wonder because, presumably, the influence (or potential influence) of any voter depends on what other voters do.

So, for example, if two parties are sitting on 0.4 and 25.4 "seats' worth" of votes respectively, then voters for either party can be argued to have the same "influence" in the sense that both parties are equally close to the next seat?  But you could also point out that the first party "started" on 0 whereas the other (in Sainte-Laguë) "started" on 24.5 (the point at which they gained the last seat, roughly speaking), so it depends what you mean by "influence"...  Set me right if I got the concept wrong entirely.

by Chuan-Zheng Lee on June 01, 2012
Chuan-Zheng Lee

(Sorry about the duplicate, my finger twitched just when I clicked "post"...)

Fixed for you - ed.

by Andre Terzaghi on June 01, 2012
Andre Terzaghi

"Influence multiple" is a something I made up on the spot to try to clarify my views on a thorny subject. I'm an engineer, so I'm somewhat mathematically literate, but I'm not any kind of practicing professional in a political field. Generally I'm fairly passive about politics, I only speak up when I get really riled and the last time that happened was under Muldoon. So I don't make any claim to having deep thoughts about political systems.

To define "influence multiple" as I've made it up, it's simply "number of seats won" divided by "the number of seat's worth of votes that caused those seats to be won".

In your example, by my non-rigorous idea of "influence multiple", once that 25.4 "seats worth of votes" had tipped over into getting 26 seats, those voters would have an "influence multiple" of  26/25.4 or 1.024, Just prior to the tipover, their "influence multiple" would be 25/25.4 or 0.984.

In the case of pure St-Lague, voters for a party that just barely got one seat went from an "influence multiple" of 0/0.5 to 1/0.5. 1.4 modified St Lague in this situation the influence multiple off the top of my head would be 1/ (1/1.4) or 1.4. In d'Hondt, the first seat influence multiple is 1/1. Of course for the a party just short of the second seat under d'Hondt, the "influence multiple" becomes 1/1.99... or 0.5.

In the case of Epsom 2008, it was one electorate seat won causing 5 seats to be allocated to ACT.

by Chuan-Zheng Lee on June 02, 2012
Chuan-Zheng Lee

I see.  Thanks for the explanation, it makes sense too; I was just intrigued by what you had in mind.  (Coincidentally, I'm an engineer too, and don't practise in a political field.)

With modified Sainte-Laguë, I think the influence multiple for a party barely getting one seat would be 1/0.7 ≈ 1.42.  In general, if the modified first divisor is m, then you need roughly m/2 "seat's worth" of votes to pick up the first seat—I've done this maths before (PDF) (in a different context, I was just trying to prove formulae for effective thresholds) if you're interested. :-)

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