# Legal Beagle by Graeme Edgeler

## 125 Responses

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• Christopher Nimmo, in reply to Brent Jackson,

I reckon it might be that people think there should be a "winner".

Wellington • Since May 2009 • 97 posts Report Reply

• Steve Todd, in reply to Brent Jackson,

It’s all to do with the differences between the percentages of votes received and the percentages of seats won in any given electorate, where the elections are party-based, Brent.

To explain, in a 5-seat electorate, if a party receives 40% of the votes, it will win two seats (40% of the seats), meaning the ‘Index of Proportionality’ for that party in that electorate is 100.0. (The quota is 16.67% - 100 / 6 – low enough for the party to win two seats, but not three.)

But, in a 4-seat electorate, 40% of the votes is enough to win two seats (50%), meaning the index of proportionality is 125.0 (50 / 40 = 1.25). (The quota is 20% - 100 / 5 – low enough for the party to win two seats.) That means the party is over-represented by 25%. I’ll call this Example 1.

Example 2. In a 3-seat electorate, 25% of the votes is enough to win one seat (33.3%), meaning the index of proportionality is 133.3 (33.3 / 25 = 1.33). (The quota is 25% - 100 / 4.) That means the party is over-represented by 33.3%.
In a 4-seat electorate, 25% of the votes is still only enough to win one seat (25%), but the index of proportionality is now 100.0. As you can imagine, other examples could be set out showing similar relationships between votes and seats for DMs of 7 >> 6, 5 >> 6, or whatever.

Now, in Ireland, in the bad ol’ days, the party in power drew the constituency boundaries in a manner that would enhance its prospects at the next election. For example, if the party knew it had 40% support in a particular part of the country, it would create a 4-seat constituency out of a current 5-seater, to increase its index of proportionality from 100, to 125. (Example 1.)

Also, in those parts of the country where the party in power knew the main opposition party had 25% support in a 3-seat constituency (index 133.3), it would create a 4-seat constituency from that current 3-seater, to decrease the opposition party’s index to 100.0. (Example 2.)

When the opposition party next came to power … well, you guessed it. (Ireland now has an independent Constituency Commission – thank goodness.)

The differences in the indexes (i.e. between over-representation, or under-representation) in odd-numbered electorates is less than in even-numbered electorates. For example, in a 5-seat electorate, if a party wins two seats (40%), the index in respect of 33.33% of the votes received (two quotas) is 120.0 (40 / 33.33 = 1.20); for 37.50% of the votes, the index is 106.7 (40 / 37.50 = 1.07); for 40% of the votes, the index is 100.0; for 42.86% of the votes, the index is 93.3 (40 / 42.86 = 0.93). The difference between the high index and the low index for these vote percentages is 26.7 (120.0 – 93.3 = 26.7).

In a 4-seat electorate, if a party wins two seats (50%), the index in respect of 40% of the votes received (two quotas) is 125.0 (50 / 40 = 1.25); for 42.86% of the votes, the index is 116.7 (50 / 42.86 = 1.17); for 50% of the votes, the index is 100.0; for 57.14% of the votes, the index is 87.5 (50 / 57.14 = 0.88). The difference between the high index and the low index for these vote percentages is 37.5 (125.0 – 87.5 = 37.5).

Therefore, it can be seen that odd-numbered electorates flatten out the proportionality indexes for any given number of seats, over varying percentages of votes received, affording fairer representation for the parties that win seats in such electorates.

This is no doubt one of the reasons why the Royal Commission recommended that, were STV to be adopted in New Zealand, 80% of the electorates should be 5-seaters. The other 20% would not exceed seven seats, or have fewer than 3 seats. It is to be noted that one or two 4-seaters, or one or two 6-seaters, were not precluded from this variation from the 5-seat norm. For example, under STV, the South Island might well have been allocated 26 MPs, either as result of this year’s census, or following the 2018 census. That would likely have meant a 1 x 6-seat electorate and 4 x 5-seat electorates.

However, having said all that, there are situations where even-numbered constituencies are provided for, regardless. They are usually seen in polities where the boundaries are unchangeable, such as for the Australian Senate where the state boundaries are fixed, and in respect of the 108-seat Northern Ireland Assembly, where six members are elected from each of that province’s 18 single-seat FPP Westminster constituencies.

None of this has much to do with STV elections at the local level in New Zealand. The National Party does not stand candidates, and Labour and the Greens appear to do so somewhat half-heartedly. As I’ve pointed out somewhere up-thread, only 18% of local authority candidates are party aligned (presumably including various local groupings that often come and go with each election cycle). Therefore, there is really no reason why STV wards and regional council constituencies cannot have a mixture of odd- and even-numbered seats, as best suits the representation requirements of each council. In a basically non-party polity (by choice of the small-n national parties), even-numbered seats are not an issue.

Wellington • Since Jul 2013 • 125 posts Report Reply

• Hannah, in reply to Steve Todd,

Ta muchly

Auckland • Since Feb 2009 • 15 posts Report Reply

• Rich of Observationz, in reply to Steve Todd,

That's most informative.

Both Labour and the Greens are running candidates in my ward. What I did wonder is why they are only running one candidate in a three seat ward - lack of people wanting to run, or a desire to put all their resources behind one candidate?

Back in Wellington • Since Nov 2006 • 5550 posts Report Reply

• Graeme Edgeler, in reply to Rich of Observationz,

Both Labour and the Greens are running candidates in my ward. What I did wonder is why they are only running one candidate in a three seat ward – lack of people wanting to run, or a desire to put all their resources behind one candidate?

Pretty sure it's the latter (in general, anyway, knowing nothing of your ward). Experience has told them not to split their vote, even under STV. People don't feel party affiliation nearly as strong in local body elections.

Wellington, New Zealand • Since Nov 2006 • 3202 posts Report Reply

• Local body politics is a bit of a nightmare for forcing weird strategic decisions, and can be very opaque from outside.

Claims that local body is non-party are weakly supported by evidence. If you look at Auckland/Wellington/Christchurch, there are clear party lines, if not as coherent or extensive as at national level, and obviously differing in detail.

Since Jul 2008 • 1452 posts Report Reply

• Graeme Edgeler, in reply to Keir Leslie,

Claims that local body is non-party are weakly supported by evidence.

I only mean it to the extent that the proportions of people who will vote for someone simply because their rosette is coloured red or blue is much lower than at general elections. I suspect that Green affiliation is stronger, tbh (although my hunch has no evidential foundation).

Wellington, New Zealand • Since Nov 2006 • 3202 posts Report Reply

• Keir Leslie, in reply to Graeme Edgeler,

I agree --- wouldn't quibble with that.

Since Jul 2008 • 1452 posts Report Reply

• Hebe, in reply to Keir Leslie,

Keir, off topic but still politics: any ideas why Labour's Chch East selection chose Poto Williams? Who may be a great choice, but no-one outside the party knows who she is. It seems odd to pass over at least two strong local candidates in such a hammered-by-earthquakes area in favour of someone who has been living in the city for eight months? What does she bring to the table?

Christchurch • Since May 2011 • 2896 posts Report Reply

• Graeme Edgeler, in reply to Hebe,

Who may be a great choice, but no-one outside the party knows who she is.

It’s Labour and Christchurch East, at least so far as the election is concerned I suspect it doesn’t matter if no-one knows who she is.

Wellington, New Zealand • Since Nov 2006 • 3202 posts Report Reply

• Hebe, in reply to Graeme Edgeler,

It’s Labour and Christchurch East, at least so far as the election is concerned I suspect it doesn’t matter if no-one knows who she is.

Not so. The electorate has undergone huge change in its demographics, many properties and areas don't exist or are uninhabited (red-zoned or too damaged to live in). Then people new to the city seeking rentals have gone out there, attracted by the beach. The effect is uncertain; not so much for the by-election (though that too is no done deal for Labour) but more for the boundary changes coming up for the general election which could make the seat shaky for Labour. The by-election will be an interesting test run.

Christchurch • Since May 2011 • 2896 posts Report Reply

• Keir Leslie, in reply to Hebe,

Yes --- 14 %age points on the party vote will be hard to make up. I'll be totally honest, I didn't go to the selection meeting, and haven't personally met Poto Williams (living on the other side of town as I do.) However, I'm told by people who've worked closely with her that she's pretty awesome. She's got a very good record of service to vulnerable communities.

Since Jul 2008 • 1452 posts Report Reply

• Steve Todd, in reply to Rich of Observationz,

I think the latter is more likely, too – concentration of resources.

In the Lambton Ward, for example, the election is wide open. Labour does not know with any certainty that its candidate, Mark Peck, is going to win one of the two vacant seats, despite the fact he is a former MP.

But, to win two seats in a 3-seat ward, requires a party receiving 50% of the votes (quota 25%). Therefore, if Labour had put up two candidates, it would have risked some of its vote “leaking” away from the running-mate (say, Peck), to other candidates, when the other Labour candidate was excluded from the count (as that other candidate surely would be). Although most votes would transfer to Peck, the leakage that would also occur could just be sufficient to deny Peck the third seat (in a tight contest). Too risky. Better to concentrate resources.

Regarding the Greens, it looks like Iona Pannett has a lock on her seat. Her final keep value in 2010 was 70.6% (up from 90.5% when first elected in 2007), so she should comfortably be re-elected again. She has worked hard on local issues in the ward, both before and after her 2007 victory, and now has a high profile.

But, again, there is no way a lesser-known Green candidate, such as David Lee (who I understand lives in Lambton, but is standing in Southern, meaning Sarah Free, who lives in Southern, had to stand in Eastern), would pick up a quota of votes in addition to Iona. Leakage away from Iona upon Lee’s exclusion would not be the issue for her that it would be for Peck, but why waste resources on something that’s not going to happen?

You might think I’m contradicting myself, having said in my previous post that, in Ireland, parties usually put up one candidate more than the number of seats they expect to win. But that is in a national party-based polity where the two main parties (Fianna Fáil and Fine Gael) have traditionally known with near certainty how many seats they will win in each electorate; it just being a question of which candidates will fill them. (The apple-cart was thoroughly upset in 2011, but that’s another story.)

That is not the situation in Wellington City. While Iona is almost certainly safe (in my view), her seat is not necessarily a safe seat for the Greens. Were she not to stand in 2016, there is no guarantee her vacancy would be filled by the Green candidate replacing her.

Wellington • Since Jul 2013 • 125 posts Report Reply

• bmk, in reply to Steve Todd,

But, to win two seats in a 3-seat ward, requires a party receiving 50% of the votes (quota 25%).

Sorry, I'm probably being dense but could you explain how to win two seats in a 3-seat ward you would need 50% off the vote? I would have assumed that 33.3% would be needed for each seat and to get two would need 66.6%. Or am I missing something?

Since Jun 2010 • 327 posts Report Reply

• Graeme Edgeler, in reply to bmk,

Sorry, I’m probably being dense but could you explain how to win two seats in a 3-seat ward you would need 50% off the vote? I would have assumed that 33.3% would be needed for each seat and to get two would need 66.6%. Or am I missing something?

If you have over 50% of the vote across two candidates, it is impossible for two other candidates to both have more votes than your two candidates. So the three winning candidates will be your two candidates, and one other.

E.g. Your Candidate 1 has 25%+1 of the vote, and your candidate 2 has 25%+1 of the vote (after the excess from candidate 1 has been apportioned), now one other candidate can have 50%-2 of the vote, but after the 25%+1 they need to be elected is taken out, no matter who the rest of the vote goes to, no other candidate can have more than 25%-3 support. It is impossible for more than three candidates to each have more than one-quarter of the votes.

If you want to see where your math goes wrong about the proportion of the votes you need to win in a two-seat race and a one-seat race.

One seat race is obvious - if you have more than half, no-one can beat you. In a two seat race, if you have more than a third, you might be beaten by one person, but you can't be beaten by two, so you're going to be in the top two, so you're in. If you want to win two seats in a two seat race, then each getting a third of the vote means no-one else can beat you, and you're both in.

If you needed 66.6% to win two seats out of three, that would imply you'd need to win 100% to win all of the seats in a race (including 100% to win a one-person race like a mayoral election), but you don't need support from everyone, just support from enough people so that no-one else can beat you.

Wellington, New Zealand • Since Nov 2006 • 3202 posts Report Reply

• bmk, in reply to Graeme Edgeler,

Thanks that explains it clearly, I knew I was missing something just didn't quite understand it and you've explained it really well.

Since Jun 2010 • 327 posts Report Reply

• Steve Todd, in reply to bmk,

Hi, bmk. I’ve just this minute seen that Graeme has beaten me to it, but, just to be polite, I’ll put up my response, anyway.

Think of it like this. In a single-seat election under STV, the winner needs 50% of the votes plus one, to be elected. No-one else can attain that many votes. The same applies in multi-seat elections. In a 2-seat ward, the two winners need one-third of the votes each, plus a little bit more, to be elected. There is then insufficient votes left over for a third candidate to receive that many votes. In a 3-seat ward, the three winners need only one-fourth of the votes each, plus a little bit more, and so on.

In other words, the quota for election is found by dividing the number of valid votes cast by one more than the number of seats being contested, and adding a little bit more. Under NZ STV, that little bit more is one one-billionth of a vote (the votes are counted by computer). For example, in the 3-seat Lambton Ward in Wellington in 2010, 10,041 valid votes were cast, meaning the initial quota was 10041 / 4 = 2510.25, plus one-one billionth of a vote = 2510.250000001. Although it never actually happens in real elections, if the three winners each attained that many votes, the runner-up candidate – the last candidate to be excluded from the count – could at most attain only 2510.249999997 votes; not enough to be elected.

Just for your information, when the votes are counted in this year’s Northland District Health Board election, at which seven candidates will be elected at-large, the (initial) quota for election will be something like 45,000 / 8 = 5625.000000001.

I should point out that Graeme covers this in a slightly simpler manner at his post, back at the beginning of this thread, under the heading *But what about in STV elections where you’re electing more than one person?* In addition, I can’t let this opportunity pass without drawing your attention to my first posting, in response to Graeme’s article, near the bottom of page 1 of these responses. If you click on the link to the dunedinstadium website, you can access several articles about STV that I have written.

Wellington • Since Jul 2013 • 125 posts Report Reply

• Steve Todd, in reply to bmk,

Having now read Graeme's reply, I realise I omitted to complete my explanation by stating that, using the Lambton Ward example, the two Labour candidates would need a total of 5,020.5 votes for both to be elected (being a quota of votes each), which is 50% of the total of 10041 votes cast.

Wellington • Since Jul 2013 • 125 posts Report Reply

• Graeme Edgeler, in reply to Steve Todd,

If you click on the link to the dunedinstadium website, you can access several articles about STV that I have written.

Steve - don't know if you'd picked this up, but Stephen Franks seems to like your work:

http://www.stephenfranks.co.nz/graeme-edgeler-on-stv/

Wellington, New Zealand • Since Nov 2006 • 3202 posts Report Reply

• bmk, in reply to Steve Todd,

Thanks, that too explains it really well. I did actually read Graeme's entire post but didn't quite grasp the maths (I guess as there was a lot of other information to take in at the same time) but both Graeme and your replies to my post have explained it clearly.

On a semi-related note what is the rationale behind the Australian system making it compulsory to rank all candidates (ignoring the above-the-line option) doesn't this just make it harder for people to vote and increase the likelihood of people not voting or just going from top-to-bottom? From my perspective the NZ option of allowing people to simply rank as many or as few as they like seems far preferable.

Since Jun 2010 • 327 posts Report Reply

• Graeme Edgeler, in reply to bmk,

On a semi-related note what is the rationale behind the Australian system making it compulsory to rank all candidates (ignoring the above-the-line option) doesn’t this just make it harder for people to vote and increase the likelihood of people not voting or just going from top-to-bottom?

I think it's related to their compulsory voting. If you want to final result to reflect the real preferences of the entire voting population, then mandatory exhaustive voting is the way to go about it. I don't think the intention is to increase the invalid vote, but to encourage voters to vote for everyone so that the final result actually reflects what people want.

But I'm just guessing. Even if that was the reason it was instituted, that's not necessarily the same as the reason it hasn't been undone.

Wellington, New Zealand • Since Nov 2006 • 3202 posts Report Reply

• bmk, in reply to Graeme Edgeler,

I think it's related to their compulsory voting. If you want to final result to reflect the real preferences of the entire voting population, then mandatory exhaustive voting is the way to go about it. I don't think the intention is to increase the invalid vote, but to encourage voters to vote for everyone so that the final result actually reflects what people want

Yeah, that's what I imagined too and certainly the intention wouldn't be to increase invalid votes. But why it hasn't been undone I guess is what I don't understand.
I certainly am glad we don't have it, or compulsory voting here. I don't like the idea of either being compelled to vote, or if choosing to vote then being compelled to rank every single candidate.

Since Jun 2010 • 327 posts Report Reply

• Steve Todd, in reply to Graeme Edgeler,

Thanks for bringing that to my attention, Graeme. I would have missed it otherwise.

My attitude is, no matter what we do as voters, someone is going to win. Therefore, we might as well take the opportunity afforded us to have our say as to who the winners will be. That is why I say people should express as many preferences for the candidates as they are able. Although Stephen Franks advises his readers to “Vote only for people you would be happy to see winning. Stop there[.]”, he also says “Only vote as far down the sequence as you actually prefer.” So we’re not too far apart.

Stephen intends to vote Young 1, Morrison 2. That is a good vote for him, because it is almost 100% guaranteed that one of those two candidates will still be there at the end of the count, so his vote is almost certainly not going to be wasted. Even if both of his two preferences are unsuccessful, it could not be said he had cast a wasted vote.

If a voter rank-orders, say, 14 out of 23 candidates, as I think I am going to do in respect of the Capital & Coast DHB, and a tiny, tiny portion of that vote ends up in the total of non-transferable votes, it can hardly be said that that tiny portion was wasted.

But, if you take the trouble to vote, and don’t bother to take the opportunity to indicate a preference for one or other of the two candidates who are most likely still to be there at the end of the count, when you have a preference for one of them, but don’t express it, then it can be said you wasted your vote.

When a candidate is excluded from the count, the counting of votes continues as if that candidate had never stood. Each iteration of the count, in both single-seat and multi-seat elections is, in effect, a new election.

Let’s say a voter really wants Kerry Prendergast to be mayor. She’s not standing this time, so that voter’s second preference becomes a first preference for one of the candidates who *is* standing. The same applies should that candidate be excluded during the count. The vote now becomes a new first preference for that voter’s third-preferred candidate, and so on.

So what happens if both Young and Morrison are excluded during the count? Let’s say there are still two candidates in the race. Stephen has now, in effect, declined to have his say as to which of the two remaining candidates should be elected, simply because he does not rate either of them.

He exhorts his readers not to “rank candidates to help make sure that at least a dog beats the genuine idiot.” The candidates he preferred are gone (with the count now treating them as if they had never stood in the first place), yet he would rather his vote be wasted (in effect, not to have been cast at all), than use it to help the dog – the lesser of the two evils he is now confronted with – beat the genuine idiot. Isn’t that akin to cutting off your nose to spite your face? If we all followed his advice, could it not then truly be said that we get the elected representatives we deserve? I think so.

I agree with you that we are all entitled to cast our votes as we each see fit, that our voting decisions are our own business, and are valid, whatever they may be – that is what I take you to be saying (in the introduction to your FPP Q+A) – but I continue to maintain that, whereas some votes are genuinely ineffective in helping to elect at least one candidate, e.g. the votes given for the runner-up candidates, some other votes are genuinely wasted, when they need not be. Stephen’s advice would see many votes unnecessarily end up in the latter category, and our (local) democracy would be the poorer for it.

Wellington • Since Jul 2013 • 125 posts Report Reply

• I just ranked all 36 District Health Board candidates. It took half a day. I had to have a lie down...

Since Mar 2008 • 110 posts Report Reply

• Steve Todd, in reply to Susan Snowdon,

One thing's for sure, Susan. No way will your vote, or any part of it, be wasted.

Wellington • Since Jul 2013 • 125 posts Report Reply

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