**UPDATE**: The legislation has been introduced and it does not fix the number of Territory seats at a minimum of two. It instead adopts my proposal to use the harmonic rather than arithmetic mean in determining seat entitlements for the territory. However, the harmonic only applies for quotients under three. That provision might need a re-visit if the Parliament ever increases in size. The statistical error provision has been repealed. The determination in July merging the NT into a single seat has been set aside and two seats restored. Legislating backwards for the harmonic mean was too difficult but under it the NT would have been entitled to two seats.

From the next determination, to take place after the next election, the new rules will apply to the territories. The NT will be entitled to a second seat if its quotient is above 1.3333 rather than the current 1.5. The ACT will be entitled to a third seat with a quotient above 2.4 rather than 2.5. As noted above, this new harmonic mean will not apply above three seats.

The legislation and notes related to it can be found at this link.

Minister’s Second Reading Speech here.

#### Original post

July’s proposed reduction of the Northern Territory to a single seat in the House of Representatives produced a flurry of activity to keep the NT’s House representation at two.

NT Labor members, supported by NT Country Liberal members, backed a proposed bill to increase the Northern Territory’s minimum House representation from one to two seats. The bill was referred to parliament’s Joint Standing Committee on Electoral Matters (JSCEM) which concluded the Electoral Act should be amended to guarantee both Territories a minimum of two seats in the House.

The government agreed to the proposal but will substitute its own better drafted legislation on the matter this week. No doubt the legislation will be guided by the JSCEM recommendations.

The problem is, after fixing Territory representation at two seats each, the JSCEM report suggests consequential amendments to remove the statistical error provisions for allocating territory representation. These were introduced in 2003 to help the Northern Territory retain two seats and JSCEM argues they are no longer necessary with the two seat guarantee.

Those error calculations currently apply to both territories. They were not enough to prevent the NT losing its second seat in 2020, but in the 2017 apportionment determination, and again in 2020, those provisions granted the ACT a third seat in the House of Representatives. Without a significant increase in population, removal of the error provisions could see then ACT revert to two seats at the election after next.

We will have to await the release of the government’s bill to see whether the JSCEM recommendations are adopted in full. *But it seems a little perverse if changes introduced to protect the Northern Territory’s second seat result in the ACT losing its third seat.*

#### A Background on Allocating House Seats to States and Territories

One year after the first sitting of each new parliament, the Australian Electoral Commissioner issues an determination on how many members of the House of Representatives each state and territory will elect at the next election. The determination the Commissioner makes is tightly defined by Section 24 of the Constitution and past High Court rulings on the section’s meaning. The timetable and procedures to be followed are set out in the Electoral Act.

Before this year’s apportionment decision on 3 July, I wrote a long post explaining the detail of how seats are allocated to states, added a second post on how this procedure has been extended to the Territories and the problems of applying the same rules to both states and territories. I added a third post on alternative methods of allocating seats, and a fourth post on the determination issued on 3 July.

In brief, apportionment of seats to states works by first dividing the total population of the six states by twice the number of the Senators to produce a national quota. The population of each state is then divided by the quota to produce a quotient, and each state is allocated a number of seats equal the whole number part of the quotient. A minimum five seats is guaranteed for original states, which is how Tasmania retains five seats. As a final step, states where the quotient has a remainder greater than 0.5 are allocated an extra seat.

The division is also applied to territories with some minor variations. The minimum number of seats is set at one, not five, though the proposed legislation will increase this to two seats per territory. Small external territories are rolled into the mainland territories, the NT including Christmas and Cocos (Keeling) Islands, the ACT including Norfolk Island, the Australian Antarctic Territory and sundry smaller territories. For Commonwealth purposes, Jervis Bay is included in the ACT though it is not administered by the self-governing ACT.

After adding these extra numbers to the territories, this year’s quotients for the territories were 1.4186 for the Northern Territory and 2.4796 for the ACT. On the basis of population alone, the NT was entitled to one seat, the ACT to two.

The NT was first allocated a second seat ahead of the 2001 election, but ahead of the 2004 election, its population fell just short of the 1.5 quotas required for a second seat. After a JSCEM inquiry, the Howard government legislated to adjust the formula to take account of statistical error in the Australian Bureau of Statistic’s population estimates.

Applying the statistical error to the 2020 determination, the NT’s quotient rose from 1.4186 to 1.4763, still not enough to earn a second seat. The error boosted the ACT’s quotient from 2.4796 to 2.5515, enough to be allocated a third seat. It was the error margin that had also allowed the ACT to be granted a third seat in 2017.

*If the government adopts the JSCEM recommendations to fix Territory representation at two seats each and removes the error calculation, it will guarantee two seats for the NT, but remove the provision that has allowed the ACT to gain a third seat at the last two apportionment determinations.*

In legislating to fix Territory representation at two seats each, the government will have to include a provision to undo July’s determination and re-instate the NT’s two states. Removing the error margin will not change the ACT’s representation for the next election as the apportionment decision has already been made.

*But it will leave the ACT at the mercy of the current half-quota rule for choosing between allocating two or three seats into the future. This when the half-quota rule has been judged by parliament as too tough in choosing between one and two seats for the Northern Territory.*

The purpose of my previous posts on allocating seats to states and territories was to outline an alternative formula that could be applied to the territories. Rather than use the half-quota rule, seats would be allocated to territories based on producing Territory representation closer to the national quota than the current formula.

The method I proposed is known as Dean’s method and applies the harmonic mean to the quotient from division rather than the arithmetic mean currently set out in legislation.

In JSCEM’s report, it accepted that the Dean method produced a seat allocation closer to the national average than the current formula, that is Dean’s method is more proportional than the current method.

Para 1.119The Committee recognises that a population-based solution, such as the Dean formula, would have a number of conceptual strengths. It acknowledges that the Dean formula would ensure that seats allocated to each jurisdiction would produce an average population per MP closer to the national average. However it recognises that there are several problems with the potential for public acceptance of this approach.

JSCEM’s third recommendation was –

Para 1.147The Committee recommends that if the Parliament does not enact a two seat floor for the Territories, it considers instead either:

- enacting a harmonic mean for allocating seats between States and Territories, with appropriate public explanation to build understanding for the reform, or
- developing options for JSCEM to consider for additional Senate representation for the Northern Territory.

So the committee accepts the argument around using the harmonic mean as providing a fairer way of allocating seats to territories if the two seat minimum is not adopted. But if the two seat minimum is adopted, it proposes to remove the error margin correction and applies the strict arithmetic mean to allocating seats for the ACT having first suggested the harmonic mean is fairer for the territories.

A better solution would be to adopt the minimum two seats per territory proposal and adopt Dean’s method, the harmonic mean, as the method of allocating further seats to territories. The harmonic mean is a much fairer method than the artifice of using statistical error, and if adopted, allows the statistical error method to be abandoned.

#### Why this Matters for ACT Representation

The ACT’s current population is such that dividing by the national quota always produces a number between 2 and 3. If the ACT is allocated two seats it will have an average population per member above the national quota. If it is allocated three seats its average population per member will be below the national quota.

The national quota in the 2020 determination, rounded to a whole number, was 172,537.

The ACT’s population after including other territories was 429,559 or 2.4897 quotas.

If the ACT were rounded down to two seats, this would be a population of 214,780 per member, or 42,243 per member above the national average.

If the ACT were rounded up to 3 seats, it would be a population of 143,186 per member, 29,351 per member below the national average.

So in this case, rounding up to three seats produces a representation closer to the national quota than rounding down to two seats.

So what formulas can be used to determine whether to round up or down? The current formula uses the arithmetic mean, where I am suggesting that the harmonic mean should be used.

The (current) **arithmetic mean** method always rounds the quotient at 0.5, down to the lower-bound seat allocation, or up the the upper-bound seat aqllocation.

The proposed **harmonic mean** rounds at a value that varies depending on the value on the lower and upper bound of seats. As the number of seats to be allocated increases, the harmonic mean converges on the arithmetic mean. (The formula for harmonic can be found in my previous post on territory representation.)

The smaller the number of seats to be allocate, such as in the territories, the larger the gap between the two rounding point methods.

In the case of the ACT where the lower bound is two seats and the upper bound 3 seats, the value are

- the
**arithmetic mean**rounds up or down at a quotient of 2.5 - the
**harmonic mean**rounds up or down at a quotient of 2.4.

To avoid using six digit population numbers, I’m going to use quota values in explaining why the harmonic mean always produces an allocation of seats with a population per member closer to the national quota than the arithmetic mean.

**Consider if the ACT had exactly the arithmetic mean of 2.5 quotas.** Rounding down to two seats would produce total under-representation for the ACT of 0.5 quotas, but rounding up would produce total over-representation for the ACT of 0.5 quotas. **The arithmetic mean rounds at the point where total over or under-representation is equal.**

But with 2.5 quotas, rounding down would produce under-representation **per-member** of (0.5/2) or 0.25 quotas. Rounding up would produce over-representation **per-member** of (0.5/3) or 0.1667 quotas. So while the arithmetic mean equates total over or under representation, at that point rounding down produces greater under-representation per-member than the equivalent over-representation per member if rounded up.

**Now consider what would happen if the ACT’s population was 2.4 quotas and the allocation of seats was rounded using the harmonic mean.** If rounded down, the total under-representation would be 0.4, and if rounded up the total over-representation would be 0.6 quotas.

But on a per-member basis, rounding at the 2.4 harmonic mean equates over or under representation per member. If rounded down to two seats, under-representation **per-member** would be (0.4/2) or 0.2 quotas. Rounded up to 3 seats, over-representation **per-member** would be (0.6/3) or 0.2 quotas. **Where the arithmetic mean rounds at the point where total under or over representation are equal, the harmonic means round where per-member under or over representation are equal.**

In other words, the harmonic mean always chooses between allocating the upper or lower bound number of sets based on producing an average population per member that is closest to the national quota. The arithmetic mean does not do this as it rounds on the basis of total over or under representation, not on a per-member basis.

In the case of the ACT, if the population is under 2.4 quotas or greater than 2.5 quotas, both methods will produce the same allocation of seats. But between 2.4 and 2.5 quotas, the harmonic mean will round up to produce a population per-member closer to the national quota, while the arithmetic mean will round down and produce representation further away from the national quota.

#### In Conclusion

The above discussion on the ACT illustrates the harsh nature of rounding to a whole number of seats at the arithmetic mean. The same observation would apply to the states, except that the difference between the arithmetic and harmonic mean is very small by the time you reach the five-seat minimum allocation for states.

In adopting the statistical error method in 2003, parliament accepted that rounding at the arithmetic mean 0.5 was harsh on the territories. It added wriggle room that allowed the Northern Territory to retain two seats in 2004, and allowed the ACT to be allocated a third seat in 2017 and 2020.

Now JSCEM proposes to remove the statistical error test on the basis it is no longer required given a two seats per territory minimum, forgetting the test still has relevance to the ACT.

As I pointed out, JSCEM accepted the logic of using the harmonic mean to allocate seats if the two seat minimum were not implemented. It should also apply the same logic for both territories, even if the two seat minimum is adopted.

In my view, fixing the Northern Territory’s under-representation problem by adopting two seats as a minimum, should not as a consequence create the potential for the ACT to be under-represented by losing its third seat.

**Links** – JSCEM report can be found at this link.

**p.s.** – Seats are allocated to state based on population, not enrolment. Compared to the ACT, the Northern Territory has many more residents under the age of 18, and far fewer over 65. For that reason, the NT has a much lower enrolment to population ratio than the ACT. So at the 2016 election, when both territories had two seats, the NT’s total enrolment was 133,020, lower than the enrolment in either of the ACT’s two seats.

The logical cut off for the application of a harmonic mean, if a harmonic mean is not to be applied to allocating seats to states, is 5 seats so that no territory has neither more seats than a state would with the same population nor a higher population per seat average than an original state can have because of their minimum number of seats.

Sustained ACT population growth above the national average could also put the ACT between the harmonic mean tipping point and the half-quota tipping point for a 4th seat, without population growth.