What would Australia look like with proportional representation?
What would Australia look like if we moved away from a single-member district, majoritarian electoral rule and adopted a proportional representation (PR) system in the House of Representatives?
In this article I examine what Australia’s Federal Parliament (specifically, the lower house, where government is formed) might have looked like under two different PR systems (D’Hondt and Webster) based on first preference votes in the 2007, 2010, 2013, 2016 and 2019 Federal elections. I also examine the disproportionality of both the actual, and hypothetical (party list) PR results in each of these elections based on the Gallagher index. Party list PR just means that voters vote for parties rather than specific candidates — it is the most common form of PR.
The motivation here isn’t to argue that we should or should not move to a PR system. This article seeks to provide purely positive information which may inform normative discussion re: the ‘best’ system for Australia, and get people thinking about what different systems may be like. One thing I’d really like to stress is that more proportional ≠ better. ‘Better’ can only be established conditional on our preferences for the features of an electoral system. So, particularly when looking at the measures of disproportionality — more proportionality simply represents a system with a preference for the representation of all views over other features of democratic systems like accountability (a bit more on this later).
If you’re interested in the Python script used to obtain these results (it’s pretty shabby but does the job), you can find it here:
Before diving into the results, I’ll briefly explain what is meant by a PR system for those unfamiliar with the terminology. Feel, free to skip this section if you already understand PR.
Proportional Representation:
In general, electoral systems are methods of translating the amount of votes won by each party to the amount of seats they gain in Parliament/whatever the relevant legislative body is.
Different electoral systems are designed to reflect different preferences over features of elections and democracy. A proportional system is any electoral system where the share of votes won by each party is approximately the same as the share of seats they gain in Parliament. Proportional representation systems reflect a preference for the accurate representation of the electorate’s political preferences over accountability.
For more in the differing political philosophies reflected by different electoral systems, I recommend reading ‘Elections as Instruments of Democracy: Majoritarian and Proportional Visions’ by G. Bingham Powell.
Electoral systems where each electorate/district corresponds to a single seat in the relevant legislative assembly are not very proportional, and often feature large discrepancies between the vote shares and seat shares of each party. This is easiest to understand by way of example:
Consider an Australian electorate using Instant-runoff voting (IRV, the current system) where 60% of the electorate have voted for the LNP and 40% have voted for the ALP. The LNP candidate will win and thus, 40% of voters are not represented in Parliament. If, however, the electorate produced, say, 10 MPs instead of one and used a proportional system, it could easily be the case that 6 LNP MPs and 4 ALP MPs were elected to Parliament, thus representing the electorate’s preferences better.
Before continuing, I’ll explain the details of the D’Hondt and Webster systems of PR. If you’re already familiar with these or don’t care about the details feel free to skip ahead to the next section. I’ll also give a brief account of the Gallagher index which will be used to quantify the disproportionality of each possible system.
The D’Hondt method works like so:
The votes for each party are counted and a ‘quotient’ is calculated for each party. 𝑄ᵢ = 𝑣ᵢ ⁄ (𝑠ᵢ + 1) where 𝑄ᵢ is the ‘quotient’ of party i, 𝑣ᵢ is the votes received by party i, 𝑠ᵢ is the seats currently allocated to party i ( naturally, this is initially 0). The first seat is allocated to the party with the largest quotient. Quotients are then recalculated (the quotient for whatever party won the first seat will have a denominator of 2 in the second round). This process continues until all seats have been filled. More succinctly, in each round, some party, i, will win a seat if and only if ∀x s.t. x≠i (Qᵢ > Qₓ).
The Webster method is extremely similar, except the quotient is calculated as: 𝑄ᵢ = 𝑣ᵢ ⁄ (2𝑠ᵢ + 1). The primary difference is that the Webster method favors large parties less than the D’Hondt method, and is, in general a more proportional system.
For more details on these two systems, the preferences/values they express and the differences between them see:
- https://en.wikipedia.org/wiki/D%27Hondt_method
- https://en.wikipedia.org/wiki/Webster/Sainte-Lagu%C3%AB_method
The index used to quantify the disproportionality of various real and hypothetical election outcomes is the Gallagher Index:
The Gallagher index takes the square of difference between the share of votes and seats for each party (to ensure that it is a positive number), and adds these up. This number is then halved to ensure the resulting number is between 0 and 100 (vote shares and seat shares are expressed as numbers between 0 and 100 not 0 and 1). Then we take the square root to ‘reverse’ the squaring of each difference (this is a crude explanation but should suffice to convey the gist of it).
With all that out of the way, I’ll just make a few points re: methodology/interpretation before diving into the results.
- I’ve assumed that, even if using PR systems, (the lower house of) Parliament will consist 151/150 seats. In practice this would likely not be the case. Realistically, were PR to be implemented there would be many large multi-member districts, with no reason to keep the number at 151/150 (particularly as proportionality tends to increase with the number of seats). However, keeping it at 151/150 makes it easier to compare between the electoral outcomes of the hypothetical PR systems and the results of the current system (i.e. we can see party A got X seats in the 2019 election but, if we had used D’Hond method, would have got Y seats).
- On that note, I’m just going to pretend that the entire country is one giant electorate for the PR hypotheticals. Again, this would almost certainly not be the case, but the proportional nature of PR makes this a good approximation regardless of where specific electoral boundaries would be.
- We’ll assume that first preference IRV votes (as recorded from past elections) are the same votes people would make under a PR system since both represent the voter’s sincere preference (this is backed up by political theory).
- Obviously, this ‘what if’ will not be perfect for many other reasons (i.e. if we did have a PR system more independents or small parties may be encouraged to run thus changing the distribution of votes), but it should be a decent approximation. Fundamentally, this is an exercise in what would be the case only under the assumptions I’ve set forth and we should be cautious in extrapolating beyond that.
- Lastly, I will assume no electoral thresholds for parties.
Results!
The following tables show how many seats each party would’ve won, based on the votes received under the D’Hondt and Webster methods, as well as the actual seats that were received using IRV. Seat shares for each method, along with vote shares are also reported.
Note: in a PR system, government would not be formed by a single party/long lasting coalition with a majority of seats. Rather, every election would feature negotiations and bargaining between multiple parties in order to create government forming coalitions (hence, ideally, representatives bargain for their constituents desires — and more people’s views are represented in the legislative process than just the majority). This is important to keep in mind when thinking about what the governments that would spring forth from these hypothetical Parliaments could look like.
2019:
In 2019 the actual (IRV) allocation of seats features a Gallagher Index of 13.47. The hypothetical outcomes using the D’Hondt method and Webster method yield Gallagher Indexes of 0.92 and 0.45.
The most obvious difference here (that I suspect will be true for each election we look at) is how many more seats the Greens would win, and conversely, how many less Labor would win, under a PR system.
2016:
IRV had a Gallagher Index of 13.37, D’Hondt had 0.84 and Webster had 0.29.
Similar comments apply re: the Greens.
2013:
The Gallagher Indexes:
- IRV: 12.79
- D’Hondt: 0.71
- Webster: 0.30
2010:
Gallagher Index:
- IRV: 11.46
- D’Hondt: 0.90
- Webster: 0.52
2007:
The Gallagher Indexes for 2007 are:
- IRV: 10.33
- D’Hondt: 0.77
- Webster: 0.28
Hopefully, this has provided a bit of a sense of what Australian Parliament may have looked like under different voting systems over the past few years. You can use your imagination to consider what kind of coalition governments these methods could’ve produced.
Trends
You might’ve noticed that the disproportionality of the House of Representatives is going up over time (due to increased first preference votes for non ALP/LNP parties). I’ve provided a few graphs of the Gallagher Index over each of the elections studied to give a better sense of this trend.
This graph shows us how disproportionate each real Parliament has been since 2007, and how disproportionate each hypothetical Parliament would have been. Since there are obviously huge differences in proportionality between between PR systems and majoritarian systems (what we currently have), the trends might be more obvious when we view the real vs. hypothetical Parliaments separately:
Here we clearly see that the disproportionality of vote share to seat share in Australian Parliament has been increasing since 2007.
With the hypothetical PR systems, disproportionality seems much more steady and fluctuations can probably be attributed to noise.
Alright, that’s all — hope you enjoyed reading, let me know your thoughts on PR for Australia!
