Tactical Senate voting

The new Australian senate voting system offers an opportunity to vote tactically with significant effect, and without much risk of making a mistake and wasting your vote. It’s worth thinking about.

For international readers, voting for the upper house of our bicameral parliament — the senate — is by a single transferable vote proportional system. Like in the US senate, each of our six states has equal representation (but by 12 senators rather than two), and votes for its senators as a single electorate, usually for half (six senators) every three years. For complex political reasons, our general election on 2 July will include a special senate election for all 12 senators per state. That combination is called a double dissolution election.

Under our old senate voting system in place for over 30 years, most people used a shorthand vote (‘above-the-line’) whereby they assigned their first preference and back-room party hacks decided all the rest, in advance — the ‘transferable’ part. Yep, really, that’s how it was. That system has now been changed to conventional single transferable vote (with partially optional, fully voter-directed transfer), as used for the upper houses in some Australian state legislatures and also internationally. We call that system ‘multi-member optional preferential’. The above-the-line voting option is being retained, but becomes just a shorthand way of voting for a party’s candidates in their list order, by numbering a box for the group instead of numbering each candidate individually.


Understanding the count

To grasp the tactical opportunity you need to understand in detail how the count works. For historical reasons this election will use an older counting system intended to facilitate manual counting, even though the count will be entirely computerised. Technically it’s ‘fixed quota with a droop’, meaning that the vote required to get elected (the ‘quota’) is equal to the total formal vote divided by the number of members to be elected plus one, and that doesn’t change through the count. The plus one bit is the ‘droop quota’, the votes left over at the end that don’t elect anyone. So at this election with twelve places to be filled per state, the quota for election will be 1/(12+1) = 7.7% of the formal votes cast in each state.

The Australian Electoral Commission provides a fair plain language description of the counting method, but it can be hard to follow and lacks detail. A better way to understand may be to run through an actual example. I suggest Australian ABC psephologist Antony Green’s summary of the 2013 senate election for the state of Queensland¹, here: http://www.abc.net.au/news/federal-election-2013/results/senate/qld/. Note that was an ordinary half-senate election for six senators, so the quota was 1/(6+1) = 14.3%. Apart from that the counting method was the same as will be used this time, but most of the 2013 vote transfers — the preferences — were precisely determined in advance by all those party hacks. That greatly simplified the counting process making it easy to follow.

It goes like this:

  1. After all votes are checked and informal ballots excluded, first preferences are tallied for all candidates — that is Antony Green’s ‘Count 1’. (Green provides summary counts for the party groups at each stage, but that is shorthand — the count is actually for individual candidates who happen to be grouped into ordered party lists.)
  2. The candidate with the most votes — Macdonald at the top of the LNP’s list — has a quota (14.3% in this case; will be 7.7% for 2016) and is elected. In fact he has almost three quotas (2.8975 quotas, nearly all via above-the-line votes for the LNP). The excess vote value over the single quota that elected him is then transferred to the next preferences — at Antony Green’s ‘Count 2’. The transfer is done according to the next vote preference for every ballot in the count for Macdonald. At the 2013 election those preferences were nearly all exactly the same (they run down the party list and after that are as assigned by the party). In 2016 with voter-assigned preferences they won’t be, at least for out-of-group transfers. Some won’t transfer at all because the voter did not indicate further preferences (the vote will ‘exhaust’, meaning it is excluded from further counting).

    Very important: Votes from an elected candidate all transfer (if a preference is indicated), but at a reduced value according to the size of the excess. In the example the value reduction is (2.8975-1)/2.8975 = x0.6549. So the votes all transfer (no arbitrary order or sample counting is used), but at just 65.49% of their original value — because part of each vote’s value has been ‘used up’ electing Macdonald. There is no dispensation in the value reduction for votes that exhaust; it is calculated as if every vote will transfer, even though in 2016 many won’t.

  3. The candidate with the next highest tally in the original count (Count 1) — Ketter for the ALP — also had a quota and is elected. His excess is likewise transferred — at Count 3 — but it’s smaller, so the transfer value is only x0.4911. After the transfers, the LNP’s second candidate, McGrath, now has a quota and is elected, and his excess is in turn transferred — at Count 4. The transfer value is (1.8975-1)/1.8975 = x0.4730 of the McGrath votes, but nearly all of those votes came via Macdonald, so their aggregate transfer value is now only (2.8975-1)/2.8975 x (1.8975-1)/1.8975 = x0.3908 (as Green quotes).
  4. After those transfers no candidate has a quota (the ALP’s second candidate, Moore, is very close on 0.9964). The count now proceeds to exclusion of candidates with no chance of election, starting with the candidate with the lowest tally. In Antony Green’s summary that is Boag of the Australian Protectionist Party — at Count 5. His votes transfer according to their next preference, but at full value because no part was used to elect another candidate. Exclusions continue, always from the lowest tally remaining in the count, until Count 36, at which point Glenn Lazarus of the Palmer United Party has a quota and is elected. His small excess then transfers — at x0.0873 — to a range of remaining candidates depending on the preferences of each vote, which differ here because they come from a range of sources.

    Important: Any of Lazarus’s votes with a next preference for an already-elected candidate, say for example Macdonald, just pass on to the next preference after that; they are not further reduced by Macdonald’s reduction factor because they did not participate in electing Macdonald. Similarly if they are directed to an already excluded candidate, they just pass on to the next preference after that (they are not excluded).

  5. After distributing Lazarus’s excess the ALP’s Moore now has a quota and is elected — at Count 37. Her small excess is then distributed at a teensy x0.0072, leaving the remaining three candidates without a quota. After excluding the lowest tally of those and transferring the votes, the LNP’s Canavan has a quota and is elected — at Count 39. That is six; The Greens’ Adam Stone is left with the droop (0.86 quotas), and is not elected.

That’s it, except as I’ve said a few things will be different this time:

  • There are twelve senators to elect, so the quota will be 7.7% not 14.3%
  • Except for the run through of each party group for above-the-line votes, preferences won’t be pre-determined, so the count will be much more complex.
  • Most ballots will be incomplete — voters can number any number of squares (above-the-line), but most will number just six groups (above-the-line) or twelve candidates (below-the-line) or perhaps as few as one group. That means many vote transfers will be incomplete (incomplete votes exhaust), so the likelihood of a candidate reaching a quota will decrease as the count proceeds.


Quota shrinkage

Shrinkage to the droop…

So what happens if, late in the count, so many votes have exhausted that there are say three places left to fill and all but three candidates have been excluded, but none of those remaining has a quota? Simple — all three are declared elected. The net result is that candidates late in the count may be elected with less than a quota, perhaps substantially less, while candidates elected earlier still required a full quota … and, importantly, only transferred votes at a value determined by subtracting a full quota.

Obviously that’s not fair. It amounts to a counting bias in favour of late-elected candidates, many of whom are from minor parties (which nevertheless managed to claim that the new voting system disadvantages them). Election specialists like Antony Green are well aware of the problem of course, but most have been downplaying it because they think the effect will be small, based largely on state upper house election experience. I’m not convinced. If, out of habit, many voters ‘just vote one’ above-the-line in the senate, the exhaustion rate may be large and the vote required to elect candidates late in the count may be a long way below a full quota.

There are ways to address the problem of course, most obviously by iteratively reducing the starting quota and repeating the count until the final candidate elected actually gets a quota. Because all of the votes will be data-entered, that would be trivial to do and something like it will probably be implemented in the future.

But, for the current election, it offers a clear tactical opportunity.


Short vs long terms

The 2016 double dissolution will elect 12 senators for each state, half for 6 year terms and half for 3 year terms. The standard way to allocate short and long terms is to recount the ballots as if they had been cast for an ordinary half Senate election, that is for 6 senators instead of 12 (not quite; there are differences of detail, but near enough). Those ‘elected’ in the recount get the long 6-year terms.

In choosing voting tactics, you may wish to consider how they might affect the likelihood of a preferred candidate obtaining a 6-year term.



What you should try to do is get your vote to the latter part of the count, where it may have significantly higher value because of the counting system deficiency. But you don’t want your vote to get there via excess transfer from an elected candidate, because that will have diminished its final value.

How? I suggest the following:

  1. Vote below-the-line. Above-the-line voting has lost all utility except for the lazy, now that you only have to correctly number six candidates with the sequence 1,2,3,4,5,6 for a below-the-line vote to be valid.
  2. Make a list of candidates whom you favour but don’t think will be elected. Vote for those first, in order from the least likely to the most likely to be elected, but respecting any candidate preference you may have.
  3. By way of insurance, and to increase the likelihood of a preferred candidate getting a six year term, make a second list of candidates you favour who are likely to be elected. After voting your first list, append your second list in order from the least likely to be elected to the most likely, again respecting any candidate preferences you may have.
  4. If you haven’t yet numbered at least six candidates, continue numbering candidates you favour until you have. Your vote will be informal if you do not number at least six candidates in the sequence 1,2,3,4,5,6. Continue numbering candidates you favour as you see fit, but avoid mistakes². I recommend that you number at least 12 in accordance with the ballot instructions. There are arguments for then proceeding to number candidates you don’t favour on a ‘least worst’ basis, but avoid numbering any candidate you viscerally despise; your vote cannot count towards their election if you don’t number them (‘putting them last’ achieves nothing).

Why? Voting for candidates you favour in reverse order of their likelihood of election gives your vote its best chance of making it to late in the count, where it will have most value, while respecting your core candidate preferences. But don’t forget the 6 year term effect.

Personally I’ll be voting in the state of Queensland and favouring Greens’ candidates … but, tactically, I won’t be giving The Greens’ Larissa Waters an early preference on my ballot. That’s because she’s certain to be elected and doesn’t need my vote. She will get a later preference from me by way of insurance and to increase her likelihood of getting a six year term. Instead I’ll have Andrew Bartlett (probable second on The Greens’ senate list) high in my preference list, because his chances of election are fairly small and I can vote tactically to increase them.

By the way, while I’m often a Labor supporter, I won’t be numbering any Labor senate candidates on my ballot because I strongly disagree with that party’s pro-coal policies, especially their support for new steaming coal mines.



  1. Green’s summary actually excludes the small percentage of 2013 below-the-line votes with their voter-assigned preferences (less than 5% of the total), but that doesn’t alter the outcome. My outline tries to recognise their existence.
  2. If you make a mistake immediately ask for a new ballot. You are entitled to one without question.
  3. This article relates to the Australian Senate. House of Representatives voting rules are very different; there you must number every square, in sequence starting from 1, for your vote to be valid. (Strictly you can make some types of mistakes with just the last square in the sequence and still be counted, but don’t push it.)



  • In psephological jargon this is tactical rather than strategic voting … even though the article is about choosing a strategy for an individual’s vote. At the level of the election as a whole, what an individual voter chooses to do cannot rate higher than tactics.
  • Dr Kevin Bonham points out that provided a below-the-line senate vote contains the clean numbering sequence 1,2,3,4,5,6, errors made with higher numbers will not render it informal. That is correct; the relevant section of the act is here: http://www.austlii.edu.au/au/legis/cth/consol_act/cea1918233/s268a.html. Nevertheless I strongly advise complying with the ballot instructions and avoiding all errors. It is far from guaranteed that the new rules will be correctly applied in every case; the senate counting task is massive.
  • Dr Bonham also strongly recommends numbering through to unfavoured candidates, so as to express a ‘least worst’ preference, which may affect the outcome. That is good advice, but as a matter of principle I won’t be following it at this election. I will not have my vote count towards the election of candidates who would destroy our snow season, our Barrier Reef, our alpine vegetation, our beaches, our southern wheat belt, our desert ecology, our future.
  • Under “Short vs long terms” I call the recount method the ‘standard method’ because it is the method provided for in the Commonwealth Electoral Act (Section 282). In fact simple order of election in the main count is the method most used historically, but, while similar, that can be shown to be slightly less fair. Under the constitution the newly elected senate decides, and has absolute discretion. It can exercise favouritism, draw lots … do whatever it likes.

21 comments to Tactical Senate voting

  • Aaron

    These new laws are great for those who like a party but can’t stand the #1 or #2 ticket holder. For example if you are a Lib voter from South Australia or Tasmania, or say a Labour voter from WA or VIC, but have no affinity for a certain senator you can positively exclude them from your vote while still giving it to the party of your choice.

  • Suz

    Actually, you have to select 6 above the line and 12 below the line now, not 6 as mentioned in this article….

  • […] can read the whole explanation here if you’re into maths (like me!) or just follow the strategic bit below……. and […]

  • Interesting. A bit difficult for those of us who have voted a certain way for 40 years to get our head around. So I will be reading this again and taking notes.

  • martin

    to Suz,
    Not disputing your numbers (which I think are wrong), but should that be an OR? So “6 above the line and 12 below the line” would become “6 above the line or 12 below the line”

  • Tim

    Failing to number a box is equivalent to putting that candidate last. Failing to number multiple boxes is like saying “if it comes down to it, I *don’t care* which of the remaining candidates is elected.” You should never leave a box blank is you prefer that candidate over any other candidate, because at the end of the day if all other candidates are excluded and there is a choice to be made, if you don’t number the boxes you won’t get a say in that choice. The best tactical way to make your vote count under all circumstances is to number every box. There is no tactical benefit to leaving boxes blank.

  • @TIm is correct — you should number as many box as you can (every).

    You say “I will not have my vote count towards the election of candidates”, but by the time it reaches that point, you only have limited choices.

    You listed 7 things you don’t want destroyed; if there are two candidates left, and you choose *not* to continue numbering, then it could mean the person who will destroy all 7 will get elected rather than the other person, who will only destroy 6/7.

    You may not like either, but if there are only two choices, and you prefer one over the other, you should continue numbering.

    Only stop numbering at the point where the candidates are equally bad, e.g. if the last two candidates would both destroy 6/7, just a different 6, and you don’t really have a preference between those two, then sure, stop, but before that put the person who will destroy 3/7 ahead of 5/7, ahead of 7/7.

    • Gerg

      You’re exactly right Sly; as I said, it’s good advice. I’m just not following it. This time.

  • John Caley

    URGENT – What Suz said. Please correct your article to say you must number at least 12 candidates below the line. Otherwise very useful

    • Gerg

      She is correct, but your concern is not. The ballot instructions in each state clearly say to number “at least 12 boxes” below-the-line, but provided a ballot contains the clean sequence 1,2,3,4,5,6 it is valid. The relevant section of the Commonwealth Electoral Act is referenced in the article – S268A(1)(b), here: http://www.austlii.edu.au/au/legis/cth/consol_act/cea1918233/s268a.html. Nevertheless I recommend complying with the instructions — see tactical point 4; indeed there are arguments for numbering many more than 12 boxes, as outlined in the second last dot point.

      Note that the 1-6 below-the-line numbering sequence required for formality has to be clean, with no numbers omitted and no repeats. And there must be no smaller numbers — a vote with a zero or negative number in any box is informal.

      I have adjusted the wording in two places above to make the matter even clearer.

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  • Gerg

    Just who is ‘likely to be elected’? William Bowe has a try:


    Read the text carefully — not just the ‘results’ tables — and be sure to note the large uncertainty. Allow for it.

  • The best and only system that works 100% is house of reps one x the most x wins
    Senate 12 x so that you just get the top 12 win very simple

  • Karl

    Thanks, Gerg; interesting idea.
    Wouldn’t your proposed tactics work just as well above the line?
    Isn’t that essentially just grouping the candidates into parties (and in their party’s preferred order, as you mentioned)?

    • Gerg

      Not really. Tactical senate voting traditionally involves avoiding voting for candidates who are sure to be elected early in the count, so that your full vote value can support lower-rated candidates you favour, later in the count. You can’t achieve that above-the-line unless those lower-rated candidates happen to be right at the top of a group, like say Lazarus in Queensland or Hinch in Victoria (not a recommendation!).

      The difference this time is I believe the counting system deficiency combined with optional preferential voting and the ‘just vote one’ habit of 30 years may significantly magnify the traditional tactical opportunity. And of course the greatly relaxed below-the-line voting rules make voting that way much more practical, with little risk of inadvertent informality.

  • SgtThursday

    Utter crap. If you deliberately vote 1, 2 and 3 for candidates who you fully expect to be eliminated (and then they are), then 4 for the candidate you actually want and expect to win… that candidate gets zero benefit from your delayed vote. There is no inflation (real or perceived) in the value of that vote

    It is only when candidates are actually elected and then the surplus is distributed that the concept of value inflation even becomes meaningful. And, if you deliberately vote for a candidate that you don’t want in order to preserve and enhance the possibility that your fractional leftover preference might mean a poofteenth of a poofteenth of a percent more than it might otherwise have if your candidate wasn’t elected earlier… that is a bizarre way of thinking.

    Vote for the candidate you most want to win. It’s not rocket science.

  • PeterPuter

    SgtThursday, I think you’ve missed the point. Please reread the 2 sections about the reduced value of an excess if you go down the line, and what happens in relation to the droop. As I understand it, candidates 1-3 in your example but using Gerg’s process are people you would like to have elected (you just don’t think they will be) – in his case Green position 2 Bartlett). The point is that rather than voting 1st preference (Waters) and then having any excess transfer to Bartlett at a reduced value. Given their likely 1st preference vote may be perhaps 1.3 quotas (if they get 10%), then that would only transfer about 0.5 of a quota to Bartlett. Gerg will vote Bartlett ahead of Waters so his vote will be Bartlett 1 full vote instead a % part of the excess. If through some wild swing, one of his first 3 candidate preferences get in, then he’s got someone he like anyway (excess quota at this stage gets pretty meaningless.) If not, his preference ends up with Bartlett, who will then either get the full benefit of his vote (rather than a percentage) and a quota, or it will pass further down his list.
    The reason he calls it tactical is that it is not without risks. If the Greens were to get a nominal 10% of the vote, split evenly after you eliminate the “not expected” candidates, then at 5%, they have 0.65 quotas each, and there is the possibility that neither get in if there are a couple of other strong candidates.
    Also, if other votes exhaust, both could still get in if they both made it after preference distributions to the 2 highest votes with 2 still to be elected. Gerg is attempting to favour Bartlet in this position assuming waters gets in because most people vote like sheep.

  • Paddy

    This is such a good article! Have to add something. I share your political views and disgust with the Labor party, but I’m still voting for SOME of them as a final preference. I want my vote to count. What’s good with this system is that I can choose (below the line) the senators from Labor who actually share my views, but have lost the argument within their party. Here in NSW there are some great Labor senate candidates. I can back them, not the right wing party machine types.

    • Gerg

      In the end I did number some Labor candidates, but I stopped at that. As the votes fall, that may mean that I abstained in the second of Ms Hanson’s candidates’ challenge for the 12th spot, which is Bonham’s risk of ceasing to number too early … exactly.

      (On the current 50% count of Queensland senate first preferences, the chances of PHON’s Roberts being elected appear slight. Ms Hanson’s excess is too small, and the flow from tiddler exclusions will probably not be enough to avoid his exclusion after ~9 are elected.)

      • Tim

        It was not a “risk”, it was practically a certainty, excepting the unlikely circumstance that all seats were filled by your preferred candidates (i.e. ones that you numbered). If there are bad candidates and worse candidates, after all your other options are exhausted you should vote for the bad ones in preference to the worse ones. Expressing a preference between a candidate that will destroy the environment, and a candidate that will destroy the environment and also incite racial violence, does not implicate you morally in the destruction of the environment, but it does implicate you in racial violence if the latter is elected.

        • Gerg

          Indeed, except humans are not always obviously rational creatures. Some of us are so pissed off by twenty years of bastardry that we may not be too concerned about abstaining in such a contest. That was the source of my exasperated, “I will not have my vote count towards…”.

          But before you write us off as emotional fools, consider that we are the result of about a million years of social gaming. And that game theory certainly does not hold that reliably favouring the least worst is always the best strategy. To play you need to turn up, to be heard. I try.