Who did your Senate vote go to?

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Introduction
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September 21 2016

If you live in one of the six Australian states, it can be difficult to determine where your senate vote ended up. This is because your vote can contribute to the election of more than one senator. Alternatively, it may not contribute to the election of any senators. The results are always presented in a way that makes it difficult or impossible to figure out who you helped to elect. In addition, the delay in finding the results means many people forget the details of what order they voted in. The 2016 election made this even more complicated by doubling the number of senators up for election.

This article is intended to help you figure out who your vote ended up with. The first section (background) is intended as an explanation of how the system works, and the second section contains explicit instructions for figuring out who your vote ended up with. Note that several simplifying assumptions were made in this analysis. The AEC publishes detailed results of the order in which candidates are elected or excluded from the ballot, but the detail can be overwhelming.

• Introduction
• Background
• Skipping elected candidates
• Instructions for finding where your vote ended up.
• Election results

It is also my hope that this article alerts you to the possibility that your vote ended up with someone very far down your list of preferences. This should be taken as encouragement to rank all, or the vast majority of candidates. Note in particular that your vote can skip candidates not just because they get excluded from the running, but because they get elected before your vote reaches them. Thus, if you rank a few minor parties first then a major party, your vote may not stick with the major party because the major party candidates are already elected by the time your preferences get distributed. Whether the remaining candidates for that party get excluded early (before they can receive your preference) is somewhat arbitrary in the sense that it depends on how far over a whole number of quotas the party gets. Although there are plenty of micro parties getting excluded first, if your party happened to get 2.0001 quotas of first preferences, it may have two senators elected and then see its remaining candidates excluded before any other preferences are distributed to it.

Note also that failing to rank all or most candidates may mean your vote is discarded early and you miss the opportunity to help decide who holds crucial balance-of-power seats in the Senate. That is, all minor parties with even a slight chance of gaining a seat should be ranked. Although your vote may seem like a drop in the ocean, many crucial decisions are made during the vote counting based on tight margins.

Background
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The Australian senate uses a mixture of proportional representation and preferential voting (aka instant runoff voting) to elect senators. To get elected, a candidate needs to obtain a ‘quota’ of votes. In counting the votes, seats are first handed to candidates who have more than one quota of first preferences. Those votes are then passed on to the voters’ next preference at a reduced value. Roughly half the senators get a seat this way, before any candidates are excluded. Then, once no more candidates have a whole quota, the candidates with the least votes are excluded one by one and their votes are redistributed. As the votes are redistributed, more candidates will obtain a quota. The remaining seats are handed out as soon as each candidate obtains a quota of votes.

The 2016 election was a double dissolution election. This means that there were 12 senators elected from each state. For a regular election, a quota consists of 1/7th (14.3%) of the votes. For a double dissolution election, a quota is 1/13th (7.7%) of the votes. The vote counting method means that the allocation of the final (12th) seat comes down to a runoff between the most popular of the two remaining candidates after the first 11 were elected, ie a runoff between candidate 12 and 13, for the 12th seat. This is why 1/13th rather than 1/12th of the total vote is required to gain election. After 12 senators are elected, in the process consuming 7.7% of the total votes each, one senator remains unelected, but also with close to 7.7% of the votes assigned to him. This means that anyone who voted for the 13th most popular candidate did not actually contribute to the election of any senators. (This is not intended to be a criticism of the method. It is very fair.) Therefor, to find out where your vote ended up, you need to know who the 13th most popular candidate is, rather than the 12 that were elected, which is all that you normally see published.

The tables below list the 13 most popular candidates from each state. The first 12 listed are now senators. The 13th candidate narrowly missed out on a seat.

How your vote was treated depends on whether you gave your first preference to a major party (ie a candidate with more than one quota of first preferences) or a minor party (ie a candidate with less than one quota of first preferences). Note that this is an emergent property of the system that I use for the purpose of explanation. The AEC treats all valid votes equally.

If you voted (with your first preference) for Labor or Liberal in any state, the Nick Xenophon team in SA, Jacqui Lambie in Tasmania, the LNP (coalition) or Pauline Hanson in QLD or the Greens in Victoria, Tasmania or Western Australia, then your vote falls into the first category and probably contributed to the election of several candidates. Assuming for the sake of simplicity that everyone voted above the line, and you ranked the Liberal party first, and they got exactly 3 quotas (23.1%), then your vote contributed to the election of the first Liberal candidate. It was then passed to the next Liberal candidate at 2/3 of its original value. It contributed to the election of that candidate. Then it was passed to the third Liberal candidate at 1/3rd of its original value. It contributed to the election of that candidate also, and was then exhausted.

In practice, the party will not get an exact whole number of quotas. For example, if they got 3.5 quotas, the votes will go towards electing the first three candidates from that party, then get passed to the fourth candidate at a reduced value (1/7th, or 0.5/3.5). From here, they either go towards the election of that fourth candidate (in which case the fourth candidate will appear further down the list) or the fourth candidate was eventually excluded, in which case the votes get passed to the next preferred candidate on each ballot.

If you ranked any minor party (ie a candidate with less than 1 quota on first preferences) above the major parties, then your vote was treated slightly differently. In each state the first 8, 9 or 10 senators were elected based on first preference votes (for the candidate or for the party). Your vote only contributed to the election of those candidates if you gave one of them your first preference, as discussed in the example above. Otherwise, your vote ended up with one of the later candidates.

The tables of results presented below are divided into two groups to clarify this. The first group in each state were elected on first preferences, and the distribution of those preferences within the party. The second group were elected after some candidates were excluded and their preferences distributed. This also marks the first point in the vote counting method where above-the-line preferences are distributed between parties.

Skipping elected candidates
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If you did not give your first preference to someone listed in the first group, it is not possible for it to contribute to the election of anyone in the first group, from that party or any other party. This is true even if you ranked a major party second behind the land rights for wombats party. Your preferences are only distributed after the wombat party is excluded, which only happens after the election of senators with a full quota of first preference votes and the distribution of those preferences. Most of the Liberal and Labor senators, plus one or two from other large parties are elected before your votes does anything.

If this is you, your vote most likely ended up with whichever candidate from the second group (including the 13th) you ranked highest.

However, it is possible that your vote skipped this candidate in the same way it skipped the major party candidates. That is, candidates are elected as soon as they reach a full quota, and any votes distributed to them after they are elected get passed on in the same way they would be if the candidate had been excluded rather than elected. Thus if you gave a higher ranking to a relatively popular minor candidate (let’s call him Fred) who was still in the running when your favourite from the second group was elected, then when Fred was eventually excluded, your vote skipped your favourite from the list because they were already elected and went to your next favourite candidate from further down the list. The 12 senators are listed in the order elected so your vote can only be passed further down the list if it skips your preferred candidate in this way.

Note however that even if your vote skips the first two or three candidates from a major party, it can still contribute to the election of one more candidate from that party in the second group. In this sense it ‘does not matter’ that your vote skipped the first few candidates, because the value it retained by skipping them will still remain with the party. This does however introduce some level of arbitrariness to the system if no more candidates from that party are elected, because your vote will be distributed at full value to the remaining candidates from other parties, while people who put the major party first get their votes distributed at a much reduced value.

Note that it is inadvisable to attempt to take advantage of this arbitrariness, as it cuts both ways. Putting a major party second instead of first to take advantage of this effect could actually cause the party to miss out on getting one more senator in the second group. Always rank the candidates according to your genuine preference.

Exhausting the value of the vote

If you vote Labor or Liberal, then your vote retains most of its value after electing the first candidate, but by the time it elects a third or fourth candidate it has exhausted most of its value. This is not the case for candidates in the second group. These candidates are elected as soon as they obtain a quota. The least popular candidates are excluded one by one, so in most cases a candidate from the second group only has slightly over 1 quota of the votes when they get elected. For example, if they had 95% of a quota, then received 15% of a quota from an excluded (or elected) candidate, they would be elected with 110% of a quota, and those votes would be distributed at roughly 10% of the value they had as received.

Instructions for finding where your vote ended up.
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The tables below list the 12 senators from each state in the order in which they were elected, as well as the candidate who came 13th. If a candidate received more than a full quota of votes, this is indicated in the right hand columns as the percentage of the vote they took and the number of quotas. The far right column lists the residual value of the votes that are transferred after the election of the candidate, as a percentage of the original value. These go to the next candidate from that party.

The table for each state is also divided into two sections. First, check all the candidates listed in the first group. If you did not give any of these candidates your first preference, your vote never went to any of them.

If you did give a candidate from the first group your first preference, your vote contributed to their election. Assuming you voted above the line or in the order indicated by the party, the far right column shows you the reduced value of your vote after it elected that candidate. Then, look down the list to the candidate you ranked second. If this candidate is also in the first group, then your vote also contributed to the election of this candidate, and was passed on at an even further reduced value, again indicated in the far right column. Keep going down the list until you get to the end of the first group. From there, your vote was passed on to one of the remaining candidates at the reduced value. If there is another candidate from your preferred party there, then your vote went to that candidate. Your vote helped to elect this last candidate, along with preference distributions from people who voted for other parties, at which point almost all of its value is consumed and you might as well consider your vote exhausted. If your party has no candidates in the second group, your vote most likely ended up with whichever of the remaining candidates you ranked highest (see discussion above on skipping candidates for possible exceptions).

If you did not give your first preference to any of the candidates from the first group, then find the candidate from the second group who you ranked most highly (even if you ranked someone from the first group above them). This is who your vote most likely ended up with, and unless they are listed in 13th place, your vote contributed to their election (see discussion above on skipping candidates for possible exceptions). Unless they took the 12th senate seat or came 13th, your vote also got distributed down the list, but at a much reduced value (see discussion above on exhausting the value of a vote).

Election Results
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