Election explainer: how does the Senate count work? At a double-dissolution election, each state will elect 12 senators, while the Northern Territory and the Australian Capital Territory will each elect two.

Following the Turnbull government’s recent changes, Australia has new rules for electing senators. How will they work in practise?

What are the basic rules?

The basic principles of electing senators are:

• we have one vote, and all votes have the same value;
• our votes are preferential, and we decide whether to fill in all the boxes or only some of them; and
• because of the preferences we express, our vote is transferable. So, if the number one preference isn’t used to elect a senator, then the number two preference will be used, and if not that then our number three and so on.

You can choose to vote below the line or above the line. Both are preferential but there is a difference. If you vote above the line the party you support decides the order of preferences for the candidates within that party. Voters will be asked to number at least six boxes above the line.

However, if you vote “1” above the line, your vote will still be formal – but preferences will only be distributed to other candidates within that party group.

If you vote below the line, you decide which candidates you support in which order. If you vote below the line you will be asked to number at least 12 boxes, but your vote will still be formal even if you only number six.

How do senators get elected?

To get elected, a candidate needs to receive a quota.

The quota is calculated as the number of votes cast, divided by the number of candidates plus one, then one is added to that total.

Let’s say there are 1.3 million votes cast in one of the states. In a double dissolution, this number is divided by 13 (12 positions to be elected plus one). This equals 100,000. Adding one means the quota will be 100,001.

Out of 1.3 million votes, 12 candidates can receive 100,001 votes – and what is left over (99,988) isn’t a quota, and isn’t enough to be elected.

If we had a Senate result in which 12 candidates each received 100,001 votes, then all 12 would be elected. But that is very unlikely to happen. Some individual candidates (like Nick Xenophon) or parties (Liberal/National, Labor, Greens) get a lot more votes than one quota – and some get a lot fewer.

So, how does the count work?

All the first preferences are counted – those which have number one for each candidate (individuals below the line and the first named candidate of the parties above the line).

Any candidates who have reached the quota are declared elected. If they received more votes than the quota, they have what is termed a surplus. Because this is a preferential system, the surplus is then distributed to the number two of the elected candidates, but at a reduced value.

Suppose the candidate elected was called Brown (Liberal) and received a total of 250,000 votes. Of these, 225,000 were above the line and are deemed to preference the number two on the Liberal list – Smith. The other 25,000 votes, made below the line, preference a range of different candidates.

The quota was 100,001, so Brown’s surplus is total number of votes minus the quota. This is equal to 149,999. His preferences will be passed on at the value of 149,999 divided by 250,000, or 0.599. This figure, 0.599, is called a transfer value. Each of the 250,000 preferences will then be counted and passed on at the transfer value of 0.599 of a vote each.

This way, the preferences of all of those who voted one for Brown are used up equally. This will be enough to give a quota to Smith, who, in addition to the 500 votes he received below the line, will get 225,000 of Brown’s votes at the value of 0.599 – which is 134,775.

That gives Smith 139,775 – a quota. Smith also has a surplus, which is calculated and distributed in a similar way.

Once all of the candidates who had a quota after first preferences have been elected and their surpluses distributed, and the same has happened to any candidates who reached a quota as a result of the distribution of surpluses, the count will now proceed to exclusions. This is where the candidate who has the fewest votes will be excluded, and their second preference will now receive the full value of that vote.

Suppose, at this point, there were ten senators elected – five Liberals, four Labor and one from the Greens, and consequently 1,000,010 votes have been used.

The article was published at Election explainer: how does the Senate count work?