In the leadup to the 2019 Federal Election there was quite a bit of talk of strategic voting. At the time I wanted to write about it but was a bit busy, now that I do have time it’s no longer of much interest but at least I’ll have it here ready for when it does come around again.
Since it was mostly discussed in terms of supporting conservative independents to defeat Liberals then I will use this situation to give concrete examples, however the same principles can apply in any appropriate circumstances regardless of the parties involved.

Strategic Voting To Change The Winner

In elections the House of Representatives in Australian Parliament we have full preferential voting, meaning that to vote you give a preference for every single candidate. In general, the best way of doing this is to simply order all of the candidates in the order in which you prefer them, and then your vote will count as best as possible in supporting your intentions. There are some complications to all systems though, and it turns out that it is possible that in certain circumstances you can gain a better outcome through ordering your preferences differently.

Here is an example, suppose there are three candidates, A,B and C, and your preference is in the order A,B,C. So A is your favourite candidate, but if it came down to B vs C, you’d prefer B.
Now suppose there are 17 voters and the ballots are as follows:
8 A > B > C
4 B > C > A
5 C > A > B

Nobody has a majority of 9, so B is eliminated, all their voters put C next so the final result is C 9 – A 8, a win for C.
Now let’s say you and one other voter change your votes from A > B > C to B > A >C. The ballots are now
6 A > B > C
2 B > A > C
4 B > C > A
5 C > A > B
Now C has the smallest number of first preferences and gets eliminated with all of their votes going to A, giving A 11 to B 6.
So not only have the A voters helped A to win by voting for B, but their votes never even end up counting for A.

If you want a real life example, imagine a Liberal held electorate with a strong challenge from an independent. There is potential that the Independent will get more first preferences than Labor and then get all of the Labor preferences allowing them to win, but if some Liberal voters change their number 1 vote to Labor, there is a chance the Labor candidates will not be overtaken so the independent is eliminated and the preferences of their voters keep the Liberal ahead.

This took a very special set of circumstances that is unlikely to arise in a real election, and you have to be really sure of how everyone is voting otherwise it will just go wrong.
For example, say our two A voters try this tactic in the situation where, before they change the votes would be

8 A > B >C
7 B >C > A
2 C >A >B
Then A wins on preferences from C, but if they change their vote then B wins.
In our specific situation, suppose lots of Liberal voters decide to vote Labor for strategic reason – then they might just help Labor to win directly – a result they most likely think even worse than the Liberal losing to the Independent. This can happen if they, say, overestimate the popularity of the Independent, or else if just too many Liberal voters try to vote strategically. So you need a very good idea of how the primary votes will go, how the preferences will go and how many voters will vote strategically.
So strategic voting is a dangerous business.

Given the very specific circumstances needed, and that most of the time it will backfire, this sort of strategic voting just isn’t worthwhile.

Strategic Voting to Change the Loser

It turns out that if you’re more interested in who loses than who wins then there are scenarios where strategic voting makes more sense. Suppose again that there are three candidates, A, B and C and your preference is A > B > C, however your primary goal is for “anyone but C” to win.

Take the votes to be the following
8 C > B >A
4 B > C > A
5 A > B > C

In this case, C wins on preferences after B is eliminated. Suppose instead that you change your vote from A>B>C to B>A>C, then we have

8 C > B >A
4 B > C > A
1 B > A > C
4 A > B > C

Now A is eliminated first and B wins on preferences.
The main point that makes this in some way safer than the previous example is that while you are changing your vote away from your favourite candidate, you are at least changing it to another candidate who you can accept as winner, meaning that it can’t really backfire in the same way as if your strategy requires you to change to vote for the one you like least.

A concrete example is the scenario from the Wentworth by-election in 2018. The main candidates were Liberal, who were likely to get the most primary votes, and Independent and Labor. Normally the Liberals would get a high primary vote, and they are unlikely to lose many votes to Labor, so the only chance of them losing is for Liberal voters to switch to independent. This means that in any scenario that sees the Liberals not win on primary then it is likely that the Independent has lots of votes that will have Liberals preferenced over Labor. The fact that the Independent was recommending Liberal preferences on How To Vote cards made this more certain. As a result, if the Independent got eliminated before Labor, their preferences would help the Liberals win, but if Labor get eliminated first, there was a chance their preferences would help the Independent to win – and this is exactly what happened. So for erstwhile Labor voters who wanted the Liberals to lose, a strategic vote for the Independent was a sensible strategy which carried no risk.

Can it go wrong?

We’ve already seen that strategic voting to change the winner can go very wrong, but strategic voting to change the loser is less risky. This is because you are changing your vote from your favourite candidate to someone else who you are also happy to see winning.
There are nevertherless a couple of things that can go wrong. Firstly, if you are wrong about the distribution of preferences you can get the wrong outcome. Secondly there are some potential longer term effects which I think means that this sort of strategic voting should be used sparingly – only when you are certain it will achieve something.

If you are wrong about preferences

Suppose you guess that the situation is the one described above, your true preference is A > B > C, but you really want C to lose and you fear that B voters will give them preferences if they get eliminated so you change your vote to B>A>C.

Now it turns out that the votes are

8 C > B >A
5 B > A > C
1 A > C > B
3 A > B > C

Now C will win when A is eliminated, but if you voted A they could have won.
This scenario is not terribly likely however since you have to be quite spectacularly wrong in your prediction of the preferences of B voters.

The following is a more likely danger, suppose after changing your vote from A to B it looks like this:
6 C > B >A
2 B > C >A
4 B > A >C
5 A > B > C

In this scenario by changing your vote from A to B, you help B beat C which is what you wanted, but since C is less popular than you thought, and the preferences of B aren’t quite as one-sided towards C, it turns out that either A or B can beat C and if you had left your vote with A then it would be

6 C > B >A
2 B > C >A
3 B > A >C
6 A > B > C

and your first preference A would win. So by voting strategically, you missed out on a chance for your favoured party to win.

What is needed for it to work

So for it to work you need the following:

• You are sure that the candidate you want to lose will be the most popular and will most likely fail to win on primaries
• There are (at least) two other candidates who could reasonably be expected to end up finishing in the last two spots.
• You have good reason to believe that one of the those candidates will receive lots of votes which will then preference the candidate you want to lose.

When it isn’t worthwhile

If the lead candidate is virtually certain to win or get very close to 50% on first preferences, or if there is only one realistic candidate to finish second then it just isn’t worth it. These scenarios don’t carry the sort of risks discussed above. If the lead candidate wins on primaries (or is so close that there will always be enough preferences from eliminated candidates to get them over) then it doesn’t matter what you do, you can’t stop them winning.

For example, you vote A>B>C:

9 C > B> A
4 A > B > C
4 B > C > A

There’s nothing you can do here!

On the other hand if there is no question of who is lasting to the final count then your vote may still stop them winning but in this case the order of elimination doesn’t come into it – whether you change your vote or not it will end up with the candidate who is up against the one you don’t want to win, nothing is gained by strategic voting.
For example, again you vote A>B>C:

8 C > B >A
6 B > C >A
3 A > B >C
here your vote is always going to end up with B against C since A is being eliminated first. It turns out that it then helps B beat C.
Another example is
8 C > B >A
6 B > C >A
2 A > B >C
1 A > C > B
here once again your vote is always going to end up with B against C but in this case C wins. No strategy can stop it.

So if these instances don’t risk giving a worse outcome then what is the problem? The main problem is that number 1 votes matter. They matter because parties get funding based on how many number 1 votes they get. They matter because first preferences are shown prominently in the count and the winner may take notice of where the preferences come from. They also matter because a lot of voters won’t support someone until they think they have a good chance of winning, so by not voting for your favourite party who may not be likely to win this time, you might be holding them back from ever winning (especially since you are also depriving them of funding).
More generally you could have a situation where the perception that an electorate can only ever be won by a conservative candidate can be turn out to be self-fulfilling as progressive voters support conservative independents in order to beat the Liberals or Nationals. Consider examples like Ballina in the NSW parliament, which the Greens won from the Nationals, or the last Victorian state election where Labor picked up seats previously seen as safe Liberal seats. Campaigns to promote strategic voting could keep such electorates in the hands of conservative independents who would support the Liberals in forming Government.