What is The Supplementary Vote and What's Wrong with it?

The supplementary vote is a form of the contingent vote invented by Labour peer Raymond Plant, the contingent vote is a more limited form of Instant run-off voting. 

 

Instant Run-off Voting allows people to rank all candidates in order or preference, if no candidate gets 50% of the vote, the candidate(s)for whom it’s mathematically impossible for them to win are eliminated, their votes are redistributed until either someone gets over 50% of votes or only one candidate is left.

Admittedly, in most elections the top 2 stay the same right until the end, it’s rare for a 3^rd place candidate to leap frog the person in second and then go on to win.
However, it does make sense and is fair if someone initially in 3^rd then goes on to win, so this to me is the best system.

The Contingent Vote on the other hand still allows the voter to rank as many or as few candidates just as in IRV, however in this case only the top two with the most votes goes onto the final round, no matter what the initial result.
All votes from eliminated candidates go to whichever of the remaining two the rest ranked highest.
If out of the remaining two, you had ranked one of them 3^rd and the other 5^th your vote would then go to the candidate you ranked 3^rd.
This is fair because, if your first and second choice had not run in the election, that 3^rd choice would have been your 1^st. Since they can't win, you run the election as if they hadn't run.

The supplementary vote takes this another step further and throws a giant turd at voters by only allowing them to rank a first and a second choice.

Why is this so bad?

It’s difficult to understand why this system was introduced. The thinking behind this might have been that voters would rank their genuine first and second preferences at the ballot box, and many do.
The problem with that contention is to actually vote like that is beyond pointless.

As you can only rank two candidates you have to second guess who will be in the top-two places to have effectively cast a ballot in the second round.

In other words...

Instant run-off voting is meant to simulate having multiple rounds of run-off election in order to find a winner. This would be how Conservative leadership elections take place.

The contingent vote is the equivalent of a simple two-round system where, no matter what the result of the first round, only the top 2 candidates go on to the final run-off.

The supplementary vote is the equivalent to having a two-round system, except the voters are not told in the second round who has been eliminated in the first round and they have to guess who has finished in the top 2 or their vote won’t even get counted. 

That’s right, it won’t even be counted.
Unlike under FPtP, where you can vote for a no hope candidate and it will at least show up that they got some support.
Under SV if you don’t think your first preference vote will be for one of the candidates likely to finish in the top two and you genuinely don’t have any preference for any of the likely top two finishers, you might be tempted to cast your second vote for an outsider you do like, just so they can see they got quite a lot of second preference votes.

No, second preference votes not for the top two finishers are not even counted, you might as well be flushing you ballot down the toilet.
In Bristol in 2016 two thirds of votes not the top two candidates did not transfer to candidates in the second round, even though it was clear before the election who the top two would be.
This could in some-ways be seen as voter suppression of the people who lack the understanding of how bad the system is.

If the idea was people would express a genuine first and second preference it utterly fails. Because you have to rank someone likely to finish in the top two in order to have a vote even be counted, the system really makes no sense and it's no surprise it was invented in someone not well versed in electoral theory.