Voting for Dummies: Part 2

I left a few points hanging in my previous post. One was that AMS, being a proportional system, makes tactical voting impossible. Tactical voting, under a first-past-the-post system, is where your preferred party is polling third, with the two despised enemies neck-and-neck at the top: you vote for the enemy you despise less, because at least it will keep out the other scum. But under AMS, where parties with even 4% of the vote get seats, voting for the less-despised enemy simply gives them a better chance of a seat, and reduces your own party’s chances of winning one.

Another complication is how we should properly refer to the two votes that you have under the AMS system, and I sidestepped this issue by calling one the ‘constituency’ vote (which is not controversial) and the other the ‘second vote’. However, even ‘second vote’ won’t do, because the ballot paper could well ask for your constituency vote in its right-hand column, and what I’ve called your ‘second vote’ in its left-hand column. This would make my terminology disastrously counter-intuitive. So a better term for the second vote is the ‘list vote’, because you cast your vote not for an individual member but for a party list.

But even ‘list vote’ isn’t the term used in official descriptions, and that’s because of a complication that I haven’t told you about. The complication is that list votes aren’t totalled and seats allocated for the country as a whole; instead the country is divided into 8 regions of 7 list seats each, and those 7 seats are allocated in proportion to the list-vote shares for that region only. Each constituency is also within a region, and it is the constituency seats for that region that are topped up. So the more widely used (but less informative) term for the list vote is the ‘regional vote’. The regional basis of the top-up also makes the election result hard to predict: you can’t just say, “X party has Y percent of the votes, so they’ll get Z seats,” because different parties can be stronger in different regions.

The third and almost last complication is both interesting and infuriating, and arises from two inherent constraints in the seat-allocation process. One is that to allocate seats in exact proportions, you would have to allow fractions – one-third each of 10 seats is 3.3333 seats per party – and that won’t do. The other is that if you avoid the fractional problem by not allocating all the seats – give the three parties 3 seats each and leave the 10th seat unallocated – that won’t do either.

The formula used to get round these problems is the d’Hondt formula, which operates like a bidding system, but with the bids rigged by the formula. In the first round, each party bids its full number of list-votes, and the party with the most list-votes wins the first seat; but for the next round, that party’s list-votes are divided by the number of seats it now has plus 1 – i.e. it’s now divided by 2 – so that party can only bid half its list-votes for the second seat, which will therefore go to a party whose list-votes are more than half those of the leader. And so it proceeds: at each round, what you can bid are your list-votes divided by the number of seats you now have plus one; algebraically

Q = V / (S + 1)

where Q is what you’re allowed to bid, V is your list-votes and S is the number of seats you currently have.

To take a simple example, if you’re the Big Party and I’m the Tiny Party, and there are 7 seats to be allocated, your bids round by round will be all of your list-votes, then 1/2 your list-votes, then 1/3 of your list-votes, then 1/4 of your list-votes, and so on, and as long as that fraction of your list-votes is more than the whole of my list-votes you’ll be allocated that seat. If my list-votes are more than 1/7 of yours, but not more than 1/6, I’ll get the last seat.

The immediate importance of d’Hondt is that you can’t convert votes into seats by simple arithmetic: if you want to know how many seats a party would get if it won a given percentage of the vote, you have to specify an assumed vote-share for each party and then run d’Hondt: anything else is mere guesswork. For a Holyrood election you have to do this for each of the 8 regions separately. You also have to specify, for each party, the number of constituency seats – d’Hondt sets the value of S in the first round to each party’s constituency seats. Running a d’Hondt calculation is an easy and mechanical task, but not all commentators do it. There’ll be a d’Hondt calculator on my website soon, and when it’s ready I’ll post the link here.

It’s the last complication of all, however, that’s the most interesting. The aim of the system is to arrive at a proportional parliament by adding to the constituency seats a top-dressing of list seats. But what if a party’s constituency seats already exceed its list-vote share? Supposing, for example, in a 100-seat parliament with 60 contituency seats and 40 list seats, the party vote-shares and constituency seats are as follows:



The Slobs are due 40 parliamentary seats, but they already have 50, and you can’t take those away; the Toads deserve 50 parliamentary seats, which are available, but then the Earwigs would get none, and they deserve 10 parliamentary seats. The problem is of course logically insoluble, because the terms of the system don’t allow it: AMS assumes that each party’s share of constituency seats will fall short of its list-vote share, giving room for a top-up.

I’ll deal in a later post with how d’Hondt resolves this conundrum – it’s a fair result in fact, but it has unexpected effects. And it will lead us, as some readers will already have guessed from the way my argument here is going, directly on to the Wings Over Scotland Devastating Electoral Initiative, which is looking as though it will play a crucial role in the 2021 election.

Voting for Dummies

Looking at blogs and Twitter, I see a disturbing lack of knowledge about how the Holyrood voting system works. Even the basic fact that you have two votes seems incomprehensible to some voters. Given that the next Holyrood election will be upon us in or before Spring 2021, and is likely to be crucial for independence, readers might welcome this short ‘Voting for Dummies’ guide.

1. You have two votes. One is called your ‘constituency’ vote, and elects the MSP for your constituency. It operates under the first-past-the-post system (FPTP). We’re all thoroughly familiar with that, so it needs no further comment.

2. Your second vote has various names – your ‘regional’ vote, your ‘list’ vote, your ‘second preference vote’ – but they’re all unsatisfactory, so for the moment let’s just call it ‘your second vote’.

3. Your two votes are votes for different things. With your constituency vote, you vote for a person, the person you want to represent you, albeit they have a party identifier attached to them. With your second vote, you vote for a party, and your ballot paper shows no candidates’ names (though it may show the name of the party leader).

4. Your second vote determines the make-up of the Parliament: in the final result, the number of seats each party has will match its share of the second vote. So if the shares of the second vote, across the whole country, were these:

SECOND-VOTE SHARES: SNP 49%, Con 24%, Lab 18%, Green 5%, LibDem 4%

then, in a 129-seat Parliament, each party would end up with the following numbers of seats:

SEATS TO MATCH VOTE-SHARE: SNP 63, Con 31, Lab 24, Green 6, LibDem 5.

This was indeed the result of the 2016 election.

5. Given that some seats are filled by the constituency vote – 73 of them out of the 129 – how does the system ensure that the final number of seats matches each party’s share of the vote? Simple: to each party’s constituency seats, it adds the number of second-vote seats that will bring that party’s total up to the required percentage. Of the 129 seats, 56 are distributed in this way. In 2016, the 73 constituency seats were:

CONSTITUENCY SEATS: SNP 59, Con 7, Lab 3, Green 0, LibDem 4,

So to bring the each party’s seats up to the required percentage, second-vote seats were allocated as follows:

ADDITIONAL SEATS: SNP 4, Con 24, Lab 21, Green 6, LibDem 1,

giving the ‘Seats to Match Vote-share’ shown above.

6. We needs actual bums to put on these seats – bums of Members of the Scottish Parliament – so where do they come from, given that the second vote is not for a person, but a party? The answer is that each party maintains a list of candidates who are called off to fill that party’s second-vote seats. So the Conservatives, for example, needed to have at least 24 candidates standing by, and Labour at least 21, to occupy those seats. The Members to whom these seats are allocated are sometimes called ‘list’ members.

7. A number of points need to be made before closing this short guide:

7a. The system as a whole is called the “additional member system”, or AMS, because it adds second-vote Members of the Scottish Parliament to the constituency Members.

7b. The final proportions of seats are based on the second vote, not the constituency vote or the total vote, because consitutency votes are notoriously prone to tactical voting. Your second vote answers the question, “Which party do you want to form the government?”

7c. Because the second vote allocates seats to lists of members, it’s often called the ‘list vote’. And because the country is in fact divided into regions for the allocation of second-vote seats – more on that in a later post – the second vote is often also called the ‘regional’ vote.

7d. Because second-vote seats are allocated proportionally, it’s not possible to vote tactically with your second vote.

I’ll take these points up in my next post, quite soon.