Quel d’Hondt!

Now that the dust is settling on Thursday’s election to Holyrood, I thought I’d have another go at comprehending the involutions and convolutions of the Scottish Parliament electoral system.  We have two votes.  The first is for a named constituency MSP.  There are 73 Scottish constituencies and members achieve seats by a first-past-the-post system (FPTP).  The second vote is for a political party (or conceivably for somebody standing as an independent).  This is the regional vote.  Scotland has eight regions, and seven MSPs are elected for each region, by a system of proportional representation known as the Additional Member System (AMS).  Therefore 56 additional members drawn from party lists make up the total of 129 seats.  The system is designed to ensure that people who backed a candidate who didn’t pass the post first still have a voice in Parliament.  A political party’s share of the vote is roughly represented by the number of seats the party gains.

It is when these two systems – FPTP and AMS – are linked, that it becomes convoluted.  In the d’Hondt system, seats are allocated to a given party by dividing the number of regional votes gained by the party by the number of seats already held by that party, plus one.  You allocate a seat to the party with the highest quotient and then reiterate the process until all the seats are filled.  Follow?  I had a look at the Glasgow results to see if it worked.  Serendipitously, if you work with percentages rather than absolute numbers, the quotients are not too messy.

The Glasgow region has eight constituencies.  In the constituency vote, the SNP picked up the lot.  In 1999, when the Scottish Parliament was reconvened, such a result would have been utterly unbelievable.  In the regional vote, the percentage vote was roughly: SNP 45%, Labour 24%, Conservative 12%, Greens 9%.  So by FPTP, the SNP have 8 seats, and the other parties, none.  Now apply d’Hondt.  Divide the percentages by the number of seats already won, plus one.

Step One:  SNP 5, Labour 24, Conservative 12, Greens 9.  You take the highest number: Labour 24.  You allocate Labour a seat.  Then you repeat the process.

Step Two:  SNP 5, Labour 12, Conservative 12, Greens 9.  Labour and Conservative each gain a seat.  (I’m probably fudging it a bit there because, using absolute numbers of votes, rather than rounded percentages, there wouldn’t have been a dead heat, but I think the end result would be the same.)

Step Three:  SNP 5, Labour 8, Conservative 6, Greens 9.  The Greens gain a seat.

Step Four:  SNP 5, Labour 8, Conservative 6, Greens 4.5.  Labour gain another seat.

Step Five:  SNP 5, Labour 6, Conservatives 6, Greens 4.5.  Another seat each to Labour and Conservative.  All the list seats are now occupied.

End result:  the allocation of regional seats is 4 to Labour, 2 to Conservative, and 1 to the Greens.

That is indeed how it panned out.

I asked a family member, who happens to be a statistician (it’s very handy to have a statistician in the family), what percentage of the electorate he reckoned would be conversant with the d’Hondt method.  He mused, “Academics, political pundits, nerdish anoraks… let’s be generous… 2.5%?”

It set me thinking; if the vast majority of the electorate are not familiar with the system by which their representatives are elected, is that a good thing?

In a Parliament of 129 seats, a party must win 65 seats in order to command an absolute majority.  The fact that the SNP won 69 seats in 2011 under this system, is extraordinary.  In 2016, the SNP won 63 seats.  But it is interesting to imagine what the new parliament would have looked like if it had comprised 73 MSPs all elected by first-past-the-post.  SNP – 59, Conservative – 7, Lib Dem – 4, Labour – 3.  The SNP would have occupied 81% of the chamber.

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