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In a Holyrood election you have two votes, the constituency vote and the list vote. The make-up of the Parliament is determined entirely by the list vote. If the parties have the following shares of the list vote, then they will have these percentages of Parliamentary seats:

  • Con Lab SNP LibDem Green

List-vote share 24% 26% 43% 2% 5% % of Parliamentary seats 24 26 43 2 5

So the list vote is the electorate's answer to the question, "All conflicting considerations set aside, which party would you like to form the Government?"

The electoral system realises the electorate's wishes by topping up constituency seats with list seats. So if the list-vote percentages and constituency seats (in a notional 100-seat parliament with 55 constituency seats and 45 list seats) are as below, the top-up will be:

  • Con Lab SNP LibDem Green Total

List-vote share 24% 26% 44% 2% 4% 100% Parliamentary seats due 24 26 44 2 4 100 Constituency seats won 6 8 40 0 1 55 Top-up 18 18 4 2 3 45 Parliamentary seats 24 26 44 2 4 100

The top-up in this case brings large numbers of seats to Con and Lab, but almost none to SNP, because that's what the list-vote shares dictate. The list-vote share is king.

This means that "splitting the list vote" loses no seats, because the split party will still get its original combined share:

  • Con Lab LabSplit SNP LibDem Green Total

List-vote share 24% 13% 13% 44% 2% 4% 100% Parliamentary seats due 24 13 13 44 2 4 100 Constituency seats won 6 8 0 40 0 1 55 Top-up 18 5 13 4 2 3 45 Parliamentary seats 24 13 13 44 2 4 100

Two factors modify this transparent and practical arrangement. One is that, for Holyrood election purposes, Scotland is divided into eight regions; the other is that, for reasons of arithmetic practicality, the method used to allocate seats to parties according to their list-vote share (the D'Hondt method) gives results that can't be predicted by simple arithmetic, and are not fully proportional.

The eight Scottish regions are Central Scotland, Glasgow, Highland and Islands, Lothian, Mid Scotland and Fife, North East Scotland, South Scotland and West Scotland. Each has 8, 9 or 10 constituency seats (the constituencies lie wholly within regions) and exactly seven list seats. The ballot is evaluated exclusively within each region: the list-vote share that applies is the list-vote share within that region, the constituency seats that are counted are the constituency seats within that region, and the list seats that are allocated to the parties are the list seats within that region. It follows that the ballot within one region has no effect on any other region. Readers should therefore treat with extreme circumspection any commentators' remarks on voting patterns, polling patterns or predicted outcomes that don't include a regional differentiation, and most don't.

Any method of allocating list seats to parties faces three arithmetic impossibilities:

- If a party already has more constituency seats than its list-vote share allows, those seats can't be taken away. (This happened to the SNP in a number of regions in 2016.) The pool of list-vote share seats available to other parties is therefore commensurately reduced, so they don't get their full quota.

- Seats can't be divided. If there are ten seats to be allocated, and three parties with equal vote-shares, the tenth seat can't be split three ways.

- All seats must be allocated: we can't just throw the tenth seat out of the window.

The D'Hondt method solves these problems by implementing a bidding system - an auction, but one where the bids are rigged in advance. Details are given here. You cannot evaluate any election predictions without a D'Hondt calculator.

Wikiscot has commissioned its own D'Hondt calculator from Derek Rogers, which can be found on the VoteHelp website here. It's free of charge, always available, no ads, no sign-in, no cookies, and lets you enter your own data to see what outcome it will produce. It also includes full data from the 2016 Holyrood election, for you to play with.

We ran four analyses, using that D'Hondt calculator:

- the 2016 election data, but adding the Alba party in each region, and giving it, in each region, 6 percent of the total vote. This 6 percent was taken from the SNP's vote. The two independence parties between them took an extra seat in four regions; nowhere did they take fewer seats. So the split gained the independence parties four seats.

- as above, but giving Alba 10 percent of the total vote. This gave the independence parties 6 more seats, with no losses.

- the 2016 election data for the South Scotland region, but splitting the SNP vote with Alba at levels ranging from 50-50 down to 90-10 (Alba gets 10 percent of the SNP vote). This region was chosen because it was the one where the SNP had its worst performance. The result was unchanged at every level of split.

- as above, but for the Glasgow region, where the SNP performed best. With a 50-50 split, the independence parties gained two seats; at 90-10, the result was unchanged.

These four sets of results are on the VoteHelp website.