STV vs AMS: Fight!

I was debating online which of STV and AMS was more proportional, and I decided to see *how* far each was from proportional, taking the last Irish and Scottish elections as examples.

The method I took was to take each party, see what % of the vote* they got, see how many seats they got, see how many seats their % of the vote would translate to under a perfectly proportional system, calculate the absolute difference, sum those and then divide by 2 (to see how many seats you'd need to change to make the numbers match)**

For Ireland, using STV, this gives you a "distance" of 22 out of 174 seats. 13% away from being perfectly proportional.

For Scotland, using AMS this gives a distance of 21 out of 129 seats. Which is 16% away.

So if you value proportionality then *for those two examples* STV was more proportional than AMS.

You could, of course, make either of them more proportional - in the Irish elections the constitutencies were only 3-5 members in size, in the Scottish elections only 56 of the 129 MSPs are elected proportionately, and those in 8 regions.

Increasing the size of the Irish constituencies, the number of MSPs elected from list votes, or reducing the number of Scottish regions would all make things more proportional***.

Of course, proportionality isn't everything. And neither of these systems is perfect. Both are massively better than FPTP**** though.

* List votes in Scotland, First preferences in Ireland.
** If you're up 1 seat of party A and down 1 seat of party B then you need to change 1 seat from A to B to make things match.
*** I strongly suspect that AV+, where the constituency seat is elected through AV and then topped up with list votes, would make the AMS more proportional. But I'd want to check that.
**** Using FPTP and the UK elections in 2024, we get a difference of 191 seats out of 650. Or 29% away.