AMS with Second Mandates

[xenon]

Aug 6, 2022 14:47:40 GMT Pete Whitehead said:

I mean where the second mandates come from in a sense doesn't matter if one regards them purely as regional members rather than constituency member as I believe should be the case (and the Richmond situation illustrates that starkly, although I'm slightly confused why Labour wouldn't win second mandates in eg. Newham or Hackney before winning one there?)

If my understanding of the BaWü rules is correct, a party can only pick up second mandates in seats it has already won if it has a mandate in every other constituency in the region, i.e. it is entitled to over half of the total seats. As for your other question, the only other place where I've noticed this is in Hull East, where Labour lose out on a seat of either sort when combined with Beverley and Holderness.

[xenon]

Aug 6, 2022 14:45:06 GMT Pete Whitehead said:

Aug 6, 2022 14:30:29 GMT xenon said:

I've scanend therough your other maps and I think this is the only case where a constituency elected an MP from a party in RL but didn't win even a second mandate in this system (aprt from Brighton Pavilion, and that is only because of the regional threshold). It is certainly counterintuitve that the cities find themselves in this situation but I suppose a consequence of a low electorate in that seat and a low turnout and low winning share, in contrast with Holborn & St Pancras on all counts (plus I suppose the oddity of the area producing one of the better Lib Dem results, although they polled fewer votes than the Conservatives.)
The solution to the 'problem' would be to keep the two Westminster seats and the two Camden seats together. Have Finchley & Chipping Barnet, Hendon & Brent North, Brent Central & Hammersmith, Chelsea & Fulham & Kensington.
N ot all of those are ideal but inevitably there are lots of sub-optimal pairings in this scheme.
I also wonder about the possibilities of including Spelthorne within the Greater London plan rather than Epsom & Ewll, though it wouldn't make any difference to the central London seats

I started the process with West London, and I figured that the only way to make Westminster and surrounds less awful was to merge Twickenham with a Hounslow seat so that Ealing Central could be paired with Hammersmith. However this would make South of the Thames an odd number which is obviously more problematic – I hadn't considered splitting Brent and Barnet, but my knowledge of London electoral geography is rather patchy (and England in general – I've struggled with everything south of Hadrian's Wall!).

As for which Surrey seat to add, I only chose Epsom as it fitted nicely with the oddly shaped "Kingston Pennisula", and IIRC was meant to be included in Kingston Borough when the boundaries were drawn up in the 60s anyway. Spelthorne could work equally as well (or badly, as I imagine many Surrey residents would see it), although it doesn't have a natural partner as such – it shares a longer border with Feltham and Heston, but is politically more similar to Twickenham.

[xenon]

Time for the penultimate region now as we turn to the East of England, with its even 58 seats making this the only region in England which stays completely intact (ironically enough seeing as it is possibly the least cohesive of the lot!) The Tories have their strongest showing by vote share here, picking up a hefty 57% share which entitles them to nine top-up seats to complement their near clean-sweep of the constituencies. Labour are second and are the only other party to benefit from first mandates, while the Lib Dems don't retain their currently sole seat of St Albans after mergers, but get a healthy boost to their seat tally through second mandates. Without that pesky threshold the Greens would have picked up a solitary seat in West Suffolk and Bury St Edmunds. There were four each of single-seaters and three-seaters, with the remaining 21 constituencies being two-seaters. The results were:

Con: 36 (-16 vs FPTP), comprising 27 first mandates and 9 second mandates
Lab: 14 (+9 vs FPTP), comprising 2 first mandates and 14 second mandates
LD: 8 (+7 vs FPTP), all second mandates.

[xenon]

And finally, the last region in this project - Northern Ireland. Fortuitously the province has an even number of seats (18), lest we be forced to cross the Irish Sea and create "Antrim East and Galloway" or some similarly horrible seat. The two issues of more parties and fewer seats to fill means that we get some strange results here, with the southernmost six constituencies all having multiple members, while the northernmost three with their more decisive partisan makeup have to settle for one apiece. The DUP take the most seats as in real life with Sinn Fein in second, although both take a hit to their seat tally. Interestingly Sinn Fein also become the only party to exclusively win constituency seats. The Alliance Party's third place finish by votes is now reflected by seats sharing that position with the SDLP, while the UUP make it back into Westminster with a couple of second mandates. Three seats had three members each, another three had two members each, and a further three had one members each. The results were:

DUP: 6 (-2 vs FPTP), comprising 4 first mandates and 2 second mandates
SF: 4 (-3 vs FPTP), all first mandates
APNI: 3 (+2 vs FPTP), all second mandates
SDLP: 3 (+1 vs FPTP), comprising 1 first mandate and 2 second mandates
UUP: 2 (+2 vs FPTP), all second mandates

[finsobruce]

Aug 10, 2022 11:42:24 GMT xenon said:

And finally, the last region in this project - Northern Ireland. Fortuitously the province has an even number of seats (18), lest we be forced to cross the Irish Sea and create "Antrim East and Galloway" or some similarly horrible seat. The two issues of more parties and fewer seats to fill means that we get some strange results here, with the southernmost six constituencies all having multiple members, while the northernmost three with their more decisive partisan makeup have to settle for one apiece. The DUP take the most seats as in real life with Sinn Fein in second, although both take a hit to their seat tally. Interestingly Sinn Fein also become the only party to exclusively win constituency seats. The Alliance Party's third place finish by votes is now reflected by seats sharing that position with the SDLP, while the UUP make it back into Westminster with a couple of second mandates. Three seats had three members each, another three had two members each, and a further three had one members each. The results were:

DUP: 6 (-2 vs FPTP), comprising 4 first mandates and 2 second mandates
SF: 4 (-3 vs FPTP), all first mandates
APNI: 3 (+2 vs FPTP), all second mandates
SDLP: 3 (+1 vs FPTP), comprising 1 first mandate and 2 second mandates
UUP: 2 (+2 vs FPTP), all second mandates

A seat that crosses the Irish sea. Now that would be 'lively'.

[bjornhattan]

Aug 10, 2022 13:18:30 GMT finsobruce said:

Aug 10, 2022 11:42:24 GMT xenon said:

And finally, the last region in this project - Northern Ireland. Fortuitously the province has an even number of seats (18), lest we be forced to cross the Irish Sea and create "Antrim East and Galloway" or some similarly horrible seat. The two issues of more parties and fewer seats to fill means that we get some strange results here, with the southernmost six constituencies all having multiple members, while the northernmost three with their more decisive partisan makeup have to settle for one apiece. The DUP take the most seats as in real life with Sinn Fein in second, although both take a hit to their seat tally. Interestingly Sinn Fein also become the only party to exclusively win constituency seats. The Alliance Party's third place finish by votes is now reflected by seats sharing that position with the SDLP, while the UUP make it back into Westminster with a couple of second mandates. Three seats had three members each, another three had two members each, and a further three had one members each. The results were:

DUP: 6 (-2 vs FPTP), comprising 4 first mandates and 2 second mandates
SF: 4 (-3 vs FPTP), all first mandates
APNI: 3 (+2 vs FPTP), all second mandates
SDLP: 3 (+1 vs FPTP), comprising 1 first mandate and 2 second mandates
UUP: 2 (+2 vs FPTP), all second mandates

A seat that crosses the Irish sea. Now that would be 'lively'.

And it would have been even livelier back in the 2001 - where five parties would have been separated by perhaps 2,000 votes at most...

[greenchristian]

So how do the final national figures compare with the actual FPTP result, regular AMS (let's go with the same constituency seats, and regional lists for the same regions), and the national voteshare?

[🏴‍☠️ Neath West 🏴‍☠️]

Aug 10, 2022 11:42:24 GMT xenon said:

And finally, the last region in this project - Northern Ireland. Fortuitously the province has an even number of seats (18), lest we be forced to cross the Irish Sea and create "Antrim East and Galloway" or some similarly horrible seat. The two issues of more parties and fewer seats to fill means that we get some strange results here, with the southernmost six constituencies all having multiple members, while the northernmost three with their more decisive partisan makeup have to settle for one apiece. The DUP take the most seats as in real life with Sinn Fein in second, although both take a hit to their seat tally. Interestingly Sinn Fein also become the only party to exclusively win constituency seats. The Alliance Party's third place finish by votes is now reflected by seats sharing that position with the SDLP, while the UUP make it back into Westminster with a couple of second mandates. Three seats had three members each, another three had two members each, and a further three had one members each. The results were:

DUP: 6 (-2 vs FPTP), comprising 4 first mandates and 2 second mandates
SF: 4 (-3 vs FPTP), all first mandates
APNI: 3 (+2 vs FPTP), all second mandates
SDLP: 3 (+1 vs FPTP), comprising 1 first mandate and 2 second mandates
UUP: 2 (+2 vs FPTP), all second mandates

Not keen on those pairings. I'd start with Armagh + Upper Bann and work round from there.

[xenon]

Now for a quick summary of the UK-wide picture, and how the results would have affected government formation.

Region	Con	Lab	LD	Brex	SNP	PC
Scotland	15	11	5	0	28	0
North West	31	39	6	0	0	0
North East	10	12	2	2	0	0
Yorkshire	25	22	4	3	0	0
East Midlands	28	16	4	0	0	0
West Midlands	35	21	4	0	0	0
Wales	15	17	2	2	0	4
South West	31	13	10	0	0	0
South East	48	19	16	0	0	0
London	26	37	11	0	0	0
East	36	14	8	0	0	0
Total (GB)	300	221	72	7	28	4

Con: 300 seats (-65 vs FPTP), comprising 191 first and 109 second mandates in 11 regions
Lab: 221 seats (+19 vs FPTP), comprising 98 first and 123 second mandates in 11 regions
LD: 72 seats (+61 vs FPTP), comprising 2 first and 70 second mandates in 11 regions
SNP: 28 seats (-20 vs FPTP), comprising 26 first and 2 second mandates in 1 region
Brex: 7 seats (+7 vs FPTP), all second mandates in 3 regions
DUP: 6 seats (-2 vs FPTP), comprising 4 first and 2 second mandates in 1 region
SF: 4 seats (-3 vs FPTP), all first mandates in 1 region
PC: 4 seats (= vs FPTP), comprising 2 first and 2 second mandates in 1 region
APNI: 3 seats (+2 vs FPTP), all second mandates in 1 region
SDLP: 3 seats (+1 vs FPTP), comprising 1 first and 2 second mandates in 1 region
UUP: 2 seats (+2 vs FPTP), all second mandates in 1 region

Grn: 0 seats (-1 vs FPTP)
Spkr: 0 seats (-1 vs FPTP)

So this leaves the Conservatives comfortably the largest party, but 26 seats short of an overall majority. Their closest shot would be cobbling together a right-of-centre coalition, but Con 300 + Brex 7 + DUP 6 + UUP 2 still only gives a total of 315 seats (assuming the Lib Dems wouldn't co-operate because of Brexit, but of course policy and voting patterns would be very different under PR, and depending on when it had been introduced Brexit - or the Lib Dems for that matter - might not have happened at all).

This suggests that the left-of-centre parties would be calling the shots - but would any potential partnership have a majority? The option with the fewest parties would be Lab 221 + LD 72 + SNP 28 + PC 4 for a very unstable 325 seat total, possibly bumped up to 331 by SDLP and Alliance. More likely would be a Lab-LD minority coalition, with confidence and supply from some or all of the smaller parties.

The Gallagher Index was 2.70 across all parties that won seats or received over 1% of the vote nationwide, compared to 11.64 under FPTP. 

I found this little project quite fun, so when I have a chance I'll have a go of previous general elections, which should be faster as I already have a spreadsheet which automatically combines the votes for each pair of seats, so it is only a case of pasting in the data and altering the map accordingly.

[xenon]

Thought I'd resurrect this thread with a bit of a different twist on my "second mandates" system.

I recently came across "Dual Member Proportional", which is a form of MMP proposed for use in various Canadian provinces where each constituency sends two MPs - one elected by FPTP, and a second allocated to achieve proportionality across the region, trying as far as possible to award the second seats to the parties in their strongest areas. This fixes the main flaw with the Baden-Wurttemberg version, where some seats in effect send three or even four MPs, and others have just one (even though the top-up MPs theoretically represent a larger region).

Similarly to Ba-Wu each candidate nominates a substitute, but if the primary candidate wins the first mandate their votes are transferred to the second candidate at 50% of their value. This gives second candidate a greater chance of success, and it makes sense that a party should win two seats in a constituency where it has an overwhelming majority before a single seat in a constituency where it barely scraped 10%. The original paper detailing the system is here in case anyone wants to read further. 

Despite these benefits, DMP is a good deal more complex than any existing form of AMS, especially in allocating the top-up seats where two parties are eligible for the same seat, as well as having a mechanism which allows a certain proportion of a party's seats to be allocated via a list (so the "top candidates" are less likely to lose out). I have therefore modified it to remove some of this complexity.

In my version, top-up seats are assigned to parties using the d'Hondt system as normal for AMS, and the first party to win a top-up seat will have its "best runner-up" elected (that is to say the candidate who won the highest share of the vote for that party but was not elected). The winner of the second top-up seat will then elect their "best runner-up", and so on until all seats are filled. If at any stage a party's next "best runner-up" stood in a constituency which has already had its second seat allocated, the next available candidate will be chosen instead so that all constituencies end up with only two MPs.

I have tested this out by modelling how elections to a devolved Scottish Assembly could have looked like if the 1979 referendum had succeeded, based on general election results. The plans back then allocated between 2 and 3 Assembly members to each Westminster constituency, but I have simply allocated two seats to each for a total of 142. I'll post maps of the first three elections (1979, 1983 and 1987) below.

[xenon]

This is the map of First Mandates in 1979: Link


and the map of Second Mandates: Link


The SNP are the main beneficiaries of the increased proportionality, winning 22 second mandates in addition to their 2 constituencies. The Liberals have 3 first mandates to 10 second mandates, and the Conservatives are almost even with 22 first mandates to 23 second mandates. Labour are obviously still the main winner in the constituencies, with 44 first mandates and 16 second mandates.

The totals were therefore:
Labour - 60
Conservative - 45
SNP - 24
Liberal - 13

Interestingly a lot of Labour's second mandates came in their Glasgow strongholds - since their top-up seats are allocated towards the end of the d'Hondt process after the imbalance with the smaller parties has been addressed, most of the second mandates in seats where they finished as runners up have already been allocated. This leaves them with seats where they remain the largest party even once their vote share has been halved. Similarly there are a few SNP and Liberal "double mandates" due to their concentrated areas of support.

In so far as creating a governing majority in our imaginary Scottish Assembly is concerned, a Lib-Lab coalition would be the only sensible option, albeit with a slim majority of 4 seats.