This is an attempt to work out how the election results would have looked in 2010 under the Regional Top-Up system for the East Midlands. There are 46 MPs in the East Midlands. Under Regional Top-Up, 36 of them would be Constituency MPs and 10 would be Regional MPs.

It is worth remembering that the smaller parties may not have stood in every seat, so their total vote is less than it would have been under Regional Top-Up. RTU allows parties to appear on every ballot in a region, even if there is no local candidate, as long as the party has candidates in at least 1/3 of the seats. Hence the electorate would have a much more even choice across every region.

This is how the East Midlands looked after the 2010 election:

The above table includes a column for how the number of MPs should look (roughly) under a directly proportional system. The Lib Dems are ten MPs short of what their vote deserves, while the Tories have 11 more MPs than they would under a pure PR system. UKIP and the BNP both had enough votes to justify an MP.

Assumptions

Let’s assume that, after the number of constituencies has been reduced in the East Midlands from 46 to 36, the MPs elected under FPTP are still returned in proportion to the 2010 result. That will give us 24 Conservative and 12 Labour MPs. The remaining 10 will be Regional MPs (RMPs).

Step 1: Add up the votes for each party

We have already done this at the top of this page; the table includes the total votes across the East Midlands for each of the major parties.

Step 2: Create Party Lists

If this were for real we would look at all of the candidates for each party across the East Midlands region, and list them in order of the percentage of the vote they received (grouped by party), removing those who were successfully elected. Each party should end up with a list of candidates in order of public popularity.

For example, the UKIP list would look like this (for the top five):

Step 3: Calculate the minimum percentage for an elected MP

Under a directly proportional system in the East Midlands, we can calculate the percentage of the vote needed to get an MP elected: 100%/46MPs = 2.17% per MP.

The Green Party, and every other party with a smaller fraction of the vote, is below the 2.17% minimum threshold for an MP in the East Midlands. We can now discount all of those parties from the following calculations.

Step 4: Assign the Regional seats

We use the d’Hondt system to distribute the 12 Regional MP seats. The maths gets a little awkward to follow here, so if you aren’t interested, skip to the last couple of lines of the table below to see how the seats are distributed proportionally.

Note that we use the number of seats won under FPTP as the starting number of seats for each party. This requires an initial step to convert the total votes into the equivalent tally as if the first 46 seats had been distributed under the d’Hondt formula. For example, the Conservatives’ 915,933 votes are divided by 1 + number of seats (24), giving 915,933/25 = 36,637.

The numbers in red indicate which party gains the seat. The number in brackets indicates the number of seats held at each stage of the calculation.

This gives us a result closer to the numbers under a direct Proportional Representation scheme. Both of the smaller parties were given the MPs that they deserved, and the Lib Dems recouped most of their missing seats.