A General Election was held in the UK on 4th July 2024 under the First Past the Post system (FPTP). The analysis below is based on data from the House of Commons Library.

For the purposes of this illustration, the speaker’s seat (Labour) is ignored. By convention other parties do not stand against that of the speaker (although in 2034, the Green party and three other small parties did). This skews the voting allocation of the elected parties. It would be better if the speaker’s seat were treated as a normal contest with the votes won being assigned to the party TVs.  This means that voters in the speaker’s constituency would be treated in exactly the same way as other voters.

Under FPTP thirteen parties and six independent candidates were elected to 649 constituencies. Labour won 411 seats (63.33% of the 649). The total elected vote (TV) for the thirteen parties was 27,768,251 of which Labour had 9,708,716. This is 34.96% of the TV and, under PREVAIL, gives Labour a quota of 225 seats - considerably less than the 411 obtained under FPTP.

The table below shows FPTP results for the 643 party seats and the quotas under PREVAIL.

Of the main national parties only Labour is over quota with 411 FPTP seats against a quota of 225. It therefore has 411-225 = 186 seats below the quota cut. These are the seats that PREVAIL will, initially, seek to transfer. The Democratic Unionist party with five FPTP seats is one over quota and Sinn Fein with seven FPTP seats is two over quota.

Two parties are on quota and eight are under quota. Of the latter, the Reform UK and Green Parties are the most significantly under quota.  

The number of seats needing to be transferred from the three over quota parties to achieve perfect proportionality is 186 +2 + 1 = 189. The measure of disproportionality for FPTP is thus 100*189/649 = 29.12.  

Percentage votes for the first party range from 70.57% down to 26.72%. There are 73 seats where the first vote exceeds 50%: Labour has 70 and Sinn Fein has 3. Percentage votes for the second party range from 42.73% down to 10.49% . Percentage votes for the third party range from 27.58% down to 4.49%. Percentage votes for the fourth party range from 19.52% down to 2.52%.

The table below gives an indication of the possibilities for transfer to under quota parties.

 The Conservative party with 133 second vote seats below the quota cut and needing only 37 to increase its FPTP of 121 to 158 can reach its quota from these seats alone. The same is true for the Scottish Nationals who need 8 seats from 9 available and for Plaid Cymru who need 1 seat from 3 available.

The remaining five under quota parties do not have sufficient second vote options below the quota cut to reach their quotas and must rely on third vote seats below the quota cut and then on second and finally third vote seats above the quota cut.  It should be noted that it is not immediately clear from the table which third vote seats will lead to transfers as this depends on the availability of stage 3 compensatory transfers.

Liberal Democrats require 9 transfers to bring their 71 FPTP seats up to their quota of 81 but with only 5 seconds and thirds in total this will not be possible.

Reform UK who need 90 seats to increase their 5 FPTP seats to achieve their quota of 95 can only gain 17 from second seat transfers below the quota cut. They do, however, have substantial third vote seats beneath the quota cut and further possibilities above the cut. 

The Green Party is in the weakest position of all. It needs to raise its 4 FPTP seats by 41 to reach its quota of 45 but with a total of only 11 second vote seats (10 of which are above the quota cut) and no third vote seats this will not be possible and it will fall very short of its quota, 

The Ulster Unionist and Alliance NI parties have no second or third vote seats below the cut and must rely on seats above the cut if they are to reach their quotas.

The transfers

The transfer protocol for PREVAIL was:

• Above quota: yes
• Upper threshold : 50%
• Lower threshold: 20%, unless first vote was less than 25% in which case 0%
• Preference criterion: least first vote

Applying PREVAIL with this protocol resulted in 146 transfers as shown in the table below. Five parties of the eight were brought up to quota. An asterisk against a party's name indicates that it was brought up to quota.

The 37 stage 1 transfers below the cut to the Conservative party include 16 compensatory transfers for the 16 stage 3 transfers. In all, of the 146 transfers made, 111 were below the quota cut and 35 above.

The table below shows the final seat allocation under PREVAIL in comparison to FPTP.

Statistics for the percentage votes of the winning candidates under FPTP and PREVAIL for all 649 seats, i.e. including independent seats, are shown below. Statistics for transferred seats only are also shown.

PREVAIL has succeeded in bringing five of the eight under quota parties up to quota and two close to quota. Only the Green Party has not fared well. Although it had a substantial vote across the country, the Green Party did not accumulate sufficient votes in come second or third in enough constituencies to gain transferred seats. Ironically, of the ten second vote seats above the quota cut, eight were above the 50% upper threshold and therefore not transferrable with the protocol used. 

Of the three over quota parties, Labour remains over quota by 42 seats and Sinn Fein by 1 seat; these 43 seats would need to be transferred to produce perfect proportionality.  The Democratic Unionist party is brought down to quota. The measure of disproportionality is 100*43/649 = 6.63. 

Under PREVAIL, Labour with 267 seats (compared to 411 under FPTP) would not have achieved an overall majority which requires 325 seats out of 649. A coalition with the Liberal Democrats, who have 77 would give 267 + 77 = 344 seats which is an overall majority.

A spreadsheet giving details of the transfer process is available here:

PREVAIL PLUS