How Prevail Works
PREVAIL aims to create a greater degree of proportionality than does First Past the Post (FPTP) by transferring some seats to the party that did not come first in the constituency. Each party that has the highest vote in at least one constituency (called an elected party) is given a quota of seats that matches its share of the vote amongst elected parties. A party that gained more seats under FPTP than its quota is said to be over quota. Likewise a party can be on quota or under quota. PREVAIL will transfer seats from over quota parties to under quota parties.
For a party that is over quota, PREVAIL guarantees that it will keep at least its quota of seats (and exactly its quota if complete proportionality is required). For a party that is under quota PREVAIL guarantees that it will not lose any seats in which it came first. A party that is on quota is not involved in the transfer process and so will retain the seats in which it came first.
PREVAIL is concerned with the degree of proportionality amongst parties. An independent candidate gaining the highest vote in a constituency is immediately elected just as under First past the Post. This is the only way an independent candidate can win a seat. Independent candidates are not involved in transfers
The quota system ensures that every vote cast for a party that is elected is used, whether or not the party came first in a particular constituency. This is in marked contrast to First Past the Post where votes cast only count if the party wins in a seat.
Calculating the quotas
A seat is called a party seat if the highest vote was obtained by a party candidate rather than an independent candidate. The total number of party seats is N. The popular votes (PV) for each elected party are added to give the elected party total vote (TV). Note that TV is less than the total number of valid votes cast in the election because votes for independent candidates are ignored.
Each party is given a quota of seats in proportion to its popular vote:
N*PV/TV
For each party, this number is rounded to the nearest whole number. This rounding may cause the total quota to differ slightly from N. The quota of the party with the largest popular vote is adjusted to correct this. In this way the proportionality is least affected.
PREVAIL will then identify which parties are over, on or under quota.
A simple measure of the degree of disproportionality is the number of seats, M, requiring to be transferred to achieve perfect proportionality. This can be expressed as a fraction of the total number number of party seats, N. Expressed as a percentage this is:
100*M/N
A percentage of zero constitutes perfect proportionality.
Seat allocation
The party that obtained the highest number of votes in a constituency is called the First Party; the party that gains the second highest number of votes is called the Second Party; the party that gains the third highest number of votes is called the Third Party; likewise for fourth and subsequent parties.
Initially PREVAIL allocates each seat as in FPTP, i.e. to the first party or to an independent candidate who came first. Seats are then transferred one by one from parties that are over quota to parties that are under quota. Seats are not transferred from parties that are on quota. If a party was first in only one seat then that seat cannot be transferred.
Parameter Settings
PREVAIL has several parameter settings. Different choices of these settings will produce different degrees of proportionality. They are concerned with the balance between constituencies and Parliament. These choices are a political decision
Transfers can be subject to a lower threshold condition: a seat in which the second or subsequent party gained less than this percentage of the vote cannot be transferred (unless the first party achieved less than 25% of the vote in which case there would be no lower limit for transfer.
The lower the threshold the greater the degree of proportionality that will be achieved. Setting the lower threshold to zero will guarantee to produce perfect proportionality.
In addition to the lower threshold, transfers can be subject to an upper threshold: seats in which the first party obtained 50% or more of the vote cannot be transferred.
A further consideration is that there may be choices available for transfer. A party that is under quota by twenty seats may have come second to over quota parties, with votes above the threshold, in thirty seats. A preference criterion is need to choose which transfers to make. Two possible criteria are to transfer seats by:
- lowest first vote percentage
- highest vote percentage of the receiving party
The first of these seeks to minimise the lost first vote percentage of transferred seats; the second aims to maximise the vote of the recipient of the transfer.
The ideal scenario for PREVAIL is that each over quota party keeps its best seats, as measured by share of vote (referred to as above the quota cut) as its quota and its remaining FPTP seats (referred to as below the quota cut) are transferred to under quota parties so that each of these has its seats increased to quota. In practice, for several reasons, this will not usually be possible:
- one or more under quota parties may dominate second and third positions thus preventing transfers to other under quota parties
- an under quota party may not have come second or third sufficiently often, and with a vote above the threshold, to reach its quota
- over parties may have come second and third
- independent candidates may have come second and third
As a result of these shortfalls in transfer one or more over quota parties will remain over quota. Seats above the cut could then be transferred in an attempt to bring parties down to quota.
It is possible for a party that is over quota to have obtained 50% or more of the vote in all of the seats in which it came first thus preventing any transfers. To overcome this, the upper threshold can be applied only in seats above the quota.
The upper and lower threshold percentages are parameters and could be set at different values. The values chosen significantly influence the extent to which proportionality can be achieved.
Collectively the rules discussed above concerning which seats can or cannot be transferred are referred to as the transfer protocol.
A protocol specifies:
- Upper threshold
- Lower Threshold
- Preference criterion
- Whether seats above the quota can be transferred
The recommendation here is for perfect proportionality achieved by: no upper threshold; no lower threshold; preference for higher receiving party vote; no transfers above the quota.
The transfer process
Transfers are from over quota parties to under quota parties. The quota cut off is determined for each over quota party. The seats beneath the cut off are those to be transferred. They are merged into single list and ranked according to the chosen preference criterion. Transferring of seats proceeds constituency by constituency.
Although the vote obtained by the party allocated set is not a particular priority for PREVAIL, the transfer process seeks to maintain as high as possible percentage vote of the seat receiving the transfer. In many cases this percentage vote may be only a point or so below that of the party which came first; in other cases, depending the lower threshold, it can be very small.
Initially, transfers are from first party to second party. If this is not sufficient then further transfers are made from first party to third party. If this is still not sufficient then before proceeding to transfers from first party to fourth, the previous transfers from first to second party can be reworked to create more opportunities for first to third party transfers. This is called retransfer.
As transfers proceed the allocation for a party that is over quota will decrease. Should it reach quota, no further transfers are made from that party. Likewise the allocation for a party that is under quota will increase. Should it reach quota, no further transfers are made to that party.
If proportionally has not been reached by the end of the transfer process then, as noted above, it is possible, if the protocol permits it, to transfer seats from above the quota cut. For the parties still remaining above quota, its seats above the quota cut are arranged into a single list and ranked according to first vote. Transfers proceed as already described.
Transferring above the quota cut will still guarantee that parties above quota will retain at least their quota - they will just not be all their best seats.
Transfers: an illustration
A small parliament has 52 seats. In two seats an independent candidate gained the highest vote. These two candidates are allocated their seats and these cannot be transferred. This leaves N=50 party seats. Six parties A, B ,C, D, E and F were elected (each came first in at least one seat). These parties are initially allocated their FPTP seats.
First Past the Post (FPTP) seats and quotas for the elected parties are shown below:
| Party A | Party B | Party C | Party D | Party E | Party F | |
|---|---|---|---|---|---|---|
| FPTP Seats | 20 | 10 | 4 | 1 | 12 | 3 |
| Quota | 12 | 8 | 4 | 1 | 15 | 10 |
| Quota Type | Over | Over | On | On | Under | Under |
| After Stage 1 | 17 | 9 | 4 | 1 | 15 | 4 |
| After Stage 2 | 15 | 8 | 4 | 1 | 15 | 7 |
| After Stage 3 | 14 | 8 | 4 | 1 | 15 | 8 |
The lower threshold is set at 20% (except, as declared above, if the first party vote is less than 25%). The preference criterion is lowest first vote.
Only parties A and B are above quota. Party A has 8 seats beneath the quota cut and party B has 2. These 10 seats are merged into a single list in descending order of first party vote percentage (shown below).
The protocol was:
- Transfer seats above the quota
- No transfers beyond the third party
- Upper threshold : 50%
- Lower Threshold : 20% (except if first vote is less than 25% in which case no lower limit)
- Preference criterion : least first vote
| Seat | First | % Vote | Second | % Vote | Third | % Vote | Stage 1 | Stage 2 | Stage 3 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | A | 35.36 | E | 28.94 | B | 25.70 | No transfer: E is now on quota. | No transfer: B is an over quota party now reduced to quota. | Transfer from A to E compensating for loss for E at seat 7. |
| 2 | A | 35.03 | F | 18.82 | E | 14.61 | No transfer: F has less than 20%. | No transfer: E is on quota and anyway has less than 20%. | No transfer. |
| 3 | A | 34.81 | E | 29.17 | F | 27.40 | No transfer: E has achieved quota. | Transfer from A to F. | No transfer. F has already obtained this seat. |
| 4 | A | 34.53 | E | 24.26 | F | 21.74 | Transfer from A to E. With three transfers, E is now on quota. | No transfer: first stage transfer has already been made. | No transfer from E to F: no compensating transfer is available further up the list |
| 5 | A | 34.05 | B | 33.74 | F | 22.66 | No transfer: B is over quota. | Transfer to A to F. | No transfer: F has already obtained this seat. |
| 6 | A | 33.92 | F | 24.06 | C | 17.49 | Transfer from A to F. | No transfer: C is on quota. | No transfer because C is on quota. |
| 7 | B | 33.05 | E | 32.76 | F | 20.04 | Transfer from B to E. | No transfer: first stage transfer has already been made. | Transfer from E to F. Compensate E at seat 1. |
| 8 | A | 32.70 | Ind | 23.36 | E | 21.68 | No transfer: an independent is second. | No transfer: E is on quota. | No transfer. |
| 9 | B | 32.65 | C | 30.17 | F | 21.11 | No transfer: C is on quota. | Transfer from B to F. B is now down to quota. | No transfer: F has already obtained this seat. |
| 10 | A | 24.84 | E | 19.23 | Ind | 19.04 | Transfer from A to E: valid because A vote is below 25%. | No transfer: an independent candidate came third. | No transfer. |
In stage 1 of the transfer process, reading the table above from the bottom upwards, party E achieves quota after the transfer in seat 4: three transfers have raised its allocation from its FPTP of 12 to its quota of 15. Party F has gained one seat from the transfer of seat 6 from party A raising its current allocation from its FPTP of 3 to 4. As a result of these transfers, Party A has its seats reduced from its FPTP allocation of 20 to 17 and Party B from 10 to 9.
In stage 2, again reading the table from the bottom upwards, seat 9 is transferred from B to F and seats 5 and 3 from A to F. This brings party A down from 17 to 15 seats and party B down to its quota of 8. Party F is up from 4 to 7 seats.
At the conclusion of stage 2, party A is above quota by 3 and party F is under quota by three. All other parties are on quota.
Stage 3 transfers begin at the bottom of the list. The only party still seeking transfers is F. Seat 7 which was originally transferred at stage 1 to E is now transferred to F. This is compensated by a transfer at seat 1 from A to E (the first, and only, seat available). Party A is down from 15 seats to 14. Party F is up from 7 seats to 8.
At the end of the transfer process, party A is two above quota and party F is two below quota. All other parties are on quota. Prior to the transfer process there were 10 seats over quota and 10 under quota so PREVAIL has achieved a significant increase in proportionality. In terms of the measure of disproportionality described above, the score achieved by PREVAIL is 100*2/50 = 4% compared to 100*10/50 = 20% under FPTP.
At this point transfers are made above the quota cut to seek two more transfers from party A to party F. If found, this would achieve perfect proportionality. Alternatively transfers can be extended to fourth and subsequent parties. The results of this are not shown here.
Discussion
A smaller party often has difficulty under First Past the Post because, although it amasses a sizeable total vote across the country, it comes first in only a small number of seats. Consequently it ends up very much under quota. PREVAIL will help allocate more seats but the degree to which this can be achieved depends on the extent to which the party came second or third and with votes above the lower threshold. PREVAIL, though, should encourage voting for smaller parties thereby helping to increase second and third vote percentages.
An over quota party is guaranteed to retain at least its quota of seats and this will tend to include its best performing seats. PREVAIL prioritises transfer of seats below the quota cut. The protocol could prohibit the use of transfers above the cut. This would ensure the quota contained at least all best performing seats.
The lower threshold provides a guarantee that every elected member will have obtained at least that percentage vote. Even though for transferred seats this will be less than the first vote, it is the case that most members are returned with less the 50% of the vote in their constituency.
The preference criterion adopted was least first vote, i..e the worst performing seats of an over quota party are the most appropriate for transfer. The alternative criterion of best second and third seats transfers favours transfer according to the performance of the party receiving the transfer. Because a lower first vote is strongly associated statistically with a higher second or third vote, there is only a little difference in the behaviour of these preference criteria. One possibility is to use best second or third vote below the quota cut and least first above it. This will slightly increase the average vote of transferred seats below the cut.
In conclusion, the protocol used greatly influences the outcome. The choice of protocol is a political decision and depends on the balance sought between achieving a representative parliament and a representative member in each constituency. FPTP has no awareness of parliamentary representation and concentrates solely on the individual constituencies. PREVAIL can be thought of as an adaptation of FPTP within which, through choice of protocol, a range of degrees of proportionally is achievable. At one extreme setting the lower threshold to 100% equates to FPTP. At the other extreme setting the lower threshold to 0% and allowing only transfers beneath the quota cut but extending these beyond the third party will result in perfect proportionality; it would mean, though electing some members with a percentage vote less than 10%.