PREVAIL creates perfect proportionality by transferring some seats to parties 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 until all parties  are on quota.

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 in which an over quota party achieved 50% or more of the vote, called majority seats, are not transferred. 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.

The transfer process

Seats are arranged in decreasing order of first vote. Transfers begin at the bottom of this list and proceed upwards. Thus the least well performing seats are the most likely to be transferred. 

Seats are transferred to one under quota party at a time until that party reaches quota. Transfers begin with the party that requires the least number of seats to bring it up to quota and ends with the party needing the greatest number of seats. If two or more parties need the same number of transfers they are ordered according to popular vote with the party having the lowest going first. 

Beginning at the bottom of the list, an under quota party initially receives seats in which it came second. If this is not sufficient to bring it up to quota then, again beginning at the bottom of the list, it receives seats in which it came third and so on. 

Moving up the list, some seats from over quota parties may not be transferred. In such seats an independent candidate or another over quota party or an unelected party may have come second, likewise third and so on, thus preventing transfer. 

Although the vote obtained by the party allocated a seat 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 though in other cases it can be very small.   

At the end of the transfer process over quota parties will be left with their quota of seats and under quota parties will have their seats increased to quota.  

It is theoretically possible for a party that is over quota to have obtained 50% or more of the vote in a greater number of seats than its quota. In this case the least well performing seats beyond its quota will be transferred. Again it is possible, particularly near the end of the transfer process, that an under quota party may not have stood in a constituency where it needs a transfer. In this case a swap can be made with another under quota party that did stand in the seat. 

Further points