Base Ratio Method for Proportional Representation (PR)

Accurate PR with a Minimum Number of At-large Seats

Mixed Member Proportional Representation (MMP)

In an MMP election voters decide how many seats each party wins. Members are elected from single-member districts and at-large.

For accurate PR, a legislature with 100 single-member districts needs 50 or more at-large seats. Small legislatures need a higher percentage of at-large seats, large ones lower.

A threshold for party representation will reduce the need for at-large seats at the expense of small parties.

MMP Voting

First, vote for your district representative. When you vote for your representative you are also casting a Party Vote for that candidate’s party. Next, vote for candidates on the Party List of your candidate’s party.

Base Ratio Method*

To achieve accurate PR with minimum at-large seats, we propose the Base Ratio Method. We describe it with basic math.

Compared to MMP systems with a set number of at-large seats, the Base Ratio Method requires far fewer at-large seats. However, the number of at-large seats will change after each election. With the Base Ratio Method, a legislature with 100 single-winner districts might need 15 to 30 at-large seats for accurate PR.

This method can achieve accurate PR for legislatures elected from multi-member districts. Fewer at-large seats would be needed compared to a similar size single-member legislature.

the Base Ratio process

Step 1:
Add up the Party Votes for each party.

Step 2
Determine the Party Ratio for each party by dividing their Party Votes by the number of district seats they won in the election.

The Base Ratio is the Party Ratio with the lowest number of Party Votes per district seat won. The party with the lowest Party Ratio will not need at-large seats. In most races, a major party will have the lowest Party Ratio.

The Party Ratio must be from a party that wins at least 8% of the district seats. This guards against the remote possibility that a small, localized party sets a low Base Ratio by winning a seat, or a few seats, while receiving relatively few Party Votes. Other parties would then need a high number of at-large seats to achieve accurate PR.

Step 3
Find the number of at-large seats required for each party to match the Base Ratio.
Example Election:
PV = Party Votes
DS = District seats
AL = At-Large seats
Party A received 300,000 PV and won 30 DS
Party B received 270,000 PV and won 24 DS
Party C received 75,000 PV and won 2 DS
Party D received 30,000 PV and won 1 DS

The Base Ratio = 10,000 Party Votes per seat because party A has the lowest Party Ratio. 300,000 PV ÷ 30 DS = 10,000 PV per seat. Party A does not need at-large seats.

A: 300,000 PV, 30 DS, 10,000 PV per seat
B: 270,000 PV, 24 DS, 11,250 PV per seat
C: 76,000 PV, 2 DS, 38,000 PV per seat
D: 30,000 PV, 1 DS, 30,000 PV per seat
The Base Ratio is 10,000 PV per seat.

Look at party C below. We calculate which is closer to the base ratio: 7 seats (2 district seats + 5 at-large seats) or 8 seats (2 district seats + 6 at-large seats). The closest match to the base ratio is 8 seats. Therefore, party C wins 6 at-large seats.

Seats needed to best match the base ratio.
PV ÷ (DS + AL) = PV per seat

A: does not need at-large seats

B: 270,000 ÷ (24 + 3) = 10,000 PV per seat
B wins 3 at-large seats.

C: Not so easy
76,000 ÷ (2 + 5) = 10,857 PV per seat
10,857 – 10,000 = 857
76,000 ÷ (2 + 6) = 9,500 PV per seat
9,500 – 10,000 = -500
500 under is closer than 857 over
therefore C wins 6 at-large seats

D: 30,000 ÷ (1 + 2) = 10,000 PV per seat
D wins 2 at-large seats (unless there is a 3-seat threshold).

11 total at-large seats.

The candidates with the most Party Lists votes win their party’s at-large seats.

Party Threshold for At-large Seats

The threshold for at-large seats could be a minimum seat requirement, or a percentage of the Party Vote.

Calculations for one and three seat thresholds:
p = Party Votes in the Base Ratio. For these examples, the Base Ratio is 10,000 Party Votes per district seat won.
n = minimum number of votes needed to gain at-large seats.

One seat minimum, p = 10,000, two options:
.5 x p = n #nbsp; #nbsp; .5 x 10,000 = 5,000 votes
1 x p = n #nbsp; #nbsp; 1 x 10,000 = 10,000 votes

Three-seat minimum, p = 10,000, two options:
2.5 x p = n #nbsp; #nbsp; 2.5 x 10,000 = 25,000 votes
3 x p = n #nbsp; #nbsp; 3 x 10,000 = 30,000 votes

Notes:
A party can qualify for at-large seats without winning a district seat.
Parties that win few district seats may a have high number of Party Votes per seat.
District seats won should count towards minimum seat requirements.

*We invented the term “Base Ratio Method” because it is descriptive. There may be an existing term for it, please inform us if you know of one.