Base Ratio Method for Mixed Member Proportional Representation (MMP)

Preserve Single-Member Districts with MMP

Apportion Seats According to Voter Support

Far Fewer At-large Members

Mixed Member Proportional Representation (MMP) Voting

In a MMP election, first you vote for a candidate to represent your district. Second, vote for at-large candidates from the party list of your favorite political party. By doing so, you cast a vote for your party, we call this the Party Vote. At-large members are used to ensure that each party wins a percentage of the seats equal to their percentage of the Party Vote.

To accurately apportion seats according to the Party Vote (PR), a legislature with 100 single-member districts may need 67 at-large seats, a 3 to 2 ratio. Small legislatures need a higher percentage of at-large seats, large ones, a little lower.

Advanced voting methods that give third parties a fair chance to win district seats will reduce the number of at-large seats needed for accurate PR. A minimum threshold for party representation could also reduce the number of at-large seats at the expense of small parties.

The Base Ratio Method will achieve accurate proportional representation with far fewer at-large seats. The trade-off: the number of at-large seats will change with each election.

We recommend MMP with the Base Ratio Method for legislatures that desire accurate proportional representation with a minimum number of at-large seats.

Base Ratio Method

To achieve accurate PR with minimum at-large seats, we propose the Base Ratio Method. It works with basic math. With the Base Ratio Method, a legislature with 100 single-winner districts might need 5 to 25 at-large seats for accurate PR instead of 67 at-large seats in conventional MMP systems.

The Base Ratio Process

Step 1: Determine the Base Ratio

Add up the Party Votes for each party. Divide each party’s Party Votes by the number of district seats it won to determine its ratio of Party Votes to district seats won. We call this the Party Ratio.

The Base Ratio will be the lowest Party Ratio. The party with the lowest Party Ratio does not need at-large seats. Other parties receive at-large seats so their ratio of district seats to Party Votes is equal (or nearly equal) to the party with the lowest Party Ratio.

Example Election:

PV = Party Votes
DS = District seats
Party A received 300,000 PV and won 30 DS
300,000 ÷ 30 DS = 10,000 PV per seat

Party B received 270,000 PV and won 24 DS
270,000 ÷ 24 DS = 11,250 PV per seat

Party C received 76,000 PV and won 2 DS
76,000 ÷ 2 DS = 38,000 PV per seat

Party D received 30,000 PV and won 1 DS
30,000 ÷ 1 DS = 30,000 PV per seat

The Base Ratio = 10,000 Party Votes per seat because party A has the lowest ratio of Party Votes to district seats. Party A does not need at-large seats. In most races, a major party will have the lowest Party Ratio and third parties will have a high number of Party Votes per district seat as they seldom win district elections.

The Base Ratio must be from a party that wins at least 7% of the district seats. This guards against the remote possibility that a small localized party sets an unusually low Base Ratio by winning a seat, or a few seats, while receiving a low number of Party Votes. Other parties would then need a high number of at-large seats to achieve accurate PR.

Step 2

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
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 of
10,000 Party Votes per seat
Party Vote ÷ (District Seats + At-large seats) = Party Votes per seat
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.

Yes, we need someone to write a proper equation for this process.

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:

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