Backgrounder:

Mathematical complexity in Sri Lanka's parliamentary election

Thursday's Sri Lankan parliamentary election promises to be the last of its kind. The new parliament members are expected to shed the very system. The system elected parliaments in 1989, 1994, 2000, 2001 and 2004.

Here is a look at the mathematical wonder of appointing Members of Parliament (MP) based on the proportional representation (PR) system of election in Sri Lanka.

A total of 196 MPs elected from 22 electoral districts would join 29 MPs to be elected based on the national PR to make the total number of MPs in parliament to 225.

Every voter in addition to his vote for the party or independent group of his choice, is entitled to indicate his preference for not more than three candidates nominated by the same political party or independent group. But the preference votes could be cast only if he/she votes for the party/independent group of his choice.

The first step is the determination of the political party/ independent group which has polled the highest number of votes in the particular electoral district or in other words the party or group which won the district. The candidate who is in that party' s list with highest number of preference votes gets elected. This is popularly known as the "Bonus Seat."

Every political party/independent group polling less than 5 percent of the total votes cast in the district is disqualified from having any candidate elected. The votes polled by such parties are deducted from the total votes polled in the district. The balance is known as the "relevant number of votes."

Assuming the final result of the Colombo district would be as shown below;

Number of votes polled in the district 1,200, 000

Votes polled by party A 645, 000

Votes polled by party B 350, 000

Votes polled by party C 150, 000

Votes polled by party D 55, 000

The A party candidate who has secured the highest number of preference votes will get elected as an MP.

The number of votes polled by D would be deducted from the total votes polled. The relevant number of votes for Colombo would then be 1,145,000

The relevant number is then divided by one less than the number of members to be elected from Colombo, i.e.: 19-1 = 18

1,145,000/18 = 63,611

The D gets eliminated as they have polled less than 5 percent.

Thereafter number of votes polled by Party A, B and C is divided by 63,611 as given below;

Party A gets the bonus seat: 1

Party A's total votes 645,000/63,611=10 remainder 8, 890

Party B's total votes 350,000/63,611= 5 remainder 31, 945

Party C's total votes 150,000/63,611= 2 remainder 22, 778

The total number of MPs elected so far would then be 18. Still one more seat remains to be filled up.

The Party B would be entitled to this 19th seat as it has polled the highest remainder.

In case where remainders are level-pegging, the last seat would be decided by drawing lots.

The national list of MPs is created as follows:

After 196 members have been elected, the Commissioner of Elections will apportion the remaining 29 seats among the political parties/independent groups in the same proportion as the votes polled countrywide by each political party/independent group.

For example:

In the last general election the total votes cast was 7,943,706. When it was divided by 29 (seats) the result was 273,920.

Party A polled 3,887,823/273,920=14 seats

Party B polled 3,498,370/273,920=13 seats

Party C and D who polled 143,307 and 132,461 were entitled to the remaining two seats.

Source: Xinhua