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Topic IndexTransforming Votes to Seats

Determining the winner(s) is usually accomplished at the electoral district level, though it may be done also at the national level. Most often senior electoral officials, with specific technical skill conduct the votes to seats formula application.

The rules governing the determination of winner(s) (the electoral formula) can be complex, especially if a scheme of proportional representation is in force. Further, determining the winner is an important political responsibility: any serious error made at this stage might generate a political crisis. Any suspicion of fraud will have the same consequence. There are various electoral formulas that fall into three main clusters:

Plurality-majority,
Proportional representation (PR), and
Semi-PR systems.

However, each of these clusters includes different formulas.

Plurality-Majority Formulas

First-past-the-post (FPTP) in single-member districts. The candidate with the highest number of votes is elected.
FPTP in multi-member districts, with no panachage allowed (the Party Block Vote): The candidates on the party list with the highest number of votes are all elected.
FPTP in multi-member districts, with panachage allowed (the Block Vote):
There are two possible ballot arrangements:
1. No distinct competition for each seat, voter has as many votes as there are seats to be filled in district. The candidates with the highest number of votes are elected.
2. Each seat in the district is numbered in a distinctive way (Seat "A", Seat "B", etc.), with one distinct competition for each seat, and each elector has a vote for each seat. In this case, the candidates with the highest number of votes for each seat are elected.
Two-Round system in single-member districts: On the first ballot, the candidate with a majority of the vote is elected. If no candidate obtains a majority, a second ballot is held at a later date.
There may be no restriction as to who may stand [at the second ballot], there may be a threshold eliminating the weaker candidates, or only the two strongest candidates may stand [at the second ballot]. In each instance the candidate with the highest number of votes is elected.
Two-round system in multi-member districts, with closed lists, no panachage allowed: Voters cast a vote for a party list. On the first ballot, the candidates on the party list with a majority of the vote are all elected. If no party list obtains a majority, a second ballot is held at a later date.
There may be no restriction as to who may stand at the second ballot, there may be a threshold eliminating the weaker party lists, or only the two strongest party lists may stand at the second ballot. In any case, the candidates on the party list with the highest number of votes are all elected.
Two-round system in multi-member districts, with panachage allowed.
There are two possible ballot arrangements:
1. Each seat is numbered in a distinctive way (Seat "A", Seat "B", etc.), with one distinct competition for each seat. Voters cast one vote for each seat. Votes are counted separately for each seat. On the first ballot, the candidate with a majority of the vote is elected. If no candidate obtains a majority, a second ballot is held at a later date (e.g. one or two weeks later). There may be no restriction as to who may stand at the second ballot, or there may be a threshold eliminating the weaker candidates, or only the two strongest candidates may stand at the second ballot: in any case, the candidates with the highest number of votes are all elected.
2. No distinct competition for each seat; voter has as many votes as there are seats to be filled. In this case, candidates who have a majority of the vote are elected. If some seats remain unfilled after the first ballot, a second ballot is to be held later, with voters casting as many votes as there remain seats to be filled. There may be no restriction as to who may stand at the second ballot, or there may be a threshold eliminating the weaker candidates. In either case, voters cast as many votes as there are members to be elected at this second ballot, and the candidates with the highest number of votes are elected.
Alternative voting in single-member districts; Voters express preferences for each candidate by numbering each one consecutively (1, 2, 3, etc.). The candidate who obtains a majority of first preferences is elected. If no candidate obtains a majority of first preferences, the weakest candidate is eliminated and the second preferences on his or her ballot papers are transferred to the candidates for whom they are expressed. If necessary, this process is repeated until a candidate obtains a majority of the vote.
Alternative vote in multi-member districts: Each seat is numbered in a distinctive way (Seat "A", Seat "B", etc.), with one distinct single-member competition for each seat. For each seat, voters express preferences for each candidate by numbering each one consecutively (1, 2, 3, etc.). For each seat, votes are counted, preferences eventually distributed and members elected as if it were a single-member seat with alternative voting (see above).

Semi-Proportional Systems

Limited vote: Takes place within multi-member districts. Voters cast a number of votes that are lower than the number of seats to be filled. The candidates with the highest number of votes are elected.
Single Non-Transferable Vote (SNTV): Takes place within multi-member districts. Same as for the limited vote, except that irrespective of the number of seats to be filled, voters cast a single vote.
Parallel Systems: This system combines members elected in local districts by plurality or majority, and regional or national members elected by PR. Both plurality (or majority) and PR apply throughout the country. Both systems operate independently of each other. Notably, PR seats are filled without any consideration of the results in single-member districts.
Parallel-Mixed coexistence systems: In this kind of mix, some districts within the country use either a plurality or majority formula, while in the other districts some form of PR is used. No formula applies to the whole country.

Proportional Representation (PR) - Multi-Member Districts

PR with closed list, no panachage between lists: the party on the party list ranks candidates. Voters cast a single vote for one of the parties. Seats are distributed in proportion to the votes cast for each party list. Within each party list, seats go to the candidates ranked higher on the party list.
PR list with panachage allowed: Voters have as many votes as there are seats to be filled. They distribute those votes as they wish among candidates, irrespective of parties. The votes cast for candidates from each party are aggregated, and seats are distributed in proportion to the votes cast for the candidates of each party. The seats won by each party go to those candidates who obtained the highest number of personal votes. It is also possible to cast a single party vote, which is deemed to be one vote for each candidate sponsored by that party.
PR list where preference votes for individual candidates are allowed: This is a diverse group with a general principle that voters vote for a party, but may register a preference for one or many individual candidates within that list, or cross out the name of one or many individual candidates within that list. Some jurisdiction’s legislation provides that individual preference votes will not be considered if they amount to less than a given percentage (e.g. 10 percent) of all ballots cast for that party, and that candidates will be elected according to their position on the party list.

At least five different scenarios have been found:
1. Scenario A - Voters must vote for a single individual candidate only. This vote is also deemed to be a vote for the party sponsoring that individual. Seats are first distributed among parties on the basis of the total number of votes cast for all candidates sponsored by that party. Thereafter, within each list, seats go to the candidates obtaining the highest number of individual votes.
2. Scenario B - Voters can only vote for a single individual candidate, and this vote is also deemed to be a vote for the party sponsoring that individual. Seats are first distributed among parties on the basis of the total number of votes cast for all candidates sponsored by that party.
  Thereafter, for each party, a "list quota" is computed. This is the result of the division of the number of votes cast for the party by the number of seats it won. Candidates whose personal preference votes are equal to or higher than the quota are elected. The votes obtained by these candidates surplus to the list quota are then transferred to the other candidates in the order of listing. However, candidates who obtained more than half of the list quota are given priority when votes are transferred, irrespective of their position on the list. The other candidates remain in the order in which they originally appeared on the ballot papers. Candidates are then elected on the basis of the order in which they appear on the amended list.
3. Scenario C - Voters may vote either for a party list or for one individual candidate within a party list. Seats are first distributed among parties on the basis of the total number of votes cast for that party and for each of the candidates representing that party.
  The total number of votes cast for a party and its candidates is divided by the number of seats won by that party, plus one. The result is an "eligibility number". As party votes are deemed to indicate an acceptance by the elector of the rank-ordering of candidates determined by the party, party votes are then transferred to the highest-ranking candidate on the list, and added to his or her personal votes.
  The surplus of party votes (i.e. the difference between the total number of party votes and the eligibility number) is then transferred to the second candidate on the party list and added to his or her personal votes, and on and on until all party votes have been allocated to individual candidates.
  Then, the candidates with the highest number of votes, both party and personal, are elected.
4. Scenario D - Voters must vote for a party list and may, in addition, vote for one or many of the candidates within that list. Seats are first distributed among parties on the basis of party votes. Then, within each list, seats will go to the candidates obtaining the highest number of individual votes, provided that at least 10 percent of the ballots cast for the party include individual preferences. Otherwise, seats go to the highest-ranked candidates.
5. Scenario E - Voters must vote for a party list. In addition, they may vote for one of the candidates within that list or cross out the name of a candidate within that list.
  Seats are first distributed among parties on the basis of party votes. Each candidate's personal votes are increased by the number of votes cast for his or her party, and decreased by the number of ballots on which his or her name was crossed out. Then, seats go to the candidates who got the highest figures after those computations have been made.
Single Transferable Vote (STV): Voters express preferences for candidates by numbering each one consecutively (1, 2, 3, etc.). The number of first preferences obtained by each candidate is counted. A quota is ascertained by dividing the total number of first preference votes cast for all candidates by the number of seats in the district, increased by one. Candidates who obtain a number of first preference votes higher than the quota are elected.
If seats remain to be filled, the second preferences on the ballot papers of elected candidates are transferred to other candidates, in proportion to the number of votes they obtained in excess of the quota. If seats remain to be filled after that operation, the weakest candidates are eliminated and the second preferences expressed on their ballot papers are transferred to other candidates
Mixed Member Proportional Systems. This system also combines members elected in local districts by plurality or majority, and regional or national members elected by PR. Both plurality (and majority) and PR apply throughout the country. However, PR seats are distributed to provide each party with an overall number of seats proportional to its share of the vote.

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