What preferential counting methods does the Voting System support?

Below are the preferential or ranked choice counting methods currently supported by the Voting System.

With preferential voting, voters rank voting options in order of preference, from their first preference to their last preference. The counting method selected will determine how those preferences are converted in election results.

Single Transferable Vote / Instant Runoff Voting / Alternative Voting

Simply Voting supports several variations of Single Transferable Vote (STV).

We offer different options for the quota used in calculating the threshold for determining winners, as well as variations of the counting methods for tabulation. The different options are described below.

Quotas

With STV, quotas are determined before tabulation begins. These quotas are used by the voting system to determine when winners are elected. Once the prescribed number of winners are elected, tabulation stops.

Option 1 - Droop quota (default)

Our default configured quota is the Droop quota. The Droop quota is calculated as:

Where:

• = number of valid votes cast (i.e. excluding abstentions and spoiled votes)
• = number of winners to elect (i.e. the number of seats to fill)

If there is a fraction, it is rounded down before adding the . The quota remains fixed and does not change from round to round. In the case of only 1 winner, this is equivalent to a simple rule.

Option 2 - Enforced "50% + 1" quota

With this quota option the threshold for determining winners is always calculated as:

Where:

• = number of valid votes cast (i.e. excluding abstentions and spoiled votes)

If there is a fraction, it is rounded down before adding the . The quota remains fixed and does not change from round to round. Note that unless redistribution of votes is activated it is mathematically impossible for more than one candidate to reach the threshold.

Tabulation

Tabulation is the process of counting ballots. The different options we offer determine the rules the voting system follows during the counting process.

Option 1 - Regular STV (default)

Ranked ballots are counted as follows:

1. On the first round of counting, each option shall receive a first preference vote for each vote indicating it as first preference.

2. Should an option meet the quota of first preference votes after any round, it shall be declared elected. If there are several options meeting the quota the one with the most votes shall be elected. If there is a tie one of those options shall be elected by random draw. Multiple options are never elected simultaneously.

3. If no option is elected or further winners are required, then the option with the fewest number of first preference votes shall be eliminated from the question. Should there be a tie for the fewest number of first preference votes, then among these, the option with the fewest number of second preference votes shall be eliminated. Should a tie persist, the procedure shall continue with third preference votes, et cetera. Should a tie still persist, the option with the fewest number of original first preference votes, shall be eliminated. Should a tie still persist, the procedures shall continue with original second preference votes et cetera. Should a tie still persist, an option shall be eliminated by random draw. Multiple options are never eliminated simultaneously.

4. When an option is eliminated, all first preference votes for that option shall be replaced by the vote's first preferred option that is not yet elected or eliminated. All second preference votes for that option shall be replaced by the vote's next preferred option that is not yet elected or eliminated, and so on.

5. This procedure of eliminating option(s) and redistributing first preference votes shall continue until all winners are elected or the number of options left equals the number of winners (this may occur due to exhausted ballots, and those options shall be declared elected).

Option 2 - STV with Redistribution of Surplus Votes

Surplus votes are the votes received by an elected option in an election that requires more than 1 winner. Surplus votes can be redistributed in full, or at a discount.

When redistributing surplus votes at a discount, the redistribution rate is calculated as follows:

Where:

• = number of votes received by the elected option
• = number of votes required for an option to be elected (the quota)

Simply Voting does not round fractions for tabulation, but rounds to 2 decimal places for displaying in reports.

STV with Redistribution is counted as follows:

1. On the first round of counting, each option shall receive a first preference vote for each vote indicating it as first preference.

2. Should an option meet the quota of first preference votes after any round, it shall be declared elected. If there are several options meeting the quota the one with the most votes shall be elected. If there is a tie one of those options shall be elected by random draw. Multiple options are never elected simultaneously.

3. When an option is elected by meeting the quota, the votes for that option are discounted (if applicable) and redistributed: All first preference votes for that option shall be replaced by the vote's first preferred option that is not yet elected or eliminated. All second preference votes for that option shall be replaced by the vote's next preferred option that is not yet elected or eliminated, and so on.

4. If no option is elected or further winners are required, then the option with the fewest number of first preference votes shall be eliminated from the question. Should there be a tie for the fewest number of first preference votes, then among these, the option with the fewest number of second preference votes shall be eliminated. Should a tie persist, the procedure shall continue with third preference votes, et cetera. Should a tie still persist, the option with the fewest number of original first preference votes, shall be eliminated. Should a tie still persist, the procedures shall continue with original second preference votes et cetera. Should a tie still persist, an option shall be eliminated by random draw. Multiple options are never eliminated simultaneously.

5. When an option is eliminated, all first preference votes for that option shall be replaced by the vote's first preferred option that is not yet elected or eliminated. All second preference votes for that option shall be replaced by the vote's next preferred option that is not yet elected or eliminated, and so on.

6. This procedure of electing and eliminating option(s) and redistributing first preference votes shall continue until all winners are elected or the number of options left equals the number of winners (this may occur due to exhausted ballots, and those options shall be declared elected).

Borda Count

Simply Voting uses the Borda Count method. Borda Count votes are counted as follows:

1. The number of points given to candidates for each ranking is determined by the number of candidates in the question. Thus, if there are five candidates then a candidate will receive five points each time they are ranked first, four for being ranked second, and so on, with a candidate receiving 1 point for being ranked last.

2. Unranked candidates are given zero points.

3. When all votes have been counted, and the points added up, the candidate(s) with most points wins.

Ranked Pairs / Tideman Condorcet

Simply Voting uses the Ranked Pairs / Tideman Condorcet method. Condorcet votes are counted as follows:

1. To tally the votes, consider each voters' preferences for each possible pair of candidates. For example, if a voter states "A > B > C" (A is better than B, and B is better than C), the tally should add one for A in A vs. B, one for A in A vs. C, and one for B in B vs. C. Unranked candidates are assumed to be equally worse than the ranked candidates. The total pairwise counts for all possible pairs of candidates based on all the votes is stored in a sum matrix.

2. Next we list every pair and determine the pair winner and the number of winning votes, called the "majority".

3. The pairs of winners, called the "majorities", are then sorted from the largest majority to the smallest majority. Ties are resolved by choosing the pair with stronger winner, then the pair with weaker loser.

4. The next step is to examine each pair in turn to determine which pairs to "lock in". This is done by drawing an arrow from the pair's winner to the pair's loser in a directed graph. Using the sorted list above, each pair in turn is locked in unless the pair will create a circularity in the graph (e.g., where A is more than B, B is more than C, but C is more than A).

5. In the resulting graph, the source (vertex with indegree of 0) corresponds to the winner.

6. To find additional winners, pairs containing the winner are removed from the majorities and steps 4 and 5 are repeated as necessary.