The HareClark electoral system is a Single Transferable Vote (STV) method of proportional representation used in multimember electorates. STV means that a ballot paper moves between candidates as determined by the elector's preferences.
Thomas Hare was an Englishman who, in 1856, proposed the idea of a proportional representation election system which was further developed and became known as the Hare system. Andrew Inglis Clark, Tasmanian AttorneyGeneral 1888 and a member of the Tasmanian Parliament, introduced a modified version of the Hare system into Tasmanian law in 1896. This system is now known as the HareClark electoral system.
Robson rotation is a process of rotating candidate names within a column so that favoured (top and bottom) positions are shared equally between all candidates. Neil Robson, a member of the House of Assembly, introduced the process to the Tasmanian Parliament in 1979.
Robson Rotation discussion paper
The ballot paper directs the voter to place the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on as the case requires, beside the names of the candidates in the order of his/her preference.
To be formal, a ballot paper must have at least the numbers 1, 2, 3, 4, and 5 with no repetitions or omissions.
A candidate is elected when his/her total number of votes equals or exceeds the quota.
The quota is the lowest number of votes a candidate needs to be certain of election.
To calculate the quota, the number of formal votes is divided by one more than the number of candidates to be elected (rounded up to the next whole number). For the House of Assembly, which elects five members per electorate, the quota is one sixth or 16.7% of the formal votes.
If five candidates each receive a quota (just over one sixth of the formal vote) then less than one quota of the votes remain.
Under HareClark, parties, groups and independents are elected to the House of Assembly in proportion to their support in the electorate. The composition of the House closely reflects the proportion of primary votes on a Statewide basis.
When a vacancy occurs a new member is elected by a recount process based on votes cast at the previous general election. Only unsuccessful candidates at the general election are eligible to contest the recount.
Only the ballot papers which were used to elect the vacating member are distributed in the recount. These votes are distributed to contesting candidates. The candidates receiving the least votes are excluded until a candidate receives a majority (50% + 1).
Parties and groups usually nominate more candidates than they expect to be elected, in order to provide a pool of candidates to contest any recount to fill a vacancy.
As a result, the voters are provided with a choice of candidates within each party, as well as a choice of candidates across parties, groups and independents.
There are two small differences. For Tasmanian Local Government elections, the number to be elected varies (depending on the election), the initial transfer value is 1 and all votes are calculated to 2 decimal places to reduce the loss of votes by fraction.
The first step is to distribute all ballot papers to the candidates according to each ballot paper's first preference. The quota is then calculated from the total formal vote.
If any candidate(s) receives more votes than the quota, he/she are declared elected, and the excess votes (surplus) are passed on to continuing candidates. Following the distribution of each surplus, any candidate(s) who has reached the quota is declared elected; and any resulting surplus again passed on.
Once all surplus votes have been distributed the candidate with the fewest votes is excluded and all of their votes passed on to continuing candidates. Further candidates are excluded until another candidate reaches the quota.
The process of distributing surplus votes and excluding candidates continues until five candidates reach the quota. In some cases the final candidate(s) will be elected without reaching the quota as all other candidates have been either elected or excluded.
In House of Assembly elections, it is common that the last elected member in a division is elected without obtaining a quota. In some cases the last two elected members in a division are elected without each obtaining a quota.
During the distribution of preferences, some votes are "lost" from the count. A small number are lost due to rounding of fractional numbers. A more significant number of votes are "exhausted" toward the end of the count, as many ballot papers do not show a preference for any remaining candidate.
Where the contest for the last seat is close, it is common for the remaining two candidates to both have less than a quota. The candidate with the least votes is excluded, and the other candidate elected without reaching the quota. The more votes that are lost during the scrutiny, the more likely that not all elected members will obtain the quota.
A less common situation occurs where remaining three candidates are contesting the last two seats. In this case, the candidate with the least votes is excluded, and the other two candidates elected without either reaching the quota.
To be elected, a candidate must obtain a quota of votes.
The first step in the HareClark scrutiny is to count the number of first preference ("1") votes for each candidate. Ticks and crosses are invalid.
After all valid first preference votes are counted, the quota is calculated.
The quota is the lowest number of votes a candidate needs to be certain of election. Any candidate with votes equal to or greater than the quota will be elected. The quota is calculated by using the 'Droop' formula:
Total formal votes (TFV) 
+1 =  TFV 
+1 = 16.7% (ignore any remainder) 
Number to be elected + 1  6 
For House of Assembly elections, the quota is the minimum number of votes a candidate requires to guarantee he/she is one of the highest five candidates.
If a candidate has more first preference votes than the quota, he/she is declared elected, withdrawn from the scrutiny and his/her surplus votes are distributed to the continuing candidates (as count 2) according to the preferences indicated on each ballot paper.
Surplus = Vote Total  Quota
Only the parcel of ballot papers received by the elected candidate at the last count (last parcel of ballot papers) are used to redistribute the surplus votes. Only in the case where a candidate is elected on first preferences, are all his/her ballot papers redistributed.
If more than one candidate has reached the quota with first preferences votes, these candidates are also declared elected after 'count 1' and withdrawn from the scrutiny before 'count 2' commences.
Ballot papers and votes are different.
Ballot papers are the medium from which candidates receive votes. The original value of a ballot paper is 1 vote, however, this can change during a scrutiny.
To distribute surplus votes the last parcel of ballot papers must have a new (reduced) transfer value. This fractional transfer value is calculated as follows:
Transfer value= 
Surplus votes

(truncate to six decimal places) 
Number of ballot papers in the last parcel 
After each count, the total number of votes counted to each continuing candidate is recalculated. Any continuing candidate who has reached the quota is declared elected and does not continue in the scrutiny.
When more than one candidate is elected with a surplus, each surplus is redistributed in order of election as separate counts.
Once all surpluses have been distributed, the candidate with the fewest total votes is declared excluded, withdrawn from the scrutiny and all of his/her ballot papers are redistributed to continuing candidates.
The exclusion of a candidate can take many counts to complete.
When a candidate is excluded, ballot papers are redistributed in the order, and at the same transfer value, they were received by the excluded candidate. Each parcel of ballot papers is distributed as a new count.
After each count, each continuing candidate's total number of votes is recalculated. Where a continuing candidate reaches the quota, he/she is declared elected and withdrawn from the scrutiny before the next count commences.
Once the exclusion is complete, the surplus of any candidate(s) elected during the exclusion is distributed (in order of election). Otherwise the continuing candidate with the fewest total number of votes is excluded.
The process of distributing surplus votes from elected candidates and excluding the candidate with the fewest votes continues until all vacancies are filled.
In the case of the Tasmanian House of Assembly, the scrutiny stops as soon as five candidates are declared elected.