Industrial Elections Voting Systems

Contents

1. Introduction
2. Choosing a Voting System
3. First-Past-the-Post System
4. Standard Preferential System – Election of One Candidate
5. Standard Preferential System – Election of More than One Candidate
6. Optional Standard Preferential System
7. Multiple Preferential System
8. Proportional Representation System
9. Senate System
10. Points System

1. Introduction

The Fair Work (Registered Organisations) Act 2009 (the Act) requires each registered organisation (that is, trade union and employer body) to include in its rules provision for the election of the holders of its offices. The Act requires an organisation's rules to provide for the conduct of secret ballots, and in most cases, ballots must be conducted by post. In meeting these requirements organisations can choose from a wide range of voting systems. This booklet explains the main features of the most commonly used voting systems and the fundamental differences between them.

There are three main categories of voting systems, namely:

• First past the post;
• Preferential; and
• Proportional representation or quota preferential.

These systems are described in Parts 3 to 10 below.

Within each system there is considerable scope for variation in relation to such matters as the method of marking votes, the definition of a formal or valid vote and the distribution of preferences. This booklet does not attempt to provide an exhaustive account of the variations within the main systems, and it may be the case that the voting rules of a particular organisation do not conform precisely to the description in Parts III to X.

2. Choosing a Voting System

In industrial organisations, as well as in other organisations, the basic aim is to choose a voting system which will ensure the election of the most popular candidates while making it relatively simple for the voter to cast a formal vote. Where voters are to choose between two candidates, the means of determining the most popular is obviously simple. However, where voters are required to choose only one of more than two candidates, or two or more from a larger list of candidates, the measurement of popularity is open to interpretation. Each organisation must assess the individual merits of each of a variety of voting systems in order to choose the one most likely to satisfy its particular needs and which will, at the same time, satisfy the requirements for the conduct of a secret ballot.

The most common method of voting is the "First Past The Post" system in which the candidate who polls more votes than any other candidate is elected – the system used for parliamentary elections in the United Kingdom. Many organisations choose this system principally because of its simplicity. However, a disadvantage of the "First Past the Post" system is that two popular candidates can split the vote, resulting in a less popular candidate winning the ballot.

An alternative approach is to opt for a preferential voting system under which voters must indicate an order of preference among a list of candidates. To be elected under a preferential system a candidate must be preferred by a majority of voters ahead of all unsuccessful candidates. The main disadvantage of preferential voting is the risk of voters inadvertently casting an informal vote by omitting or duplicating a number, especially where the number of candidates is large. However, an organisation can reduce this problem by making provision in its rules to "save" votes which would otherwise be informal due to erroneous marking.

A variation to the concept of preferential voting is the "Points" system in which points are awarded to candidates in direct relation to a voter's expressed preference for them, i.e. a first preference is counted as one point but is worth ten times the value of a tenth preference. In this system the candidate with the lowest number of points is elected. The major drawback of this system is that it is possible for a candidate to be unsuccessful despite receiving an absolute majority (i.e. over 50%) of first preference votes.

A further alternative approach is the "proportional representation" or "quota preferential system". This system also requires voters to indicate an order of preference among a list of candidates, but candidates must secure a quota of votes to be elected. When a candidate is elected with surplus votes over the quota, those votes are transferred on to candidates remaining in the count according to the next preference but at a transfer value of only a fraction of a vote. Proportional representation ensures that minority groups obtain representation according to their relative support. As a consequence, a particular faction or group cannot obtain a disproportionately large number of available positions. Whether this is a desirable outcome or not is a matter for individual organisations to decide. From a practical viewpoint, the counting of votes under proportional representation systems has the disadvantage of being relatively complex and time-consuming.

3. First Past the Post System

Election of one candidate only

1. In this system, a candidate is elected with a simple majority of votes, that is, the highest number of votes in the count, but not necessarily more than half the votes.
2. Voters are required to mark ballot papers by one of the following methods:
   • using ticks;
   • crosses;
   • numbers;
   • striking out the names of candidates for whom they DO NOT wish to vote.
3. The result of a ballot is ascertained by counting the number of votes shown against the name of each candidate – the candidate with the highest number of votes is elected.
4. When only one candidate is to be elected, and there are more than TWO candidates on the ballot paper, it may be that one candidate is so strongly supported that he/she receives more than half the votes. However, it is often the case that a candidate will be elected with considerably less than half the votes.

Election of more than one candidate

5. A similar system for electing more than one candidate is referred to as the block-vote method.
6. Here it is not uncommon for voters to record their votes in a manner set out in a how-to-vote ticket or block.
7. The block-vote method is similar in principle to the "First Past The Post" method. It provides for voters to mark their ballot papers in a manner similar to that outlined above, in which case voters are usually (but not always) required to vote for the exact number of candidates to be elected. The rules of some organisations provide that a ballot paper will be deemed formal if it contains votes for fewer candidates than are to be elected.
8. Votes are counted in the same way as for the election of only one candidate. Successful candidates are those who receive the highest number of votes.
9. A sample tally sheet to elect three candidates is at Table 1, showing an example in which voters have been required to vote for the exact number of candidates to be elected.

Table 1 First past the post system – election of three candidates

Candidates
A	–	200	410	–	–	–	–	9	619	Elected
B	–	200	–	–	79	–	15	–	294
C	150	–	–	67	–	23	–	–	240
D	150	–	–	–	79	–	–	9	238
E	–	–	410	–	–	23	15	–	448	Elected
F	150	–	–	67	–	–	15	–	232
G	–	200	–	67	–	23	–	–	290
H	–	–	410	–	79	–	–	9	498	Elected
Total formal votes	450	600	1230	201	237	69	45	27	2859
Formal ballot papers	150	200	410	67	79	23	15	9	953
Informal ballot papers									47
Total ballot papers									1000

Candidates A, H and E elected.

4. Standard Preferential System

Election of one candidate

1. In this system, a voter is required to indicate a preference for each candidate on the ballot paper by using the numbers 1, 2, 3 etc. up to the number of candidates.
2. A candidate must poll an absolute majority (i.e. in excess of 50%) of all formal votes to be elected.
3. If, after all first preference votes have been counted, no candidate has obtained an absolute majority of all formal votes, then the candidate with the fewest number of first preference votes is excluded (first preference votes are the number 1s). That excluded candidate's second preference votes are then distributed to the remaining candidates.
4. If after that exclusion no candidate has obtained an absolute majority of formal votes, the next remaining candidate with the fewest votes is excluded and ALL of his/her votes (i.e. first preference votes PLUS those votes received from the first excluded candidate) are distributed to the remaining candidates.
5. The above process is continued until one candidate obtains an absolute majority of formal votes and is elected.
6. If at any exclusion, the next available preference is for a previously excluded candidate, then that preference is disregarded and the vote is distributed to the continuing candidate for whom the next available preference is shown.
7. This system of voting is used to elect a (single) member of the House of Representatives. Information on the election of members of the House of Representatives is available from any AEC Office.
8. A sample tally sheet to elect one candidate is at Table 2.

Table 2 Standard preferential system – election of one candidate, absolute majority = 477

	A	B	C	D	E	F	G	H	Total formal votes	Informal ballot papers	Total ballot papers
1st preference votes	112	55	330	18	42	297	39	60	953	47	1000
D excluded – 18 votes transferred	–	3	–	(18)	–	13	2	–
Progressive total	112	58	330	EX	42	310	41	60	953
G excluded – transferred	2	8	4		–	27	(41)	–			41 votes
Progressive	114	66	334		42	337	EX	60	953		total
E excluded –transferred	1	3	7		(42)	6		25			42 votes
Progressive	115	69	341		EX	343		85	953		total
B excluded –transferred	3	(69)	20			6		40			69 votes
Progressive	118	EX	361			349		125	953		total
A excluded – transferred	(118)		57			20		41			118 votes
Progressive	EX		418			369		166	953		total
H excluded – transferred			43			123		(166)			166 votes

5. Standard Preferential System

Election of more than one candidate

1. In this system the first successful candidate is elected in the manner outlined in the Standard preferential system: election of one candidate. When the first candidate is elected all ballot papers are sorted back to first preference votes.
2. Then, all ballot papers containing a first preference vote for the first elected candidate are distributed to the remaining candidates according to the second preference vote on each of them. A candidate receiving an absolute majority of votes remaining is shown in the count as the second successful candidate.
3. If no candidate has then received an absolute majority the candidate with the fewest votes is excluded and his/her votes (first preference and those received from the previously elected candidate) are distributed to the next available preference among the remaining candidates. This process is continued until a candidate has obtained an absolute majority of votes remaining in the count. This candidate is the second elected.
4. After the first and second candidates have been elected all ballot papers are sorted back to first preference votes. The ballot papers containing the first preference votes of the two elected candidates are sorted to the next available preference and are distributed among the remaining non-elected candidates. A candidate receiving an absolute majority of votes remaining in the count shall be the third successful candidate.
5. If no candidate has then received an absolute majority, the candidate with the fewest votes is excluded and his/her votes (first preference and those received from the previously elected candidates) are distributed to the next available preference among the remaining candidates. This process is continued until a candidate has obtained an absolute majority of votes remaining in the count. This candidate is the third elected.
6. If there are more than three candidates to be elected, the above process is repeated until the required number of candidates have been elected.
7. A sample tally sheet to elect three candidates is at Table 3.

Table 3 Standard preferential system – election of three candidates, absolute majority = 477

First election	A	B	C	D	E	F	G	H	Total formal votes	Informal ballot papers	Total ballot papers
1st preference votes	112	55	330	18	42	297	39	60	953	47	1000
D excluded – transferred	–	3	–	(18)	–	13	2	–			18 votes
Progressive	112	58	330	EX	42	310	41	60	953		total
G excluded – transferred	2	8	4		–	27	(41)	–			41 votes
Progressive	114	66	334		42	337	EX	60	953		total
E excluded – transferred	1	3	7		(42)	6		25			42 votes
Progressive	115	69	341		EX	343		85	953		total
B excluded – transferred	3	(69)	20			6		40			69 votes
Progressive	118	EX	361			349		125	953		total
A excluded – transferred	(118)		57			20		41			118 votes
Progressive	EX		418			369		166	953		total
H excluded – 166 votes			43			123		(166)
transferred			461			492		EX	953
F elected
Second election	A	B	C	D	E	F	G	H	Total formal votes	Informal ballot papers	Total ballot papers
1st preference votes	112	55	330	18	42	297	39	60	953	47	1000
F elected – transferred	10	–	5	–	2	(297)	18	262			297 votes
Progressive	122	55	335	18	44	EL	57	322	953		total
D excluded – transferred	–	3	–	(18)	1		2	12			18 votes
Progressive	122	58	335	EX	45		59	334	953		total
E excluded – transferred	1	3	7		(45)		3	31			45 votes
Progressive	123	61	342		EX		62	365	953		total
B excluded – transferred	3	(61)	20				1	37			61 votes
Progressive	126	EX	362				63	402	953		total
G excluded – Transferred	2		4				(63)	57			63 votes
Progressive	128		366				EX	459	953		total
A excluded – transferred	(128)		82					46			128 votes
H elected	EX		448					505	953
Third election	A	B	C	D	E	F	G	H	Total formal votes	Informal ballot papers	Total ballot papers
1st preference votes	112	55	330	18	42	297	39	60	953	47	1000
transferred	10	–	5	–	2	(297)	280	EL			297 votes
Progressive	122	55	335	18	44	EL	319	60	953		total
H elected – transferred	1	2	–	–	–		57	(60)			60 votes
Progressive	123	57	335	18	44		376	EL	953		total
D excluded – transferred	–	3	–	(18)	–		15				18 votes
Progressive	123	60	335	EX	44		391		953		total
E excluded – transferred	4	3	7		(44)		30				44 votes
Progressive	127	63	342		EX		421		953		total
B excluded – transferred	3	(63)	20				40				63 votes
Progressive	130	EX	362				461		953		total
A excluded – transferred	(130)		70				60				130 votes
G elected	EX		432				521		953

F, H and G are elected.

6. Optional Standard Preferential System

1. In this system:

   For the election of one candidate, the voter need only indicate a preference for the candidate of his/her first choice, but may mark a preference for all or some of the remaining candidates on the ballot paper.

   For the election of more than one candidate, the voter may be required to either:

   • indicate a preference for at least the number of candidates to be elected ( voters may indicate a preference for all or some of the remaining candidates) or
   • indicate a preference for less than the number of candidates to be elected.

   That choice will depend upon the requirements of the particular organisation's registered rules.
2. The method of counting the votes is similar to that for the standard preferential system. However, under optional preferential voting, whenever a ballot paper shows no preference for a continuing candidate, that ballot paper is said to be exhausted.
3. A candidate will be elected when he/she obtains an absolute majority of those votes remaining in the count at any stage.
4. A sample tally sheet to elect one candidate is at Table 4.
5. Note that at the completion of candidate H's exclusion, a total of 154 ballot papers have become exhausted, and the number of formal votes remaining in the count is reduced to 799 votes.

Table 4 Optional standard preferential system – election of one candidate

	A	B	C	D	E	F	G	H	Exh*	Total formal votes	Informal ballot papers	Total ballot papers
1st preference votes	112	55	330	18	42	297	39	60	–	953	47	1000
D excluded – transferred	–	2	–	(18)	–	9	1	–	6			18 votes
Progressive	112	57	330	EX	42	306	40	60	6	953		total
G excluded – transferred	–	6	3	–	–	24	(40)	–	7			40 votes
Progressive	112	63	333		42	330	EX	60	13	953		total
E excluded – transferred	–	3	5		(42)	5		25	4			42 votes
Progressive	112	66	338		EX	335		85	17	953		total
B excluded – transferred	–	(66)	5			1		36	24			66 votes
Progressive	112	EX	343			336		121	41	953		total
A excluded – transferred	(112)		30			16		23	43			112 votes
Progressive	EX		373			352		144	84	953		total
H excluded – transferred			40			34		(144)	70			144 votes
C elected			413			386		EX	154	953

*Exh = exhausted

7. Multiple Preferential System

1. The multiple preferential system accomplishes, with one ballot, the election of more than one candidate by a majority number of electors who cast formal votes.
2. The optional multiple preferential system described below is an outline of one variation of this method of voting. The optional system is the most commonly used form of multiple preferential voting in elections for industrial organisations.
3. Under this system, voters are required to mark a preference for at least the number of candidates to be elected. They may, if they wish, express a preference for all or some of the remaining candidates.
4. Votes are classified into two categories:
   • Preferences marked on a ballot paper up to the number of candidates to be elected are called primary votes. They have equal value and are credited to the candidate for whom they are cast, whether they are marked 1, 2, 3 etc. up to the number of candidates to be elected.
   • All preference votes beyond those primary votes are called secondary votes and rank according to their numerical number.
5. The total number of primary votes for each candidate is counted and the candidate having the fewest number of primary votes is excluded from the count and his/her preferences are distributed among the continuing candidates.
6. Ballot papers on which an excluded candidate has obtained a primary vote are examined and distributed to continuing candidates according to the first of the secondary votes expressed on each ballot paper. For example if there are three candidates to be elected, the vote of an excluded candidate will be distributed to number four on the ballot paper. When the distribution of those secondary votes has been completed and new progressive totals obtained for each remaining candidate, the candidate then having the fewest number of votes is next excluded and his/her preferences distributed.
7. All ballot papers in the possession of a candidate at the time of his/her exclusion are transferred to continuing candidates according to the next available preference. This process of exclusions is continued until one more than the number to be elected remain in the count. The lowest ranked of those continuing candidates is then excluded and the remaining candidates are declared elected.
8. At all times care must be taken to ensure that a ballot paper is not transferred to any continuing candidate more than once.
9. Because voters are not required to indicate a preference for all candidates, it is often the case that ballot papers being distributed contain no secondary vote for any continuing candidate. Ballot papers containing no secondary vote for any continuing candidate are deemed exhausted and are added into a total of exhausted votes on the tally sheet.
10. An example of a tally sheet to elect three candidates is at Table 5
11. Note that at candidate D's exclusion the 76 exhausted votes represent 76 ballot papers which contain no secondary vote for any continuing candidate.
12. Some variations to the multiple preferential system are:
    • Marking a preference for all candidates – here voters must express a preference for all candidates on the ballot paper for a vote to be formal. Counting is carried out as previously described with the exception that there will be no exhausted ballot papers.
    • Transferring first preference votes only – only those votes of an excluded candidate's primary votes which were first preference votes are passed on to continuing candidates. Again, it is not necessary to account for exhausted votes.
    • Marking a preference for all candidates and transferring ballot papers only once.
13. Under this variation voters must express a preference for all candidates for their vote to be formal. Primary and secondary votes are as previously described in the optional multiple preferential system, however, ballot papers are not passed between candidates on more than one occasion, but are passed on only once. For the purposes of accounting and balancing at each stage of the count, exhausted and contingent votes are taken into account.

Under this variation:

Exhausted Votes relate to those ballot papers containing a primary vote for a candidate being excluded, and which also contain a primary vote for a previously excluded candidate. Those ballot papers are not transferred on to continuing candidates, but are deemed to be exhausted and set aside as having been finally dealt with.

Contingent Votes at a particular exclusion are those secondary votes received prior to his/her exclusion by the candidate being excluded; that is to say, all ballot papers which, during any previous exclusion, were received by the candidate now being excluded, from a candidate previously excluded. Those ballot papers are not transferred on to continuing candidates a second time, but are set aside as having been finally dealt with.

Table 5 Multiple preferential system (optional) – election of three candidates

First election	A	B	C	D	E	F	G	H	Exh*	Total formal votes	Informal ballot papers	Total ballot papers
1st preference votes	112	55	330	18	42	297	39	60	–	953	47	1000
2nd votes	83	230	50	180	70	20	40	280		953		preference
3rd votes	107	120	142	79	101	95	222	87		953		preference
Total votes	302	405	522	277	213	412	301	427		2859		primary
E excluded – transferred	80	8	14	18	(213)	12	36	45				213 votes
Progressive	382	413	536	295	EX	424	337	472		2859		total
D excluded – transferred	22	28	15	(295)		12	25	117	76			295 votes
Progressive	404	441	551	EX		436	362	589	76	2859		total
G excluded – transferred	19	17	41			108	(362)	80	97			362 votes
Progressive total	423	458	592			544	EX	669	173	2859
A excluded – 423 votes transferred	(423)	18	75			140		60	130
Progressive total	EX	476	667			684		729	303	2859

Candidates H, F and C are elected.

*Exh = exhausted

8. Proportional Representation System

There are several variations of this system. The example below is an outline of the basic procedures for one of those variations.

Under the system of proportional representation a candidate is elected when he/she polls a number of votes equal to or greater than a quota. The voter indicates preferences for candidates by using the numbers 1, 2, 3 etc.

1. A quota is determined as follows:

   Quota = Total number of formal votes = (result) + 1 (disregarding any remainder)

   Number to be elected + 1

2. Candidates receiving a number of first preference votes greater than or equal to a quota are declared elected. Any votes of these elected candidates which are surplus to the quota are transferred to the remaining candidates at a transfer value. If no candidate receives a number of first preference votes greater than or equal to a quota then the candidate with the fewest votes is excluded from the count in accordance with paragraph 8 below.
3. The transfer value determined for the distribution of the surplus votes of a candidate elected from first preference votes is calculated as follows:

   Transfer Value = Number of elected candidate's surplus votes (i.e. those in excess of quota)

   Number of first preference votes received (i.e. the number of ballot papers)

4. The ballot papers of each elected candidate are re-examined (commencing with the candidate with the largest surplus) and the total number of second or next available preferences for each unelected candidate is multiplied by that elected candidate's transfer value. The resultant numbers are in each case the number of votes which are credited to the relevant unelected candidate.
5. Whenever, as a result of the distribution of an elected candidate's surplus votes, a candidate obtains a total equal to or greater than the quota, that candidate is the next elected.
6. The transfer value determined for the distribution of surplus votes of a candidate elected following a transfer is calculated as follows:

   Transfer Value = Number of (this) candidate's surplus votes

   Number of ballot papers received in the last transfer

7. In the transfer of this elected candidate's surplus votes, only those ballot papers received in the preceding transfer from a previously elected or excluded candidate are distributed to unelected candidates. All of those ballot papers are re-examined and the total number of them expressing next available preferences for each unelected candidate is multiplied by that elected candidate's transfer value. The resultant numbers are in each case, the number of votes which are credited to the relevant unelected candidate.
8. Where, after the distribution of all elected candidates' surplus votes has been completed, no other candidate has obtained a number of votes equal to or greater than the quota, the candidate with the fewest votes is excluded from the count. All of the ballot papers held by an excluded candidate are then distributed to the candidates remaining in the count (i.e. all unelected candidates who have not been excluded) according to the next available preference expressed on those ballot papers. These ballot papers are transferred at the transfer value they were received by the excluded candidate.
9. Similar exclusions are carried out until a candidate eventually obtains a number of votes equal to or greater than the quota, and is, as a consequence, elected.
10. The surplus votes of any candidate elected as a result of the transfer of votes from an excluded candidate are dealt with in accordance with paragraphs 6 and 7 above.
11. The process of distributing surpluses and excluding candidates continues as necessary, until either the number of candidates to be elected are elected or all candidates except the number to be elected have been excluded. In the latter case, unexcluded candidates not already elected are declared elected.
12. Where, at any stage in the count, a ballot paper contains no preference for any one candidate remaining in the count, then that ballot paper is deemed exhausted and is set aside as being finally dealt with.

A sample tally sheet to elect three candidates by the method outlined above is shown at Table 6.

Table 7 is a worksheet for determining the transfer values for each elected candidate.

Note that when ballot papers are transferred from an excluded candidate to a continuing candidate, they are transferred at the same transfer value as that at which they were received by the excluded candidate. For example, consider the exclusion of candidate G.

Table 6 shows that 1574 votes have been transferred to continuing candidates. Those 1574 votes are represented by:

• 1221 first preference ballot papers each at value of 1.00 vote;
• 57 ballot papers received from elected candidate B each at value of 0.447464 vote;
• 71 ballot papers received from elected candidate H each at value of 0.145118 vote;
• 231 votes received at candidate A's exclusion;
• 87 votes received at candidate C's exclusion.

However, the 87 votes received at candidate C's exclusion may well be represented by:

Candidate C's exclusion

	Ballot Papers	Value Each	Votes
From C's first preference votes	34	1.00	34
From C's receipt of votes at distribution of B's surplus	45	0.447464	20
From C's receipt of votes at distribution of H's surplus	103	0.145118	15
From A's first preference votes	6	1.00	6
From C's receipt from A of votes originally B's surplus	27	0.447464	12

13. Members of the Australian Senate are elected by a method of proportional representation. Details of the Senate voting system are set out in Part 9.

Table 6 Proportional representation system – election of three candidates

Number of voters 25 000 Quota = 24 880 = 6220 +1 = 6221
Number of formal votes 24 880 3 + 1
Number to be elected 3

A B C D E F G H Exh* Total Informal
formal ballot
votes papers

Table 6 Proportional representation system – election of three candidates

1st preference votes	691	11 259	1084	727	1623	2398	1221	5877	–	24 880	120
B elected – votes transferred	310	(5038)	227	3584	157	226	25	509	–		5038 surplus
Progressive	1001	6221	1311	4311	1780	2624	1246	6386	–	24 880	total
H elected – votes transferred	2	EL	52	6	33	62	10	(165)	–		165 surplus
Progressive	1003	6221	1363	4317	1813	2686	1256	6221	–	24 880	total
A excluded – 1003 votes transferred	(1003)	–	77	559	113	23	231	EL	–
Progressive	EX	6221	1440	4876	1926	2709	1487	6221	–	24 880	total
C excluded – transferred	–	–	(1440)	933	199	221	87	–	–		1440 votes
Progressive	EX	6221	EX	5809	2125	2930	1574	6221	–	24 880	Total
G excluded transferred	–	–	–	731	70	699	(1574)	–	74		1574 votes
Progressive total	EX	6221	EX	6540	2195	3629	EX	6221	74	24880
D elected
Candidates B, H and D elected
*Exh = exhausted

Table 7 Worksheet

Note that votes transferred are calculated to the nearest whole number

Table 7 worksheet

	A	B	C	D	E	F	G	H	Exh*	Ballot papers transferred	Surplus votes transferred
B elected	693	EL	507	8010	351	504	57	1137	–	11259	–
11 259 ballot papers transferred
B transfer	310.08	–	226.86	3584.15	157.05	225.52	25.50	508.76	–	–	5038
value	= 5038 = 0.447464
11259 Actual votes transferred	310	–	227	3584	157	226	25	509	–		5038
H elected – papers transferred	15	EL	356	38	229	428	71	EL	–	1137	1137 ballot
H transfer	2.176	–	51.66	5.51	33.23	62.11	10.30	–	–		165
value	= 165= 0.145118
1137 Actual votes transferred

9. Senate System

The Senate voting system is a proportional representation system and is used to elect members of the Australian Senate. A small number of industrial organisations have also adopted this system for the election of their office-holders. As with other proportional representation voting systems the counting of votes under the Senate system is a complex and time consuming procedure. Only the essential features of the system are outlined in this booklet – further information on the election of members of the Senate is available from any AEC office.

Election of Senators

The essential features of the Senate system of election are as follows:

1. To secure election, candidates must secure a quota of votes. The quota is determined by dividing the total number of formal first preference votes in the count by one more than the number of Senators to be elected for the State or Territory and increasing the result by one.
2. Should a candidate gain an exact quota, he or she is declared elected and his or her ballot papers are set aside as finally dealt with as there are no surplus votes.
3. For each candidate elected with a surplus, commencing with the candidate elected first, a transfer value is calculated for all his or her ballot papers. All those ballot papers are then re-examined and the number showing a next available preference for each of the continuing candidates is determined. Each of these numbers of ballot papers is multiplied by the transfer value. The resulting numbers, ignoring any fractional remainders, are added to the continuing candidates respective progressive totals of votes.
4. Under certain circumstances the transfer of a surplus may be deferred until after an exclusion or bulk exclusion (see step 6.)
5. Where a transfer of ballot papers raises the number of votes obtained by a candidate up to a quota, the candidate is declared elected. No more ballot papers are transferred to that elected candidate at any succeeding count.
6. When all surpluses have been distributed and vacancies remain to be filled, and the number of continuing candidates exceeds the number of unfilled vacancies, exclusion of candidates commences. Bulk exclusions are proceeded with if possible, otherwise exclusions of single candidates take place.
7. Steps (3), (4) and (6) are continued, as necessary, until either all vacancies are filled or the number of candidates in the count is equal to the number of vacancies remaining to be filled. In the latter case, the remaining candidates are declared elected.

Description of Senate Scrutiny

1. At a Senate election a candidate is elected on receiving a number of votes equal to or exceeding a quota. When a candidate is elected with surplus votes over and above the quota, those votes are not wasted, but are transferred on. All of the elected candidate's ballot papers are transferred to continuing candidates according to the next preference but each is regarded as representing only a fraction of a vote. This process continues until the required number of candidates have obtained a quota and are elected.
2. The quota is calculated by dividing the total number of formal ballot papers by one more than the number of candidates to be elected and adding one to the result, disregarding any remainder.

   e.g. Say there are 6 senators to be elected from 248 003 formal votes.

   The quota= 248 003 + 1 = 357 430
   (6+1)

3. For each candidate elected with a surplus of first preference ballot papers over the quota, a transfer value of these surplus ballot papers is calculated by dividing the successful candidate's total of surplus first preference votes by the total number of the candidate's first preference ballot papers.

   e.g. If Smith gains 60 340 votes when the quota is 35 430 the surplus votes total 24 910.

   Their transfer value is 24 910 = 0.4128273118
   60 340

   The result is taken to the eighth decimal point, without rounding.
   So, the transfer value is 0.41282731

4. All ballot papers for the elected candidate are then re-examined and the number of next available preference votes for each of the continuing candidates is determined and multiplied by the transfer value. The resulting numbers, rounded down to the nearest whole number, are added to the continuing candidates' respective numbers of first preference votes.

   e.g. Smith's 60 340 ballot papers gave 33 000 ballot papers to Jones.

   As the transfer value is 0.41282731 Jones receives 13 623 votes.

   (33 000 x 0.41282731); the remainder is ignored.

   Again, a candidate is elected when the number of votes obtained exceeds or equals the quota

5. When a candidate is elected by gaining a quota through a transfer of votes, a transfer value is then calculated for that candidate's surplus. This is done by dividing the surplus votes by the total number of ballot papers the candidate has received (first preferences plus transferred ballot papers).

   e.g. Jones received 22 390 first preference votes and 13 623 votes on transfer, so Jones reaches a quota and is elected with 583 surplus votes.

   The total number of ballot papers received by Jones is 55 390
   (22 390 first preferences + 33 000 transferred from Smith)

   Transfer value is 583 (surplus votes)
   55 390 (total ballot papers received)

   = 0.01052536

   This transfer value is applied to Jones's ballot papers which are then transferred to continuing candidates according to the next available preferences shown on the ballot papers.

6. When transfers have been completed in respect of all candidates who obtained a surplus above a quota as a result of the above procedures, the candidate who has the fewest votes is excluded and that candidate's ballot papers are distributed to the remaining continuing candidates according to the next available preferences. All ballot papers received by the candidate at a particular transfer value are transferred together, beginning with those with a transfer value of 1. The above steps continue until either all vacancies are filled or all candidates except a number equal to the number of vacancies remaining have been elected or excluded. In the latter case unexcluded candidates not already elected are declared elected.
7. In certain circumstances, 2 or more candidates may be excluded simultaneously.
8. A more detailed description of Senate scrutiny procedures are contained in the AEC's publication: Senate Scrutiny Procedures Handbook.

10. Points System

1. In this system, voters are required to mark a preference for all candidates by marking their ballot paper with consecutive numbers (1, 2, 3… and so on).
2. In the examples at Tables 8 and 9, 100 voters are to elect four persons from a total of eight candidates.
3. Usually, one of two methods is adopted for counting the votes, both of which produce identical results, either:
   • Each candidate is allocated a number of points equal to the numerical preference vote he/she receives (i.e. a first preference is counted as one point, a third preference as three points and so on). All the "points" are tallied for each candidate. The four candidates with the fewest number of points are elected.
   This is the system shown in Table 8, or
   • "Points" are applied as follows: a first preference is counted as eight points, a second preference is counted as seven points … and an eighth preference is counted as one point.
   All the "points" are tallied for each candidate. The four candidates with the highest number of points are elected. This is the method shown at Table 9.
4. Note that candidate "D" has obtained 51% of first preference votes, yet under this system of voting is not elected. Candidates B, H, G and F are elected before candidate "D".

Table 8 Points system – election of four candidates

Preferences	1	2	3	4	5	6	7	8	Total no. of prefs	Total points
Candidate A	2	1	2	–	2	40	43	10	100	641
Equivalent points	2	2	6	–	10	240	301	80
Candidate B	7	43	29	18	2	–	–	1	100	270	Elected 1
Equivalent points	7	86	87	72	10	–	–	8
Candidate C	6	1	6	4	6	17	14	46	100	640
Equivalent points	6	2	18	16	30	102	98	368
Candidate D	51	2	1	3	4	2	1	36	100	397
Equivalent points	51	4	3	12	20	12	7	288
Candidate E	2	3	2	5	14	30	40	4	100	596
Equivalent points	2	6	6	20	70	180	280	32
Candidate F	16	5	5	20	50	3	1	–	100	396	Elected 4
Equivalent points	16	10	15	80	250	18	7	–
Candidate G	6	15	25	30	20	3	–	1	100	357	Elected 3
Equivalent points	6	30	75	120	100	18	–	8
Candidate H	10	30	30	20	2	5	1	2	100	303	Elected 2
Equivalent points	10	60	90	80	10	30	7	16
Total	100	100	100	100	100	100	100	100	800	3600

Candidates B,H, G and F elected.

Table 9 Points system – election of four candidates

Preferences	1	2	3	4	5	6	7	8	Total no. of prefs	Total points
Candidate A	2	1	2	–	2	40	43	10	100	259
Equivalent points	16	7	12	–	8	120	86	10
Candidate B	7	43	29	18	2	–	–	1	100	630	Elected 1
Equivalent points	56	301	174	90	8	–	–	1
Candidate C	6	1	6	4	6	17	14	46	100	260
Equivalent points	48	7	36	20	24	51	28	46
Candidate D	51	2	1	3	4	2	1	36	100	503
Equivalent points	408	14	6	15	16	6	2	36
Candidate E	2	3	2	5	14	30	40	4	100	304
Equivalent points	16	21	12	25	56	90	80	4
Candidate F	16	5	5	20	50	3	1	–	100	504	Elected 4
Equivalent points	128	35	30	100	200	9	2	–
Candidate G	6	15	25	30	20	3	–	1	100	543	Elected 3
Equivalent points	48	105	150	150	80	9	–	1
Candidate H	10	30	30	20	2	5	1	2	100	597	Elected 2
Equivalent points	80	210	180	100	8	15	2	2
Total	100	100	100	100	100	100	100	100	800	3600

Candidates B,H, G and F elected.