## Sunday, January 22, 2006

### One-vote-one-value Calculating the Transfer value and segmentaton of the propotionalo representaton count - discussion paper

This paper seeks to address a number of issues related to the mechanics and formulas used in counting of multimember proportional representation ballots with the aim of establishing a one vote one value voting system

The following Issues of concern have been identified

1. Calculating the Transfer Value

2. Segmentation and distribution of votes allocated to candidates who are excluded from the count

1. Calculating the Transfer Value

The current formula used to calculate an elected candidate's surplus is seriously flawed and MUST be reviewed before the Sate Government implements a system of proportional representation. The greater the number of candidates to be elected the greater the distortion in the one vote one value principle.

This submission seeks to highlight and address issues related to the formula used in calculating the transfer value used in distributing and counting proportional representation election as it currently applies to the Australian Senate, Victoria's new Upper house and Victoria's Local Government Act.

This submission seeks review and calls on the State Government to amend current legislation so as to maintain the one vote one value principle and correct calculation of the proportionality of the vote.

This submission outlines for comparison two models used in calculating the Transfer value.

1) The method used by the Victorian Electoral Commission (VEC) as outlined in the current legislation and

2) The preferred Alternative method that takes into account the proportional value of each vote and the candidate's surplus.

Existing legislation and current formula used by the Victorian Electoral Commission (VEC)

The Victorian State Government adopted the use of Proportional Representation as a method of electing Local Government Councillors to multi-member electorates and has also proposed in electing members of the new State's Legislative Council in Victoria

The VEC uses the current system and adopted formula (see below) mainly to "simplify" the counting process.

The problem that exists with the system used by the VEC is that it does not support the "One vote - One value" principle in that each vote is not transferred at a value equal in proportion to every other vote.

Each vote should be equal in value but with the system currently adopted there is a serious distortion in the value of the vote that has already been attributed to elected candidates and subsequently re-valued in the transfer of any surplus

The formula currently used to calculate the "Surplus Transfer Value" is value of the candidate's surplus (Sv) divided by the total number of ballot papers (P) received by the candidate (Sv/P).

On the face of it this formula appears to provide for the proportional allocation of a candidates surplus and, yes, this is the case in respect to votes if those votes are all of equal value.

The problem with the current formula is that it seriously distorts the calculation of the transfer value when a candidate's surplus is made up of votes allocated to the candidate of different values (i.e. votes received from an earlier transfer of a candidates surplus.)

The formula used by the VEC distributes each ballot paper at the same value even though some ballot papers have different values allocated to them then other votes. As a result of this distortion used ballot papers originating form previously elected candidates' that have a lower value are inflated at the expense of votes of a higher value that are devalued when calculating the value of any new surplus transfer.

The distortion in the value of the vote can and will produce a different outcome and result of the election, as is outlined in the example count sheet below.

Whilst the VEC might try and argue that the overall outcome is still the same (and yes the result may be the same) this is not always the case.

The likelihood of the system distorting the outcome of the election is significantly increased in Municipal elections where the voter sample is smaller in number. The bigger the voter sample the less chances of the results being different.

The impact of this distortion is further exacerbated with an increase in the numbers of candidates to be elected, as would be the case in an un-subdivided municipality.

This impact of this distortion is significant when determining the result of the ballot, where there are two or more candidates with the same value of allocated votes during the count. The value and correct weighting of the vote determine the order of elimination and election. Depending on which candidates votes are distributed, and in what order, the election result can change based on the formula used.

The main objection to the system currently outlined in current legislation and used by the VEC is that it distorts the "One vote – One value" principle in that some votes have a disproportional value of votes to other votes that should be equal. The current system favours major political parties whose votes will increase in value at the expense of votes allocated to minor candidates.

The Alternative method/formula.

There is a very simple correct alternative formula that should be used in the calculating of the transfer value.

The "Surplus" (S) value divided by the "Candidates Total Value' of votes (Ctv) and then multiplied by the value of the vote (Vv) allocated. (S/Ctv*Vv)

This formula supports the "One Vote – One Value" principle and is easily calculated and maintains the correct proportionality of the vote as opposed to the distortion that exists within the formula used by the VEC/LGA.

Example:

Below is an example count sheet demonstrating the differences in the two systems.

The example is based on a small voter sample of 1800 votes. The number of candidates to be elected is three and the quota has been calculated at 1800 divided by 4 = 450. There are five candidates A, B, C, D, E and their preference allocations is as follows:

 Candidate A Pref 1,2,3,4,5 Candidate B Pref 2,1,5,4,3 Candidate C Pref 2,3,1,4,5 Candidate D Pref 3,4,5,1,2 Candidate E Pref 5,4,3,2,1 and 2,3,4,5,1

The Primary vote received by each candidate was: (Shown in numerical order for clarity)

# Candidate

Candidate A

600

Candidate B

350

Candidate C

300

Candidate D

300

Candidate E

255

Candidate A had received in excess of a quota and was declared elected and the value of the surplus votes was calculated and allocated to the next candidate in order of preference. As this was the first transfer of a Surplus the original value of the votes used was at full value (1). In this case the calculation of the Transfer value of the votes is the same using both the VEC and the Alternative formula.

 No of Ballot Papers (P) 600 Value of Vote (Vv) 1 Candidates Total Vote (Ctv) 600 Quota (Q) 450 Surplus (S) 150 Transfer Value (Tv) 0.250 Tv x P 150

The allocation of Candidate A's surplus vote (150) to Candidate B elects Candidate B and inturn provides a second surplus value that needs to be distributed.

It is at this point that the difference between the two formulas becomes apparent.

Surplus Transfer of B
(Alternative formula)

# VEC Formula

Primary Vote

Surplus of Candidate B received from Candidate A

No of Ballot Papers (P)

350

600

950

Value of Vote (Vv)

1

0.250

Candidates Total Vote (Ctv)

500

500

Quota (Q)

450

450

Surplus (S)

50

50

Transfer Value (Tv)

0.100

0.025

0.053

Tv x P

35

15

50

### Formula

((Ctv-Q)=S) / Ctv * Vv

((Ctv-Q)=S) / P

As shown the use of the VEC formula has devalued the value of Candidate B's primary vote and inflated the proportional value of the surplus received from Candidate A destroying the "One Vote – One value" principle. Where as in the Alternative formula the proportional value of the vote is maintained – thus maintaining the "One vote – One value principle"

If we view the full count sheet for each system.

Count Sheet - Alternative Model - Correct weighted vote value

 Quota 450 Elected 0 1 2 3 Candidate A 600 Quota Candidate B 350 500 Quota Candidate C 300 300 315 440 440 Candidate D 300 300 335 460 Quota Candidate E 250 250 250 Elimin Remainder 10 1800 1800 1800 1800

Candidates A, B and D declared elected. – maintains One vote – One value principle

Count Sheet - VEC model.

 Quota 450 Elected 0 1 2 3 Candidate A 600 Quota Candidate B 350 500 Quota Candidate C 300 300 332 457 Quota Candidate D 300 300 318 443 Candidate E 250 250 250 Elimin Remainder 10 1800 1800 1800 1800

Candidates A, B and C declared elected. – does not fulfil One vote- One value principle

2. Segmentation and distribution of votes allocated to candidates who are excluded from the count

The other issue of concern related to the current method of counting the ballot and system of proportional representation is the distribution segmentation of ballot papers in redistributing votes allocated to candidates for are subsequently excluded during the count.

Aggregated segmentation

Under the current provisions ballot papers allocated to a candidate that is to be excluded from the count are segmented and redistributed according to a predetermined prescribed order.

The first transaction is the distribution of Primary "first preference" ballot papers allocated to the candidate to be excluded

Second and subsequent transactions based on the value of any other ballot papers (from highest value to lowest value) to be distributed. This includes secondary-primary votes (primary votes that came to a candidate via a second or lower preference distribution) and ballot papers received as a result of a previous transfer of a candidate surplus (if any).

All ballot papers that have the same value are collated and distributed in a single transaction.

There is a strong argument against the validity and need for the segmentation of distribution which can produce a different outcome in the results of the election.

Of particular concern is the aggregated distribution of secondary-primary votes which when used in conjunction with the current paper-based-formula, used to calculate the surplus transfer value, can change the order of election.

This system was designed and adopted to ease the manual counting of ballot papers and in doing so limit the number of separate transaction calculations required. It was also adopted to minimise the extent of distortion arising from the method used to calculate the surplus transfer value (as outline above)

It was at the time considered a reasonable trade off to be able to quickly determine the result of an election were counting of the ballot was done manually.

The requirement for segmentation is reduced where the counting of the ballot is undertaken with the aid of computer technology and where the calculation of the surplus transfer value is based on the value of the vote as opposed to the number of ballot papers (see above).

Alternative Methods:

1. Single Transaction option

All ballot papers belong to a candidate could be transferred in one single transaction (no segmentation).

This is a simpler and cleaner approach then the method of segmentation currently used it is based on the assumption that the distribution of votes allocated to the candidate to be excluded is distributed simultaneously. With the use of computer technology in the counting of the ballot a single transaction system could readily be implemented without the need for segmentation. - One transaction per candidate.

2. Full Segmentation – First in First out

If segmentation is to be retained then the preferred method is to segment and distribute each parcel of ballot papers determined by the order in which the ballot papers were received - First in first out. This option would require multiple transactions and with the aid of computer technology can readily be implemented. This option is preferable to the current system of aggregated segmentation and distribution of votes of the same value.

3. Single Transferable Vote by Meeks Method

Another alternative, preferable to the existing aggregated segmentation system. would be use the "Meeks Method" of distribution. The "Meeks method" is currently used in New Zealand elections and involves a comprehensive re-iterative distribution of preferences. New Zealand - Department of Internal Affairs: STV Information - Meek's Method

Conclusion/Recommendation

1. The formula, as currently legislated, used to calculate the Surplus Transfer value (Tv) MUST be changed so as to provide for a one vote one value voting system whilst correctly calculating the proportional value of the vote. The formula used must be based on the proportional value of the voting papers as opposed to just the number of ballot papers to be distributed (see item 1 above)

2. The `current system of segmentation in the distribution of the preferences should be reviewed with the any of the three alternative methods as outlined above be adopted in preference to the system currently in use. (see Item 2 above)