A fair voting system

Preferential voting

If a candidate in an election does not achieve a majority of first preference votes, the winner is determined by the allocation of subsequent second, third and so on preferences.

How Preferential voting works: 

There are two systems of preferential voting: Full preferential and optional preferential voting.  With full preferential voting, voters are required to indicate their first preference by placing a “1” against a candidate’s name, then make a second preference and so on for the number of candidates on the ballot paper.  Optional preferential voting only requires the voter to make a first preference.

If a candidate does not get an absolute majority of first preference votes, then the candidate with the least number of votes is eliminated and those votes are allocated to the other candidates according to the number of second preference votes.  If no majority has been achieved, the next candidate with the least number of primary votes is eliminated and those votes are allocated to other candidates according to the second preference or third preference and so on if the second preferences have been exhausted.

Supporters of preferential voting say:

  1. The winning candidate is the most preferred or least disliked candidate by the entire electorate.
  2. Voters who support minor parties know that their votes will count towards deciding the winner.
  3. Parties sharing overlapping philosophies and policies can assist each other to win.

 Opponents of preferential voting say:

  1. Vote counting is complex under current manual procedures.
  2. The process is costly and time consuming, potentially delaying a result.
  3. Some people don’t like having to choose more than one candidate.
  4. Preferential voting makes voting more difficult.  Some people do not like having to rank their preference of candidates.  They either neglect to do so or make mistakes, leading to higher levels of informal voting.
  5. Some people do not like being forced to make a preference for candidates they do not support.
  6. A candidate not supported by most of the electorate could still win.

What do you think?  Have your say.  Join the conversation below.

 

Drawing of Electoral Boundaries

Sometimes people find themselves in a new electorate when voting comes around.  That’s because electoral boundaries - approximately 100,000 people within an area - are sometimes changed to reflect changes in the movement of people and the demographic makeup of the area.  Electoral authorities regularly hold hearings to review boundaries. Political parties are not allowed to participate in the hearings so as to avoid the perception of manipulation of the system in their favour.  Some people do not think electoral boundaries are being decided fairly.

What do you think?  Have your say.  Join the conversation below.

 

How we vote 

Postal voting

Postal voting is designed for people who cannot attend a polling place in their electorate.  

How voting works:

Once a person has voted, the ballot paper is placed in a sealed envelope which does not contain any voter identification, and then is placed in another sealed envelope that contains the name and address of the voter.  When it is received by the electoral authority the outside envelope is used to confirm the person has voted. The ballot paper is removed from the inside envelope and place in a pile for counting. The system is designed so the identity of the voter cannot be linked to the ballot paper, thus ensuring tick the person’s vote is anonymous.

Opponents of postal voting claim that the system is open to abuse because votes can be tampered with and there is nothing stopping the voter’s personal details being copied. 

What do you think?  Have your say.  Join the conversation below.

Early voting

Early voting is officially known as 'Pre-Poll' voting -- voting before the actual day of the election or poll.  When voting early, voters are required by law to give a valid reason for their request to vote before election day.

How early voting works:

For the 2019 federal election, early-voting or pre-poll voting centres opened in each electorate three weeks before election day in metropolitan areas and two weeks before election day in rural areas. 

According to AEC figures, 2980498 people voted early for the 2016 federal election.  In 2019, 4766853 people voted early -- a 60% increase in early voting compared with the 2016 election. 

Vote Australia recognises that early voting is convenient for those who need it.  Should all voters be allowed to vote before all issues have been fully debated?

What do you think?  Have your say.  Join the conversation below.

COMMENTS

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  • Peter Newland
    commented 2021-11-12 20:40:04 +1100
    It’s great to see Borda seriously considered as in Erik Jochimsen’s PLERS!

    Before commenting on improvements necessary for PLERS, readers may like to try out my new interactive spreadsheet at https://tinyurl.com/ElectionReformOz. It allows easy comparison to contrast and compare different vote counting sytems. It covers the main voting systems including Borda – of which PLERS is a variant, as is my DCAP system.

    In a Preferential voting election where ALL preferences are filled in, Borda, PLERS and DCAP give exactly the same relative results. The main difference is that DCAP uses a metric which is more meaningful to voters because it rates each candidate with the percentage of voters who put that candidate in the top 50% of candidates.

    However, with Optional Partial Preferential Voting, DCAP maintains exact linearity by “NORMALISING” each partial vote to fill all preferences left blank with a totally fair preference value that rigorously maintains the one-vote-one-value standard. To the best of my knowledge Borda and PLERS do not do that. PLERS makes an improvement by filling in blanks with the value of the worst preference number, but that diverges from strict linearity.

    DCAP also has rigorous algorithms to linearly translate normalised CANDIDATE preferential Votes into normalised PARTY preferential votes to allow fair multi-member Proportional Representation. E.g., this will fix the shocking 12% error rate in the 2020 ACT election when 3 of the 25 MLAs elected were elected despite preferences proving that three of the eliminated candidates beat the three wrongly elected by the flaws inherent in traditional voting systems.

    Now specific comments on PLERS:
    PLERS would be improved with modifications to give fair interpretation of votes which may otherwise be treated as informal, expiring, or exhausting after the first few preferences.

    PLERS’ technique of replacing all blanks in Optional Preferential Votes with the preference value for the least preferred candidate changes PLERS from strictly linear to non linear because it unfairly biases against all the candidates who are not preferenced. Consideration of the PLERS example 2, 3 and 4 illustrates how ‘normalisation’ would improve PLERS.

    PLERS Example 2 can be written: A:B:C:D:E:F = :2::1:3:4. PLERS says:
    “Candidates A and C have not been given a preference, so are considered equally last. “
    But what is equal last? Equal last is not a preference rating 6 out of 6, or 5 out of 6 for both A and C. A fair representation is to allocate (or “normalise”) that to 5.5 each, so that A:B:C:D:E:F becomes 5.5:2:5.5:1:3:4.

    Note that if Candidate F was also not preferenced in the original vote (i.e. :2::1:3:-) then A to F would normalise to 5:2:5:1:3:5. The key to normalising is that the sum of the preference numbers in a normalised vote must add to the same as the sum of the numbers from 1 to the number of candidates. If votes aren’t correctly normalised, then the count is no longer precisely linear.

    PLERS Example 3: A:B:C = 3:2:-
    If there was a tie between Candidate A and B then this vote clearly favours B and should be permitted to count in a tie-break. Hence the fairest solution is to normalise this vote to A:B:C = 2:1:3, rather than declaring the vote informal. The objective of normalisation is to minimise wasted votes and to make a fair and just system.

    PLERS Example 4: A:B:C:D:E:F = 1:Not You:4:3:3:2
    If there was a tie between Candidate D or E and any other candidate it is just and fair to allow that vote to support C or D. Similarly, if there is a tie between C and any other candidate except B, this vote clearly rates C as not worse than 4th, certainly not 5th or 6th . Hence this vote can and should be allowed to influence the result. Hence the fairest solution is to ‘normalise’ this vote to A:B:C:D:E:F = 1:6:5:3.5:3.5:2.

    Such normalisation is easily done by simple computer algorithms as a vote is lodged on-screen or as a ballot-paper is scanned.

    Note that if PLERS were to use normalisation, then the PLERS candidate ranking would be the same as my DCAP ranking, though expressed in a different metric. The DCAP metric gives the percentage of voters who rank a candidate’s (Candidate Acceptance Percentage) in the top 50% of candidates. DCAP rankings of: 100%; 50%; and, 0%, corresponds to: Unanimous 1st Preferences; an average preference of (N+1)/2; and, Unanimous last preference: or in PLERS Ranking that corresponds to: N; N/2; and, 0.

    So effectively DCAP and PLERS are directly equivalent apart from DCAP’s use of normalisation to put partial and full preferential votes on an equal footing.

    Normalisation has the distinct advantage that it facilitates SPLIT Partial Preferential Voting where a voter faced with say 31 Parties fielding say 101 candidates (as in a Federal Senate Election in proportional representation of HSW’s 6 Senators), then voters can choose to vote, for example, using preference numbers 1, 2, 3, 4, 5, 6, 7 for their first few preferences then finish with 25, 26, 27, 28, 29, 30, 31 for the Parties they detest while omitting the preference numbers 8 to 24 for the Parties they know nothing about. The normalisation algorithms then fill in all the blank preference numbers on that vote with the “don’t know, don’t care” value of 16 (the average of the missing numbers).

    This normalisation process is described in more detail in documents describing my DCAP vote counting system at https://tinyurl.com/ElectoralReformOz. Normalisation is totally fair when any blank preference numbers and resolvable anomalies (e.g., as in PLERS Examples 3 and 4 above) are normalised so that the sum of the normalised preference numbers (allocated to each candidate in the vote being normalised) equals the sum of the numbers from 1 to the number of candidates, (i.e. Sum=N*(N+1)/2 where N is the number of candidates).

    In multi-member electorates, when voting for Candidates but attempting to achieve proportional representation of Parties, things get messy. It is oxymoronic (probably worse) to (allegedly) expect fair proportional representation from laws allowing optional preferential voting for Candidates rather than voting for Parties. PLERS appropriately calculates the proportional representation of each party by limiting each Party to the same number of Candidates being considered. However, this would be more accurate with normalisation which can then be applied (as in DCAP) to Parties with any number of Candidates giving more accurate, more linear results.

    Concerning linearity, see my DCAP documents showing that Hare-Clark exaggerates the non-linearity of the eliminate-distribute (instant-run-off?) method of ‘counting’. For example, I’ve proved that in the ACT 2020 election, 3 of the 25 MLAs elected would have lost a one-on-one run-off election against a Candidate from a different Party who was eliminated in the (so-called) ‘count’ for their electirate. That could have far-reaching effects on whether a government actually earned the right to govern. Fortunately, the ACT 2020 the results were not even close. However, the non-linearity of current preferential vote ‘counting’ methods increases greatly as the candidates are more evenly matched, giving more chaotic results.

    This applies in single-member electorates and even more so in multi-member electorates.

    Election theory needs an overhaul. Arrow uses some poor assumptions and hence made wrong conclusions. E.g., Borda fails Arrows tests, but the fact is that Arrow failed to realise that Borda is absolutely correct in all circumstances where there is full preferential voting. And that’s why normalisation is necessary for accurate linear results using optional preferential voting.

    Pundits say that Borda fails Arrow’s criteria, but I’ve proven Arrow wrong by showing that a narrow absolute majority may hide the fact that far more voters would be more accepting of a different candidate while the nominal absolute majority ‘winner’ was a far more convincing winner, on preferences, of the wooden spoon as the least preferred candidate. Why is it so? The problem is that current vote ‘counting’ systems are obsessed with first and near first preferences while totally ignoring last or near-last preferences which are, not always, but in some cases, more important if we want to achieve more stable consensus government.

    A clear but extreme example is where there are 4 candidates where Candidate A gets 51% of first preferences but 49% of last preferences and another candidate gets zero% first preference but D gets 100% of second preferences. Then, no matter what other preferences Candidates B and C get, it is clear that D is actable to 100% of voters while A is unacceptable to 49% of voters and does not deserve election despite a narrow ‘absolute majority’. That’s why Borda is right and Arrow is wrong. My spreadsheet shows exactly that example – and allows readers to try other combinations also.
  • Erik Jochimsen
    commented 2021-11-02 22:16:15 +1100
    I have designed a voting system called the “Preferential Linear Electoral Ranking System” (PLERS) which is a means of achieving the benefits of preferential voting, without its complexity and shortcomings.

    I have gone through the steps and now have PLERS on a website.

    The address is www.netspeed.com.au/erikjoch

    My aim is to have this system replace our current Australian government voting systems.

    Regards Erik Jochimsen
  • Peter Newland
    commented 2021-08-23 20:54:27 +1000
    Troy Arnould: In answer to your question: it is secret voting. However, one of the safeguards against electoral fraud protocols I proposed could allow a person to choose to reveal their vote but only by choosing to have a receipt printed and then admitting that the receipt in their possession was their own vote receipt. But nothing on the receipt identifies the voter: it only identifies the place of voting and a unique random number that does not even identify the time of voting. That’s all now detailed in the url link spelled out in words in my previous comment, but I updated security recommendations some weeks ago.

    Also, since my original comment, I have better understood and explored the theory behind what began as an empirical approach that worked – but I wasn’t sure why. All I knew was that it was wrong to be obsessed with 1st preferences when sometimes last preferences were more important. Now I have changed the name from APR to DCAP. Candidate Acceptance Percentage is, in FACT, the exact Percentage of voters who Accepted the Candidate as being in the top 50% of Acceptable Candidates.

    Further, I was surprised to prove that Arrow’s Impossibility Theorem is wrong, and that my DCAP counting method guarantees to give a fair result in all cases. DCAP gives the same results as the Borda count of a FULL preferential voting election, but DCAP expresses the result in a consistent user-friendly way.

    In addition, DCAP easily and fairly handles PARTIAL Preferential Voting as well as SPLIT-Partial preferential voting. SPLIT Partial preferential voting makes it far easier for voters faced with, e.g., 123 candidates from 31 Parties to choose from to elect 6 Federal Senators for NSW. Currently, voting 1-6 for your top 6 Parties risks having zero say over who wins Senator 5 or 6 and hence who may hold the balance of power. But voting 1 to 31 Parties in order of preference is very difficult, let alone preferencing 123 Candidates. in order of preference. To overcome this, a SPLIT vote allows voters to vote (e.g.) 1-7 for their favourite Parties and 25 to 31 for their least favourite parties without having to preference the many micro parties they know nothing about. DCAP allows split votes to be counted fairly, and even to automatically correct voting errors where a voter’s intention is clear.

    DCAP is totally immune to strategic voting: even if a voter voted 1-7 and 93 to 99 for 31 parties, DCAP algorithms automatically translate 93 to 99, to 25 to 31. So, voters collectively get what they voted for, with no strategies available to distort a vote. However, no vote is ever immune from Party, Media or Government misinformation and propaganda.

    Borda is often criticised (by Arrow theory, and by numerical example) as being capable of ignoring an absolute majority. The same applies to DCAP and to its previous guises as: APR (Average Preference Rating); WPC (Weighted Preference Counting); or, CPV (Consensus Preference Voting). Until recently, I conceded that an absolute majority should override WPC/APR/Etc.
    I was wrong.
    Borda/WPC/APR/DCAP override very narrow absolute majorities ONLY, repeat O N L Y when that is in fact the BEST result. This can only happen when the ‘winner’ has a minuscule absolute majority margin compared while that ‘winner’ more strongly deserving the ‘wooden spoon’ as the MOST DISLIKED candidate on preferences.

    Other ‘counting’ methods suffer from erratic tipping points and that’s why they can and do get it wrong – often when it matters most in determining the last one or two candidates elected in multiple representative electorates where such winners often hold the balance of power. In contrast, Borda and DCAP are totally ‘linear’: i.e., they have no sudden tipping points, where changing one vote can tip preferences towards a totally different candidate. This is because Borda and DCAP never eliminate candidates, never distribute preferences, they fairly take into account all preferences for all candidates, in filling all vacancies and every vote has the same say over every vacancy.

    Current eliminate & distribute ‘counting’ methods are inherently flawed: they can not guarantee fair results; plus they facilitate strategic voting trying to game the system.
    Further, some claim that partial preferential voting (but not SPLIT partial preferential voting) skews the system in favour of larger parties. In contrast, DCAP actually guarantees a “fair voting system”.

    Why the D in DCAP?
    DCAP results can seem extremely counter-intuitive. E.g.: With 4 candidates, DCAP will correctly declare candidate D, with ZERO first preferences but 100% 2nd preferences, as the CLEAR STRONG DCAP winner with a DCAP score of 66.67% despite: Candidate A getting an ‘absolute majority’ with 51% of first preferences, but with a DCAP of only 51% due to A’s getting the largest share, 49%, of 4th-or-last preferences; and Candidate B getting 25% of both 1st and last preferences; and, C receiving 24% of first preferences.

    Although absolutely correct, this DCAP result is counter-intuitive and contrary to Arrow’s Impossibility Theorem. Hence the ‘D’ in DCAP to acknowledge that my D’Nalwen Certainty Theorem and DCAP guarantees a fair election counting method, and disproves Arrow’s so-called “Impossibility Theorem”, D’Nalwen being my surname in reverse. Full details are in the url link in my previous comment.
  • Troy Arnould
    commented 2021-08-23 09:50:39 +1000
    Does it allow for secret voting or are all votes associated to a user and searchable/traceable?
  • Cayden
    followed this page 2021-06-15 10:17:44 +1000
  • Peter Newland
    commented 2021-06-04 08:44:15 +1000
    The statement: “The winning candidate is the most preferred or least disliked candidate by the entire electorate” is simply incorrect as can be easily proved. The fact is that the preferential voting system is seriously flawed because it effectively ignores last and near-last preferences.

    Now preferential VOTING is the best system available. Period. However: the so-called ‘counting’ method is seriously biased towards 1st preferences while totally ignoring last preferences. The result is that a candidate can “win the wooden spoon” as being the MOST DISLIKED candidate by a healthy margin and YET be declared the ‘winner after preferences’ by a narrow margin.

    This is proved in simple numerical examples at https colon slash slash tinyurl dot com slash ElectoralReformOz all one word. This is not just an obscure theoretical problem: it is a real issue that can and does gets candidates elected AGAINST the voters preferences. The above link shows that 3 of the 25 MLAs elected in the 2020 ACT election were elected against voters preferences – and the link names those wrongly elected and those wrongly eliminated including giving the exact counts showing how the eliminated candidate won against the ‘elected’ candidate in a virtual one-on-one run-off election as determined by the actual preference votes at the ElectionsACT website.

    The link also introduces the authors Average Preference Rating (APR) system of fairly counting preferential votes to guarantees to always exactly follow whatever preferences voters have marked. APR allows SPLIT Partial Preferential voting which allows voters to mark their first few, and their last few, preferences: the SPLIT option makes it easier for voters faced with ballot papers such as vote 1-32 Above the Line, Or 1-140 below the line.

    APR is very VERY fast to count provided that all votes are SCANNED &/OR DIGITISED. Votes could be scanned on site and a VERY small file uploaded from each polling place and amalgamated very quickly at the main electoral office. The reason for the small file size and speed of counting is that no votes are ever distributed, every preference mark is taken into account and the system is totally fair. The system easily allows multiple parallel audit trails that make election fraud extremely difficult – it ist even possible to allow a voter to check that their particular vote was actually counted and recorded correctly in the count by using unique random vote IDs generated when the voter votes – plus candidates, parties and media could get near real-time info re individual polling booths or electorate tallies as votes are counted. The system allows even a close Australian Federal Senate Election results to be available within hours of polls closing.
  • Peter Newland
    followed this page 2021-06-04 08:44:11 +1000

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  • commented on A fair voting system 2021-11-12 20:40:04 +1100
    It’s great to see Borda seriously considered as in Erik Jochimsen’s PLERS!

    Before commenting on improvements necessary for PLERS, readers may like to try out my new interactive spreadsheet at https://tinyurl.com/ElectionReformOz. It allows easy comparison to contrast and compare different vote counting sytems. It covers the main voting systems including Borda – of which PLERS is a variant, as is my DCAP system.

    In a Preferential voting election where ALL preferences are filled in, Borda, PLERS and DCAP give exactly the same relative results. The main difference is that DCAP uses a metric which is more meaningful to voters because it rates each candidate with the percentage of voters who put that candidate in the top 50% of candidates.

    However, with Optional Partial Preferential Voting, DCAP maintains exact linearity by “NORMALISING” each partial vote to fill all preferences left blank with a totally fair preference value that rigorously maintains the one-vote-one-value standard. To the best of my knowledge Borda and PLERS do not do that. PLERS makes an improvement by filling in blanks with the value of the worst preference number, but that diverges from strict linearity.

    DCAP also has rigorous algorithms to linearly translate normalised CANDIDATE preferential Votes into normalised PARTY preferential votes to allow fair multi-member Proportional Representation. E.g., this will fix the shocking 12% error rate in the 2020 ACT election when 3 of the 25 MLAs elected were elected despite preferences proving that three of the eliminated candidates beat the three wrongly elected by the flaws inherent in traditional voting systems.

    Now specific comments on PLERS:
    PLERS would be improved with modifications to give fair interpretation of votes which may otherwise be treated as informal, expiring, or exhausting after the first few preferences.

    PLERS’ technique of replacing all blanks in Optional Preferential Votes with the preference value for the least preferred candidate changes PLERS from strictly linear to non linear because it unfairly biases against all the candidates who are not preferenced. Consideration of the PLERS example 2, 3 and 4 illustrates how ‘normalisation’ would improve PLERS.

    PLERS Example 2 can be written: A:B:C:D:E:F = :2::1:3:4. PLERS says:
    “Candidates A and C have not been given a preference, so are considered equally last. “
    But what is equal last? Equal last is not a preference rating 6 out of 6, or 5 out of 6 for both A and C. A fair representation is to allocate (or “normalise”) that to 5.5 each, so that A:B:C:D:E:F becomes 5.5:2:5.5:1:3:4.

    Note that if Candidate F was also not preferenced in the original vote (i.e. :2::1:3:-) then A to F would normalise to 5:2:5:1:3:5. The key to normalising is that the sum of the preference numbers in a normalised vote must add to the same as the sum of the numbers from 1 to the number of candidates. If votes aren’t correctly normalised, then the count is no longer precisely linear.

    PLERS Example 3: A:B:C = 3:2:-
    If there was a tie between Candidate A and B then this vote clearly favours B and should be permitted to count in a tie-break. Hence the fairest solution is to normalise this vote to A:B:C = 2:1:3, rather than declaring the vote informal. The objective of normalisation is to minimise wasted votes and to make a fair and just system.

    PLERS Example 4: A:B:C:D:E:F = 1:Not You:4:3:3:2
    If there was a tie between Candidate D or E and any other candidate it is just and fair to allow that vote to support C or D. Similarly, if there is a tie between C and any other candidate except B, this vote clearly rates C as not worse than 4th, certainly not 5th or 6th . Hence this vote can and should be allowed to influence the result. Hence the fairest solution is to ‘normalise’ this vote to A:B:C:D:E:F = 1:6:5:3.5:3.5:2.

    Such normalisation is easily done by simple computer algorithms as a vote is lodged on-screen or as a ballot-paper is scanned.

    Note that if PLERS were to use normalisation, then the PLERS candidate ranking would be the same as my DCAP ranking, though expressed in a different metric. The DCAP metric gives the percentage of voters who rank a candidate’s (Candidate Acceptance Percentage) in the top 50% of candidates. DCAP rankings of: 100%; 50%; and, 0%, corresponds to: Unanimous 1st Preferences; an average preference of (N+1)/2; and, Unanimous last preference: or in PLERS Ranking that corresponds to: N; N/2; and, 0.

    So effectively DCAP and PLERS are directly equivalent apart from DCAP’s use of normalisation to put partial and full preferential votes on an equal footing.

    Normalisation has the distinct advantage that it facilitates SPLIT Partial Preferential Voting where a voter faced with say 31 Parties fielding say 101 candidates (as in a Federal Senate Election in proportional representation of HSW’s 6 Senators), then voters can choose to vote, for example, using preference numbers 1, 2, 3, 4, 5, 6, 7 for their first few preferences then finish with 25, 26, 27, 28, 29, 30, 31 for the Parties they detest while omitting the preference numbers 8 to 24 for the Parties they know nothing about. The normalisation algorithms then fill in all the blank preference numbers on that vote with the “don’t know, don’t care” value of 16 (the average of the missing numbers).

    This normalisation process is described in more detail in documents describing my DCAP vote counting system at https://tinyurl.com/ElectoralReformOz. Normalisation is totally fair when any blank preference numbers and resolvable anomalies (e.g., as in PLERS Examples 3 and 4 above) are normalised so that the sum of the normalised preference numbers (allocated to each candidate in the vote being normalised) equals the sum of the numbers from 1 to the number of candidates, (i.e. Sum=N*(N+1)/2 where N is the number of candidates).

    In multi-member electorates, when voting for Candidates but attempting to achieve proportional representation of Parties, things get messy. It is oxymoronic (probably worse) to (allegedly) expect fair proportional representation from laws allowing optional preferential voting for Candidates rather than voting for Parties. PLERS appropriately calculates the proportional representation of each party by limiting each Party to the same number of Candidates being considered. However, this would be more accurate with normalisation which can then be applied (as in DCAP) to Parties with any number of Candidates giving more accurate, more linear results.

    Concerning linearity, see my DCAP documents showing that Hare-Clark exaggerates the non-linearity of the eliminate-distribute (instant-run-off?) method of ‘counting’. For example, I’ve proved that in the ACT 2020 election, 3 of the 25 MLAs elected would have lost a one-on-one run-off election against a Candidate from a different Party who was eliminated in the (so-called) ‘count’ for their electirate. That could have far-reaching effects on whether a government actually earned the right to govern. Fortunately, the ACT 2020 the results were not even close. However, the non-linearity of current preferential vote ‘counting’ methods increases greatly as the candidates are more evenly matched, giving more chaotic results.

    This applies in single-member electorates and even more so in multi-member electorates.

    Election theory needs an overhaul. Arrow uses some poor assumptions and hence made wrong conclusions. E.g., Borda fails Arrows tests, but the fact is that Arrow failed to realise that Borda is absolutely correct in all circumstances where there is full preferential voting. And that’s why normalisation is necessary for accurate linear results using optional preferential voting.

    Pundits say that Borda fails Arrow’s criteria, but I’ve proven Arrow wrong by showing that a narrow absolute majority may hide the fact that far more voters would be more accepting of a different candidate while the nominal absolute majority ‘winner’ was a far more convincing winner, on preferences, of the wooden spoon as the least preferred candidate. Why is it so? The problem is that current vote ‘counting’ systems are obsessed with first and near first preferences while totally ignoring last or near-last preferences which are, not always, but in some cases, more important if we want to achieve more stable consensus government.

    A clear but extreme example is where there are 4 candidates where Candidate A gets 51% of first preferences but 49% of last preferences and another candidate gets zero% first preference but D gets 100% of second preferences. Then, no matter what other preferences Candidates B and C get, it is clear that D is actable to 100% of voters while A is unacceptable to 49% of voters and does not deserve election despite a narrow ‘absolute majority’. That’s why Borda is right and Arrow is wrong. My spreadsheet shows exactly that example – and allows readers to try other combinations also.