A fair voting system

Anglo’s emphasis that: “DOESNT MATTER HOW MANY THEY WIN BY, IT’S THE ONE WIN THE MOST VOTES WHO THE MOST PEOPLE WANT ELECTED”
Is
NOT NECESSARILY true. It is sometimes true, sometimes FALSE.

A simple example makes this clear:
Suppose 100 voters must choose between 4 candidates, A, B, C, & D. If A gets 35 votes, B 30, C 25 and D 10 votes. Then Anglo says A won regardless of preference votes.
So here’s a question for Anglo: if 65 voters voted A as LAST preference; while 90 voters voted D as 2nd preference; then 65 voters are upset if A is declared the winner, but not one single voter is upset if D is declared the winner.
So, who do you say deserves to win?

And here’s a really curly question:
Suppose A gets 51 1st preference votes and 49 last preferences and D gets the same 10 1st preference votes and 90 2nd preference votes. Anglo and most would say A won with an absolute majority. But considering that 49 voters are upset if A wins, but not one single voter is upset if D is declared the winner; then who is the fair winner that most voters would prefer?
So, who do you say deserves to win?

Now those examples are extreme, but they teach us the FACT, known for many centuries, that most elections systems of counting votes can’t guarantee a fair count in all cases. This has been taken to the extreme to claim that it is IMPOSSIBLE to have a vote-counting system that is always fair: that’s “Arrow’s Impossibility Theorem”. However, Arrow got it wrong: the FACT is that the Borda Count and my DCAP Counting systems both guarantee a fair count in any preferential election that has full preference voting where voters number every box.

DCAP and Borda Counts both declare D to be the winner in both of the examples above.

So HOW do election counting methods get it wrong sometimes?

It is because all the common vote-counting methods are obsessed with 1st preferences and totally ignore last preferences. The first example above shows this clearly, A’s 65 last preferences are of far greater significance 35 1st preference votes. But most vote-counting system ignore such inconvenient truths.

So WHY do we continue to use counting methods that fail us when it matters most?
Well, so far, politicians don’t seem to want to know that there actually are fair vote-counting systems. Hmm, why not? Some suggest it’s because they prefer a system which makes it easier for the big parties to control everything.

There is a free interactive Excel spreadsheet on DropBox accessible via
https://tinyurl.com/ElectoralReformOz that allows readers to easily check variations of the two examples above and to see what the results would be for elections considering:

• 1st past the post;
• After Preference Distribution;
• Condorcet Winner;
• Highest 1-on-1 Most wins;
• Highest 1-on-1 Highest margin total;
• Borda Count;
• DCAP.

The seats determine government. If there is a clear winner in your seat, i.e. someone has more that 50% of the first preference votes, but you did not vote for this person, your vote becomes worthless. A party can have the majority of the votes but not win the majority of the seats – i.e. they have won the popular vote and mandate of the people – but they do not get to govern.
Proportional representation is a better system than geographical representation via seats. This would make preferential voting obsolete. You just choose one candidate, who can live anywhere in Australia – for federal elections – or anywhere in the state for state elections. This will make gerrymandering and electoral boundary disputes a thing of the past. The argument that voters can be better represented by having a local represent them – is also outdated. In practice I don’t see it working very well. We don’t have to travel long distances to get an impression of a candidate. We have mass communication, social media, online news – all just a click away. It’s not 1901 anymore. And with proportional representation you can still vote for a local candidate if you want to.
In the case of a federal election there would be a long list of candidates – per party – to choose from. The long lists consist of candidates chosen for merit and ability, not geography. You choose one candidate, and your vote is equal to anyone else’s vote in the whole of Australia.

Preference votes are in preference of only 2 things, the old 2 parties being in power every time their is an election. Thats not a democratic vote, as it is rigged for preference to old parties keeping in control… the one with the most votes should be the elected winner, not the second or third most liked getting extra votes cause they are not who was voted for. DOESNT MATTER HOW MANY THEY WIN BY, ITS THE ONE WIN THE MOST VOTES WHO THE MOST PEOPLE WANT ELECTED. Who comes up with this bs, I know the 2 major parties so that their control is not let go. Never will be a fair election this way.

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.

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

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.

Does it allow for secret voting or are all votes associated to a user and searchable/traceable?

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.