John de Wit, less empty negative comments please.

I’m happy to answer real questions if you’re not yet clear how DCAP works to guarantee fair results. I sympathise – it took me ages to fully understand why current voting systems fail voters and then years to work out how to correct it and then to twig to the simple maths behind it and finally to be able to give simple examples that demonstrate it.

E.g. it is not obvious that my DCAP system is correct when it will declare that Party D, of 4 parties standing, and with 45% first preferences is the winner despite Party A having 51% first preferences. But that is correct IF, repeat IF, in the election Party A had 49% of 4th (or LAST) preferences and party D had 55% of 2nd preferences. I have proved that particular case, no matter what preferences parties B and C get within the values I specified. Can anyone prove me mathematically &/or logically wrong there? No way! The correct Proportional results in a 100 seat electorate is NOT A=51 seats and D=45 Seats. The correct results is A=27 Seats and D=41 seats with B&C sharing the remaining 33 seats.

So, it will not be a majority Government for A in its own right. Rather, it will be a minority government, of probably D in coalition with B or C; or, a slim chance of A running a minority government. Apart from the speculation of who will arrange a coalition; who can logically prove I’m wrong and that that voters preferences showed that they collectively wanted A as a majority government? It can’t be done unless you ignore voters’ clear collective preferences. The fact is that a marginal “absolute majorities” may be a real win; or, a travesty of electoral justice simply because Distribution of Preferences (AKA Instant Run Off) and First-Past-The-Post systems are inherently incapable of guaranteeing a fair result.

I have proved that. I challenge anyone to prove me wrong.

Peter Newland,
Your arithmetic is very complex compared to a single vote for the party of your choice. There is no assumption that you should agree with every policy of that party. You just choose the party and candidate you think is best.

For those interested, the simple arithmetic to convert my earlier example with preferences
1 2 3
A 40 0 60
B 40 60 0
C 20 40 40
into number of seats earned under Proportional Preferential counted by Borda or DCAP
First, Preference AVerages (PAVs)
PAVa = (40×1 + 0×2 + 60×3)/100votes = 2.2
PAVb = (40×1 + 60×2 + 0×3)/100votes = 1.6
PAVc = (20×1 + 40×2 + 40×3)/100votes = 2.2
B, with PAV = 1.6 is clearly the closest to unanimously first preference of PAV=1.
A and C tie for second place with PAVs = 2.2.
A’s downfall is that it is significantly more unpopular than it is popular.

Then, to translate that into seats, first calculate DCAP scores where
DCAP=100x(1-(PAV-1)/(Cn-1)).
DCAPa= 40, DCAPb=70, and DCAPc=40 , which adds to 150.
So, scaling that to the 100 seat vacancies and with rounding (arbitrarily, in favour of 1st preference tallies to remove the dead heat for 2nd place),
we get A=27 seats, B=47 seats and C=26 seats.

For more explanation, including on Borda, see https://tinyurl.com/ElectoralReformOz starting with the 1-page [Absolute Majority v Democracy.pdf] and then perhaps browse the [0-Voting Reform – how … ] directory.

John de Wit, those arguments are seriously flawed.
Using Proportional Representation without Preferences, as you propose, effectively assumes that a vote for a party totally agrees with that party and has no preference for any of the other parties. No wonder people are reluctant to vote under such conditions – who could possibly endorse every policy of a party???

More to the point, the arguments you gave in no way refutes my proof that Preferential Proportional representation adds value because it is well able to discriminate between parties with equal primary votes based on the collective preferences of the voters.