Getting to exact proportionality
First I'd like to note that Proportional representation may mean proportional to anything. The US house of Reps says that it uses 'PR' because representation is aimed at being proportional to population. (Ignoring that DC, PR (puerto rico this PR), and territories have no voting representation.)
Often I fear that 'proportional' is a must-have in new electoral systems. For many the solution is to add -PR to the name of a system, and voilà.
In this thread I want to talk about systems that measure party support directly and allocate seats numbers in proportion to that directly measured party support, and aim for 'exact' proportionality. List-PR and MMP are the main candidates here I think.
Thresholds and rounding are two obstacles to exact proportionality that are often found in PR systems that aim for exact proportionality.
Systems that ask voters to directly choose voters are often criticized for giving parties too much power. However the reality is that parties have an important role in bringing like-minded people together to form governments, and are powerful in any system.
For me, a central issue is the avoidance of barriers to entry for new parties. It is the possible rise of new parties that keeps the existing ones honest. So for me we should also value voting systems with low-enough barriers to entry.
I am of course leading the discussion towards my idea...
This is to give voters a second choice of party vote. It means that every voter can express a wish to vote for a new party, but still has a useful vote in the event that the new party fails to pass the threshold.
With such a system, every voter can vote for a party that has enough support to wins seats. Proportionality can be very close to exact. The perverse incentives created by vote-discarding thresholds are eliminated. And support for new parties is easily seen and measured, and turns into seats when large enough. Oh, and it is very easy to understand and implement. And you can retain a threshold.
I have been working on this for a long time. It is a current issue in NZ, where a 2012 review of MMP acknowledged the threshold as a problem, but did not find a good solution. There is another review under way at present.
I have a website at www.ott.nz with more details
I would very much appreciate feedback and suggestions.
Here is how the modified voting paper might look
And here is the detailed results table
@frenzed If the goal is exact PR then why even have a threshold. I thought we did not want exact PR.
But more on topic I think you are making 2 assumptions you do not know you are making. You assume at all existing parties are independent and uncorrelated. More mathematically, the assumption is that the parties form an orthogonal basis for a political space. This is quite clearly false and I hope I do not need to explain why.
Secondly, by having all of a voters endorsement put towards one party you are preventing exact PR. In fact I would think that in general this effect is larger than the effect you are brining up here. To do this properly you would need to know the vector representation of each voter in the space defined by the parties. Having that you could calculated exact PR.