It is entirely possible to transform an election utilizing the score/range voting method (or the single selection method, or the approval method) into a multi-winner proportional representation election. That is, there is a method for implementing a proportional representation (multiple winner) election (e.g. for a legislature) without the involvement of parties, which could utilize strategic hedge simple score voting:

“Tranches” correspond to seats in a legislature, but also, approximately, to non-majority groups or interests. Here are the fundamental parameters and variables:

T = The Total Number Of Tranches (e.g. (one less than) the number of seats to be filled).

N = A Tranche Number (these tranche numbers run from 1 to T – a “strongest winner” is at the top, and the tranches form “layers,” with tranche #1 below the strongest winner, tranche #2 below tranche #1, and so on).

W = The Strongest Winner’s Total Number Of Votes.

B = The “Base”, or end point beneath each tranche. (for a given N (or tranche number), as determined by the equation below).

B = W * ( 1 - [(N /( T + 1 )]^2 )

Example:

Strongest Winner’s Total = 310

Total Number Of Tranches = 7

(For a total number of seats = 8)

For each tranche number (N) there is a base number (B):

B = 310 * ( 1 - ( N/ 8 )^2 )

Strongest Winner is --> 310 (This candidate has the Strongest Winner’s Total, and wins the “top” seat.)

Tranche Number 1 Winner is at or above --> 305.15625 – but is below the strongest winner (This is the “B”, that is, the base for this Tranche #1).

Tranche Number 2 Winner is the strongest one at or above --> 290.625 – but is below base #1.

Tranche Number 3 Winner is the strongest one at or above --> 266.40625 – but is below base #2

Tranche Number 4 Winner is the strongest one at or above --> 232.5 – but is below base #3

Tranche Number 5 Winner is the strongest one at or above --> 188.90625 – but is below base #4

Tranche Number 6 Winner is the strongest one at or above --> 135.625 – but is below base #5

Tranche Number 7 Winner is the strongest one at or above --> 72.65625 – but is below base #6

Tranche Number 8 Winner would be the strongest one at or above --> 0.0 (However, #8 cannot be a winner; the total number of tranches is only 7.)

The strongest winner is elected.

== Please amend this:

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Then the candidate with the number of votes equal to or above the Tranche Number 1 base is the winner in that tranche.

Then the candidate with the number of votes equal equal to or above Tranche Number 2 base is the winner in that tranche.

And so on, down to Tranche Number 7.

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== To read as:

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Then the candidate with the largest number of votes equal to or above the Tranche Number 1 base, but below the stronger winner, is the winner in tranche 1.

Then the candidate with the largest number of votes equal equal to or above Tranche Number 2 base, but below base 1, is the winner in tranche 2.

And so on, down to Tranche Number 7.

Note that we could evaluate the winner of tranche 7 first, and the winner or tranche 6 next, and so on, and get the same result, since the order in which the evaluations are performed is irrelevant.

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The scores of the winners cluster around W, the strongest winner, and “thin out” as the tranche number increases. This is because the equation describes a parabolic curve. Note that always-corruptible political parties are not involved in this proportional election method at all (it is a party-less method). It is not exactly “proportional” in the sense that the tranches do not necessarily reflect the interests of groups, yet it effectively provides a “voice” for such minority groups.

The “bases” distribute according to an inverted and translated graph of a parabolic curve, so the formula is very simple. You could visually examine this at:

http://www.webmath.com/plot.html

Of course, as with all methods, a sufficient number of candidates are required to facilitate the procedure.

There is one very severe problem left to be solved if this solution is to be completely realistic. I will solve it after a little rest. Thanks for the patience!

(Note: I would have put this in the “Multi Member Voting Systems” thread, but I screwed that up because it’s so hard to “get everything right” with something new like this. Sorry.)