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 )
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:
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.
== To read as:
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.
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:
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.)