I'm trying to create a voting system that implements RRV, yet I'm unable to fully understand the explanation from an example that I found at rangevoting.org. I'm struggling to understand the following part
each ballot is given a new weight = 1/(1+SUM/MAX), where SUM is the sum of the scores that ballot gives to the winners-so-far, while MAX is the maximum allowed score (e.g. MAX=99 if allowed scores are in the range 0 to 99).
I have the following table which explains what I've achieved so far. I'm not sure if that is correct.
On the image on the second "third round formula" (supposed to be fourth) please consider the last cell (b9) to be (b16) it is a typo, and also the arrows to the right are pointing to the formula rather than the cell.
Yeah, that's all wrong :)
A voter's score for a candidate in each later round should be equal to the score that voter gave in the first round, divided by one plus (the sum of the scores they gave to already-elected candidates divided by (the maximum score times the number of candidates elected.))
Example: round 2, voter 1, candidate 1.00. The score should be $5 / ( 1 + (7/9) )$ or $2.8125$; NOT equal $5 / ( 1 + (37/9) )$ or $0.978$.
You're dividing by the total score for the candidate, when you should be dividing by the voter's score for the candidate (which, unfortunately, is a quite-a-bit-messier equation to do in Excel.)
Oh wait; since you're not dynamically determining the winner, the equation isn't so bad. B9 should
=1/(1+B5/9)*(B2)(which I'd simplify asB2*(1+B5/9)).Another error: always base the score on the first-round (initial) scores! so B16 should be
=1/(1+((B5+B2)/(9+9)))*B2(a moot point, since candidate 1.00 was already elected, but I hope you get the idea.)