Single distributed vote: Difference between revisions

#Acquire candidate scorescores form voters and normalizerepresent them in [0,1] into a matrix. Voter, v, rates candidate, c, with score, <math>S_{v,c}</math>.

In a 5 winner race, the following example will show the progression of redistribution at each step for a single voter. This voter scored the winners 0.4 | 0.7 | 110 | 0 | 0.2 in the sequence in which they won. The ballot weight formula is

Note that the ballot weight is always a value in [0,1] and will sum to 1 across all candidates for each voter at all times. The score matrix is the original one and the winner is the same as the [[Score voting]] winner. In the next round, the ballot weight is redistributed to the next potential winners in proportion to the score given to them. For the second winner, this amount would be

\frac{S_{v,c}}{ S_{v,c} + 2 \times \Sigma_{winners j} S_{v,j}} = \frac{0.7}{ 0.7 + 2 \times 0.4} = \frac{7}{ 15}

At the end of this round the second winner has 7/15 of the ballot weight leaving 8 /15 with the first. Following the same formula the third winner has 10/32 of the ballot weight at the end of the third round. This is because 8/32 and 14/32 needed to be left with the first and second winners respectively. Note that later winners can receive more ballot weight if they are scored higher than prior winners. The fourth round has no effect since the voter gave a score of zero to that winner. In the final round, the winner receives 2/44 since the first three winners had to hold 8/44, 14/44 and 20/44 of the ballot weight. Another, example can be seen pictorially in the accompanying image.