Approval/Plurality: clarification

[Bart Ingles]

Bart Ingles wrote:
> 
>> C = computed total  (always 50%, unless there is a first-choice majority
> or no approval majority is possible)
> F = first-choice total
> A = Approval total  (note the "A - F" term is equivalent to
> "second-choice total")
> W  = Weighting factor  (see below)
> 
> If a candidate has a first-choice majority, the minimum weight factor is
> 0 (the Approval vote is unused).  If not, the easiest way to find the
> winner is to work backwards from the totals for each candidate, to find
> the weight factor required for that candidate to reach 50%.  The formula
> to do this is:
> 
> W = (T/2 - F) / (A - F)

where: 
T = First choice total for all candidates combined

> 
> The candidate with the lowest weight factor is the winner, at 50%.  This
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        (with an adjusted total of 50% of the first-choice vote^ )

> weight can then be used to compute the other totals using the first
> formula.  If the lowest weight factor is greater than 1, then 1 is used
> and the final vote is equivalent to Approval with no majority (using a
> factor greater than one would give approval votes more weight than the
> first-choice vote).
> [...]