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There is only 1 substantial diverence between your formulation and my one: In the case of a old voting and a drastically changed membership and previously unconsidered arguments: You give the new membership the right to vote simply, while I wanted a system in which the votes of the now inactive members would still be counted. May be my system was made clear. Therefore I will give some exampels:
A) Old voting: 10 members voted, case was simple a or b, result a=8; b=2
new voting: from the 10 voters of old 2 are still active both had of old voted with a, 2 new members vote also result a=1; b=4
To get a chance to overcome the old vote at all the active member ship does need more wieght on the votes (which is considered justified because they have heard all arguments). In the old vote 10 members had voted in the new only 5 therefore:
Weights: lowest common multiple of 10 and 5 is 10 => old votes 10/10=1, new votes 10/5=2
Members activ in both votings have of course only one vote and that is counted in the new wiegth.
Result:
a: ( 8 votes of old minus 2 votes changed by still active members ) multiplied by wieght 1 plus 1 new vote multiplied by weight 2:
(8-2)x1+1x2=8
b: ( 2 votes of old minus 0 votes changed by still active members ) multiplied by wieght 1 plus 4 new vote multiplied by weight 2:
(2-0)x1+4x2=10
Result changed from a to b.
B) Old voting: 9 members voted, case was a, b, c; result a=4; b=3; c=2
new voting: from the 9 voters of old 3 are still active 2 had voted b, 1 voted with c.
3 new members voted
Result a=2; b=3; c=1
Result:
Weights: lowest common multiple of 9 and 6 is 18 => old votes 18/9=2, new votes 18/6=3
a: ( 4 votes of old minus 0 votes changed by still active members ) multiplied by wieght 2 plus 2 new votes multiplied by weight 3:
(4-0)x2+2x3=14
b: ( 3 votes of old minus 2 votes changed by still active members ) multiplied by wieght 2 plus 3 new votes multiplied by weight 3:
(3-2)x2+3x3=11
c: ( 1 votes of old minus 1 votes changed by still active members ) multiplied by wieght 2 plus 1 new vote multiplied by weight 3:
(1-1)x2+1x3=3
Result unchanged a even so b had a relative majority in the group of active members.
The mathematics are a bit complex, but the result especially in narrow cases does take the old votes more into account. But I am not adamant on these, if the simpler solution is wanted I can go with that as well.
Respectfully
Findegil
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