On 17 January 2012 23:39, Pavitra <celestialcognit...@gmail.com> wrote:
> On 01/17/2012 05:03 AM, Arkady English wrote:
>> On 15 January 2012 15:24, Tanner Swett <swe...@mail.gvsu.edu> wrote:
>>> On Sun, Jan 15, 2012 at 9:15 AM, 441344 <441...@gmail.com> wrote:
>>>> Amend Rule 1950 by replacing the text
>>>> {
>>>> Adoption index is a switch possessed by Agoran decisions, whose value is
>>>> either "none" (default) or an integral multiple of 0.1 from 1.0 to 9.9.
>>>> } with the text
>>>> {
>>>> Adoption index is a switch possessed by Agoran decisions, whose value is
>>>> either "none" (default) or an integral multiple of 0.1 greater than
>>>> or equal to 1.0.
>>>> }.
>>>> }.
>>>
>>> The reason there's an upper limit is that someone once submitted a
>>> proposal with an adoption index hundreds of digits long. The only
>>> reasonable solution, I think, is to limit adoption indices to exactly
>>> 35.
>>>
>>> —Machiavelli
>>
>> Shouldn't adoption indices be capped to the maximum number of votes
>> which may be cast on that proposal.
>>
>> So, if there are N players, each with 1 vote to cast on a proposal
>> submitted, any adoption index greater or equal to N would require
>> unanimity to pass (because if 1 player votes against it there are only
>> (N-1) players to vote in favour, so it will never meet the adoption
>> index).
>>
>> This becomes a problem if the number of votes available to cast does
>> not remain constant through the voting period - although that could be
>> fixed by allowing adoption indices to be a linear function of
>> MaxVotes, and setting any adoption index greater MaxVotes to
>> MaxVotes.
>>
>> Arkady
>
> Adoption indices are tied to fractions. A proposal with an adoption
> index of N requires an N/(N+1) majority to pass. The total number of
> voters is irrelevant.
On the contrary.
When I wrote, my understanding of the adoption index was that it
worked as follows:
A proposal passes if:
Vf/Va > A, where Vf and Va are the number of votes for and against and
A is the Adoption Index.
If that is true, what I've written is true.
But, you say, the condition is actually:
Vf/(Vf+Va) > A/(A+1).
However, these two conditions are identical. If we take the second
condition and multiply each side by (Vf+Va)(A+1) the adoption
condition becomes:
Vf(A+1) > A(Vf+Va).
Multiply out brackets:
VfA + Vf > VfA + VaA.
Subtract VfA from each side:
Vf > VaA
And finally divide by Va:
Vf/Va > A.
And the thing here is that total votes DO matter. There are Tv = Vf+Va
voters, so if 1 person votes against (i.e. Va = 1) the highest
possible adoption index that could be reached is (T-1). Thus by
setting the adoption index greater than (T-1) a proposal can only pass
unanimously (even if T is unknown).
