[lqfb-main] Yet another proposal for application of Schulze Method for referendums

[Jan Behrens]

On 06/01/11 03:37, Jan Behrens wrote:
> What about the following approach, being similar to the SSS idea:
>
> Alternative a ∈ A \ {s} is attainable if and only if N[a,s] > N[s,a] and
> (a) there is no supermajority requirement to replace the status quo s by
> alternative a or (b) alternative a has the supermajority required to
> replace the status quo s by alternative a.
>
> Alternative a ∈ A is eligible if and only if ( a ≡ s ) or ( ( a is
> attainable ) and ( a is in the smith set ) and ( s is not in the smith
> set ) ).
>
> A winner is an alternative a ∈ A with (1) alternative a is eligible and
> (2) ab ∈ O_final for every other eligible alternative b.
>
>
> For background information see http://m-schulze.webhop.net/schulze1.pdf


Requiring the winner to be within the smith set might be a bad idea.

Consider:
51%: B > A > SQ
49%: A > SQ > B

With SQ = status quo, and a supermajority requirement of 2/3

100% of the voters prefer A to the SQ
51% of the voters prefer B to A or SQ

The smith set only contains B. Thus A could not win in my proposal.

Using the supermajority smith set (SSS) doesn't help either, at it 
contains A,B,SQ.

I thus come to the conclusion that neither the SSS approach nor the 
smith set approach are acceptable.


Jan Behrens