[EM] A four bit (sixteen slot) range style ballot

[Kristofer Munsterhjelm]

Kevin Venzke wrote:
> Another thing it occurs to me to note:
> 
>> --- En date de : Lun 14.6.10, Kristofer Munsterhjelm
>>> Approval passes ordinary Majority. If a certain
>> candidate
>>> (or set) is approved by a majority of the voters, any
>>> candidate that has a hope of beating it must also be
>>> approved by a majority.
> 
> If you interpret Approval such that multiple approved candidates means
> multiple candidates tied in first, then Approval satisfies Majority
> because it is impossible (in any method) for more than one candidate to be
> the strict first preference of a majority.
> 
> It seems to me you have to interpret Majority to be referring to strict
> first preferences only, else methods like Schulze will fail it:
> 
> 33 A>B
> 33 A=B
> 34 C>B
> 
> Here only A has a majority of "top" preferences but the Condorcet winner
> is B.

That's a point. Let's say that this means that Majority can only work 
when a majority ranks a single candidate top. Then I think Approval will 
satisfy that variant of Majority, as well; if a majority approves only 
of a single candidate, that candidate will win, even if the minority 
approves of everybody but that candidate. The reasoning would then be: 
if a majority approves of more than one candidate, Majority doesn't come 
into play, as there's no majority with a strict preference.

In other words, Approval would be a system where your ballots are 
limited to ballots of the sort:

A > B = C
A = B > C
A = B = C

It would "work", but it's a big hack and definitely doesn't meet 
universal domain - thus you could argue that the situation weakens the 
Majority criterion, making it easier to pass.