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

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> At 10:09 AM 6/13/2010, Kevin Venzke wrote:
> 
>> --- En date de : Sam 12.6.10, Abd ul-Rahman Lomax 
>> <abd at lomaxdesign.com> a écrit :
>>
>> > Plurality allows voters to place a candidate at the "top of
>> > their preference listings."
>>
>> That is inadequate to satisfy the criterion, which refers to candidates
>> plural. Woodall's Majority is equal to what has been called "Mutual
>> Majority" on this list.
> 
> Sure. It's more general in application than the simple restatements of 
> the Majority Criterion. However, the plural includes the singular.
> 
> What I see with Plurality is that if a majority of voters put the same 
> set of candidates at the top of their preference listings, on the 
> ballot, that candidate will win. That they only put one candidate 
> doesn't violate or negate that statement.
> 
> Below, Mr. Venzke provides a definition of preference listing, which 
> considers it a ballot.
> 
> My point, though, is not to insist upon one particular interpretation, 
> but to show that interpreting and applying a preferential voting 
> criterion, as Woodall's Majority Criterion was intended to be, to a 
> voting system that isn't constructed as expected, is not a way to 
> objectively judge the system, because one then has to make a series of 
> possibly biased judgments.
> 
> This really comes out when we start to examine Approval voting. If a 
> majority of voters prefer a candidate over all others, showing that on 
> the ballot, with Approval voting, that candidate must win. If they 
> conceal this preference by also approving someone else, that candidate 
> might lose. So ... does aproval voting satisfy this Majority Criterion?

Approval passes mutual majority if you alter it in such a way that 
Plurality, Minmax, etc., also pass it: "If everybody equal-ranks a 
certain set at first place, then someone from that set should win". 
However, that is not what Woodall intended, and it reduces mutual 
majority to simple Majority - in which case, why care about mutual majority?

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.
A greater Approval system using DSV or official strategizing under 
influence of a poll would still meet Majority in terms of approval 
ballots submitted to the final stage, but perhaps not in terms of rank 
or rate ballots originally intended - some might, others might not.