[EM] Fair and Democratic versus Majority Rules

[Kristofer Munsterhjelm]

robert bristow-johnson wrote:
> 
> On Nov 15, 2010, at 8:40 PM, Bob Richard wrote:
> 
>> On 11/15/2010 4:58 PM, fsimmons at pcc.edu wrote:
>>> When majority rules, a 51 percent majority can have their way in 
>>> election after election. But what other
>>> possible standard is there for democracy and fairness besides 
>>> "majority rule?"
>>
>> For seats in legislative bodies, proportional representation.
> 
> for which STV or a more Condorcet-like ordering (what would the name of 
> that be? Kristofer Munsterhjelm had a Schulze ordering for Oakland) does 
> well. here in Vermont we just had an election where for my state senate 
> district, we voted for 6 out of about 15 and the top 6 vote getters win 
> seats, but that method sorta sucks.

Condorcet doesn't give proportional representation. If you have an 
example like:

51: D1 > D2 > D3 > D4
49: R1 > R2 > R3 > R4

and pick the first four, all the Ds will win.

Proportionality is something different. Quota-based proportionality is 
best shown by the Droop proportionality criterion, that if more than x 
Droop quotas rank y candidates first, at least the minimum of x and y of 
those candidates should be included in the outcome. A Droop quota is 
here (number of voters)/(number of seats + 1).

I suspect that one can't have both quota proportionality and 
monotonicity, so I've been considering divisor-based proportional 
methods, but it's not clear how to generalize something like Webster to 
ranked ballots. I did try (with my M-Set Webster method), and it is, to 
my knowledge, monotone, but it's not very good in the single-winner 
instance.

Perhaps one could make multiwinner Condorcet logic, something like "if 
the voter ranks both A and B over both C and D, then consider that a win 
of the {A,B} council over {C,D}", and then treat the matrix as a 
Condorcet matrix. The problem with this is that while you can't split up 
single candidates, you can split up councils - e.g. by voting A>C>B>D - 
and it's quite unclear how to score such splits in a "contest of councils".

> for me, if it's a single winner: "If a majority of voters select 
> Candidate A over Candidate B then, if at all possible, Candidate B 
> should not be elected" is the only sensible rule, because of the 
> converse is so clearly contrary to the concept of the will of the 
> majority.  Any method that cannot be guaranteed to accomplish that risks 
> the question: e.g. "Why should Bob Kiss be the mayor of Burlington when 
> 587 more voters expressed on their ballots that they thought Andy 
> Montroll was a better choice?".
> 
> i think you can argue that Condorcet compliant is always preferable out 
> of point by contradiction.  if there is a CW and you elect someone else, 
> that is always a failure.

I think counterarguments would make use of that the majorities are not 
necessarily the same. Those who see no point in Condorcet would say: "if 
the leftists prefer A to B and the right-wingers prefer A to C, that's 
still short of majority rule".