[EM] smith/schwartz/landau

Kristofer Munsterhjelm km_elmet at t-online.de
Mon Apr 2 05:13:24 PDT 2018

On 03/28/2018 04:36 PM, Juho Laatu wrote:
>> On 28 Mar 2018, at 14:05, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:

>> But it's not that implausible; and if it's true, that means that 
>> whatever makes a Condorcet loser deserve to win, if anything, must 
>> come from information not provided by the pairwise matrix.
> Note that the problems between matrix and ballot information mainly
> emerge from the clone criterion. One could say that pure clone
> independence / existence of clone candidates can not be measured from
> the matrix only (without doing the "overkill"). The non Smith Set
> arguments are more neutral (e.g. minmax style arguments) with respect to
> using the matrix only vs also the ballots (matrix is enough). The
> "overkill" is the problem that forces d not to be elected also when
> there are no technical clones. (Smith Set criterion is close to the
> clone independence criterion.)

It's not just clones. Since the example's collapsed ballots are of the form

m: A>d
n: d>A

with m>n, majority implies that A should be elected. In the uncollapsed 
example, that means that the set {A, B, C} is first on a majority of the 
ballots, so any method that passes mutual majority must elect from this set.

That's perhaps a stronger example of how a generalization of majority 
forces one of {A, B, C} to be elected, since the point of mutual 
majority (as I see it, at least) is that a majority can get the 
candidate they want to be elected, elected, without having to coordinate 
beforehand to rank the candidates in the same order.

It's hard to be opposed to such a property. I imagine it's easier to say 
"okay, the pairwise matrix doesn't supply enough information" and 
require that the method use more than just the pairwise matrix to decide 
the winner.

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