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RCD, or Favoring. The View from the Candidate Set. Candidate Set with desired Optimum ω K = ω k1 k2 k3  . Leads to ERC set ARG = ω ~ k1 ω ~ k2 ω ~ k3    . From Candidates to ERCS. Satisfaction Guaranteed.

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Rcd or favoring

RCD, or Favoring

The View from the Candidate Set


From candidates to ercs

Candidate Set with desired Optimum ω

K = ω

k1

k2

k3

Leads to ERC set

ARG = ω ~ k1

ω ~ k2

ω ~ k3



 

From Candidates to ERCS


Satisfaction guaranteed
Satisfaction Guaranteed

To say that an ERC [ω ~ k] is satisfied by a ranking

  • Is to say that candidate k has been dismissed as demonstrably inferior to ω

  • If we satisfy a set of ERCS A, we have shown that the desired optimum is better than anything else in the underlying candidate set from which A arises.


The eye of the optimum
The Eye of the Optimum

  • Look at a constraint C from the P.O.V. of the desired optimum.

  • The ordering relations in the candidate set simplify to have only three distinct classes:

    C

    L: a,b,c,… the things that beat ω

    e: ω,d,f,… those that look the same

    W: g,h,k,… those ω beats


Rcd ranks
RCD Ranks

  • The essential ranking move is to amalgamate into a stratum every constraint that can be safely ranked.

  • These fuse to W or e --- they never supply a ‘leading L’


Rcd eliminates
RCD Eliminates

  • We then eliminate every ERC which supplies W to a constraint in the stratum.

  • What is the underlying candidate set for this ERC group?

  • C

  • L: a,b,c,… the things that beat it

  • e: ω,d,f,… those that look the same

  • W: g,h,k,… those it beats


Rcd eliminates1
RCD Eliminates

  • We then eliminate every ERC which supplies W to a constraint in the stratum.

  • What is the underlying candidate set for this ERC group?

  • C

  • L: a,b,c,… the things that beat it

  • e: ω,d,f,… those that look the same

  • W: g,h,k,… those ω beats


Candidates filtered
Candidates Filtered

The W group includes all those candidates that are worse than, beaten by, the optimum over the stratal constraints:

  • C

  • L: a,b,c,… the things that beat it

  • e: ω,d,f,… those that look the same

  • W: g,h,k,… those ω beats


Recursing onward
Recursing Onward

We continue with the set of ERCS that bear e everywhere in the stratum --- the unsolved ‘residue’ of the stratum.

What candidates are these ERCs based on?

  • C

  • L: a,b,c,… the things that beat it

  • e: ω,d,f,… those that look the same

  • W: g,h,k,… those it beats


Recursing onward1
Recursing Onward

We continue with the set of ERCS that award e in the stratum --- the unsolved ‘residue’ of the stratum.

What candidates are these ERCs based on?

  • C

  • L: a,b,c,… the things that beat it

  • e: ω,d,f,…those that look the same

  • W: g,h,k,… those it beats


Onward with the equals
Onward with the Equals

  • We continue with those candidates that are equal to the desired optimum on every constraint in the stratum.

  • These suboptimal status of these residual candidates is not explained by any constraint in the stratum.

    • They are the unexplained ‘residue’.


Summary
Summary

  • RCD pulls to the front all those constraints in which the desired optimum ω sits at the very top of the order imposed by the constraint on the cand. set.

    • Any ERC constructed from the cand. set will show W or e on these C’s.The desired optimum ωeither beats or is the same as everybody on such C’s.

  • We dismiss all candidates beaten by ω.

  • Wecontinue with those just-as-good-asω, trying to find constraints to defeat them.


The favoring hierarchy
The Favoring Hierarchy

  • This view sees the RCD hierarchy as one that favors ω at every stage to the degree possible.

    • See Samek-Lodovici & Prince 1999.

  • At each stage, we look to grab those constraints for which ω is at the top – those which ‘favor’ it.

  • If ω is favored all the way through, it wins!

  • A ‘residue’ is the collection of still-viable competitors


And fred
And FRed?

  • Similar remarks may be made about FRed

  • With the reminder that in FRed, we never lump constraints into strata

  • We pursue the unexplained residue for each constraint separately

  • Because we want to know everything about its relations to other constraints


Admirable qualities of ercs
Admirable Qualities of ERCs

  • Work across candidate sets.

    • An ERC is an ERC no matter where it comes from

    • The ‘favoring’ account is most direct for a single candidate set. Even generalized, it remains tied to the details of specific sets of specific data.

  • Provide a full account of the possible explanations for the status of each defeated candidate

  • Sit within an easily manipulable logic in which all questions about ranking can be answered directly.


Challenge
Challenge !

  • We argue with limited candidate sets and limited constraint sets.

  • What relations of optimality and/or bounding are preserved as we

  • [1] enlarge the candidate set while keeping the constraints constant

  • [2] enlarge the constraint set while keeping the candidate set constant.