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RCD, or Favoring

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

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  1. RCD, or Favoring The View from the Candidate Set

  2. 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

  3. 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.

  4. 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

  5. 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’

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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’.

  12. 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.

  13. 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

  14. 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

  15. 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.

  16. 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.

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