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

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1 RCD, or Favoring The View from the Candidate Set

2 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  

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 ω either beats or is the same as everybody on such C’s. We dismiss all candidates beaten by ω. We continue with those just-as-good-as ω, 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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