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RCD, or Favoring

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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

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.

- 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

- 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’

- 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

- 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

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

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

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

- 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’.

- 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.

- 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

- 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

- 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.

- 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.