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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.