# RCD, or Favoring - PowerPoint PPT Presentation

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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

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## RCD, or Favoring

The View from the Candidate Set

Candidate Set with desired Optimum ω

K = ω

k1

k2

k3

ARG = ω ~ k1

ω ~ k2

ω ~ k3



 

### 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

• 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

• 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

• 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 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

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

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 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

• 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

• 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

• 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?

• 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.

### 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.