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This study focuses on optimizing candidate satisfaction in a ranking constraints system. The process involves identifying and eliminating inferior candidates based on specified constraints. By following the RCD methodology, a hierarchy is created favoring the desired optimum candidate through each stage, ultimately leading to the satisfaction of the optimized candidate set. The approach involves recursively analyzing candidate groups based on their relations to constraints, filtering out candidates worse than the optimal, and iterating towards reaching the ideal solution. The pivotal role of ERCs, restructuring of candidate sets, and the system's ability to handle varying constraints are explored.
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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 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? • 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 • 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.
