OKlibrary  0.2.1.6
Marx2008.hpp File Reference

Plans regarding investigations of a case-study for the logical analysis of data. More...

Go to the source code of this file.


Detailed Description

Plans regarding investigations of a case-study for the logical analysis of data.

The underlying article is [Limits to non-state market regulation: A qualitative comparative analysis of the international sport footwear industry and the Fair Labor Association, Regulation and Governance , 2008].

Bug:
Update needed
  • All entries (and also in other files) need to be updated according to the standards established in Annotations/DataAnalysis.tex.
  • This should be considered a bug, since the implementations and discussions do not follow the specifications anymore.
Todo:
Create milestones
Todo:
Data
  • The paper tries to determine the causes for a range of multinational footwear companies joining the Fair Labor Association.
  • The underlying QCA truth table data given in the paper is summarised in the following combinatorial matrix.
    Marx_CM : mrc2ocom(matrix(
     [0,1,1,1,1],
     [1,1,1,1,1],
     [1,1,1,1,1],
     [0,1,1,1,1],
     [0,1,0,1,0],
     [1,0,0,0,0],
     [1,1,1,0,0],
     [1,0,0,0,0],
     [undef,0,0,0,0],
     [1,0,1,0,0],
     [0,0,1,0,0],
     [1,1,1,1,1],
     [0,0,0,0,0],
     [1,0,0,1,0],
     [1,0,0,0,0],
     [1,0,1,1,0],
     [0,1,1,0,1]),
     ["Nike","Adidas", "Puma", "Reebok", "New balance", "Diadora", "Fila", "Karhu", "Kelme", "Mizuno", "Saucony", "Asics", "Brooks", "Decathlon", "Lotto", "Kappa", "Umbro"],
     ["Union", "NGO", "Public", "Change", "FLA"])$
       
  • Note here that the variables have the following (to be elaborated) definitions
    1. "Union" - represents the presence or absence of "institutional embeddedness", such as the presence of strong union forces within the company.
    2. "NGO" - represents the presence or absence of "non-governmental organisation" pressure on the company.
    3. "Public" - represents whether the company is publicly traded or not.
    4. "Change" - represents whether the company has previously started to change prior to joining the FLA, introducing codes of conduct and review etc.
  • Also note that for "Kelme", "Union" is undefined, and the value is not given in the paper. This seems be to be due to the fact that there is no available data for Spain (the country in which Kelme operates). How to treat such "unknown" conditions in our system?
  • It seems that in the analysis done by Marx that Kelme is considered then as two configurations. So we have
    Marx_CM : mrc2ocom(matrix(
     [0,1,1,1,1],
     [1,1,1,1,1],
     [1,1,1,1,1],
     [0,1,1,1,1],
     [0,1,0,1,0],
     [1,0,0,0,0],
     [1,1,1,0,0],
     [1,0,0,0,0],
    
     [0,0,0,0,0],
     [1,0,0,0,0],
    
     [1,0,1,0,0],
     [0,0,1,0,0],
     [1,1,1,1,1],
     [0,0,0,0,0],
     [1,0,0,1,0],
     [1,0,0,0,0],
     [1,0,1,1,0],
     [0,1,1,0,1]),
     ["Nike","Adidas", "Puma", "Reebok", "New balance", "Diadora", "Fila", "Karhu", "Kelme1", "Kelme1", "Mizuno", "Saucony", "Asics", "Brooks", "Decathlon", "Lotto", "Kappa", "Umbro"],
     ["Union", "NGO", "Public", "Change", "FLA"])$
       
Todo:
Functional analysis
  • With this data, we have the following full DNFs and CNFs representing the various functional extensions of the data (for the unspecified configurations / logical remainders)
    /* DNF assuming liberal extension */
    Marx_LibDNF_FF : 
      [[gv("Union"),gv("NGO"),gv("Public"),gv("Change")],
       [{-gv("Change"),gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),gv("Union")}]$
    /* CNF assuming liberal extension */
    Marx_LibCNF_FF:
      [[gv("Union"),gv("NGO"),gv("Public"),gv("Change")],
       [{-gv("Change"),-gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {-gv("Change"),gv("NGO"),-gv("Public"),-gv("Union")}]]$
    /* DNF assuming conservative extension */
    Marx_ConDNF_FF : 
      [[gv("Union"),gv("NGO"),gv("Public"),gv("Change")],
       [{gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),gv("NGO"),gv("Public"),-gv("Union")}]]$
    /* CNF assuming conservative extension */
    Marx_ConCNF_FF :
      [[gv("Union"),gv("NGO"),gv("Public"),gv("Change")],
       [{-gv("Change"),-gv("NGO"),gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {-gv("Change"),gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public"),gv("Union")}]]$
        
    Note that the data doesn't contain any conflicts.
  • Where for each of the above we get the following minimum representations
    /* Minimal representations of the liberal extensions */
    all_minequiv_bvsr_sub_cs(Marx_LibDNF_FF[2],Marx_ConDNF_FF[2]);
      [{{-gv("Change"),gv("NGO"),-gv("Union")},
        {gv("Change"),gv("NGO"),gv("Public")}},
       {{gv("Change"),gv("NGO"),gv("Public")},
        {gv("NGO"),gv("Public"),-gv("Union")}},
       {{gv("Change"),gv("NGO"),gv("Union")},
        {gv("NGO"),gv("Public"),-gv("Union")}}]
    
    
    all_minequiv_bvsr_sub_cs(Marx_LibCNF_FF[2],Marx_LibCNF_FF[2]);
      [{{-gv("Change"),-gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),gv("NGO")},
        {gv("Change"),-gv("Public"),-gv("Union")},
        {gv("NGO"),-gv("Union")}}]
    
    
    /* Minimal representations of the conservative extensions */
    all_minequiv_bvsr_sub_cs(Marx_ConDNF_FF[2],Marx_ConDNF_FF[2]);
      [{{gv("Change"),gv("NGO"),gv("Public")},
        {gv("NGO"),gv("Public"),-gv("Union")}}]
    
    all_minequiv_bvsr_sub_cs(Marx_ConCNF_FF[2],Marx_LibCNF_FF[2]);
      [{{gv("Change"),-gv("Union")},{gv("NGO")},{gv("Public")}}]
       
    Note here that the conservative DNF and liberal CNF correspond to the analysis chosen by Marx in the paper.
Todo:
Relational analysis
  • Other than the basic DNFs and CNFs given in "Functional analysis", we also have the relational viewpoint, where we consider the output variable as a variable like any other, and then we consider all rows in the data table as true.
  • The question is: what to consider false?
  • If we assume nothing is false, then {{}} is the minimal DNF for any such truth table.
  • One method for constructing a non-trivial relational model is to assume that the behaviour is functional on the rows in the truth table (otherwise we would have observed the contradictory rows).
  • In this case we get
    Marx_RelLibDNF_FF : 
      [[gv("Union"),gv("NGO"),gv("Public"),gv("Change"),gv("FLA")],
       [{-gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),gv("FLA"),gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),gv("FLA"),-gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),gv("Union")}]]$
    
    Marx_RelLibCNF_FF : 
      [[gv("Union"),gv("NGO"),gv("Public"),gv("Change"),gv("FLA")],
       [{-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")}]]$
     
    
    Marx_RelConDNF_FF : 
      [[gv("Union"),gv("NGO"),gv("Public"),gv("Change"),gv("FLA")],
       [{gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")}]]$
     
    Marx_RelConCNF_FF : 
      [[gv("Union"),gv("NGO"),gv("Public"),gv("Change"),gv("FLA")],
       [{-gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {-gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),-gv("NGO"),gv("Public"),-gv("Union")},
        {-gv("Change"),gv("FLA"),gv("NGO"),-gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),gv("Public"),gv("Union")},
        {gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")},
        {gv("Change"),gv("FLA"),-gv("NGO"),gv("Public"),-gv("Union")},
        {gv("Change"),gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")}]]$
       
    with minimum representations
    /* Minimal representations of the liberal extensions */
    all_minequiv_bvsr_sub_cs(Marx_RelLibDNF_FF[2],Marx_RelConDNF_FF[2]);
      [{{-gv("Change"),-gv("FLA"),gv("Union")},
        {-gv("Change"),gv("FLA"),gv("NGO"),-gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public")},
        {-gv("FLA"),-gv("NGO")},{-gv("FLA"),-gv("Public")}},
       {{-gv("Change"),-gv("FLA"),gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public")},
        {-gv("FLA"),-gv("NGO")},{-gv("FLA"),-gv("Public")},
        {gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")}},
       {{-gv("Change"),-gv("FLA"),gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Union")},
        {-gv("FLA"),-gv("NGO")},{-gv("FLA"),-gv("Public")},
        {gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")}}]
    
    
    all_minequiv_bvsr_sub_cs(Marx_RelLibCNF_FF[2],Marx_RelLibCNF_FF[2]);
      [{{-gv("Change"),-gv("FLA"),-gv("NGO"),gv("Public"),gv("Union")},
        {-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public")},
        {gv("Change"),-gv("FLA"),gv("NGO")},
        {gv("Change"),-gv("FLA"),-gv("Public"),-gv("Union")},
        {-gv("FLA"),gv("NGO"),-gv("Union")},
        {gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")}}]
    
    
    /* Minimal representations of the conservative extensions */
    all_minequiv_bvsr_sub_cs(Marx_RelConDNF_FF[2],Marx_RelConDNF_FF[2]);
      [{{-gv("Change"),-gv("FLA"),-gv("NGO")},
        {-gv("Change"),-gv("FLA"),gv("Public"),gv("Union")},
        {gv("Change"),-gv("FLA"),gv("NGO"),-gv("Public"),-gv("Union")},
        {gv("Change"),gv("FLA"),gv("NGO"),gv("Public")},
        {-gv("FLA"),-gv("NGO"),gv("Union")},
        {gv("FLA"),gv("NGO"),gv("Public"),-gv("Union")}}]
    
    
    all_minequiv_bvsr_sub_cs(Marx_RelConCNF_FF[2],Marx_RelLibCNF_FF[2]);
      [{{-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public")},
        {gv("Change"),-gv("FLA"),-gv("Union")},
        {gv("Change"),gv("FLA"),-gv("NGO"),gv("Union")},
        {-gv("FLA"),gv("NGO")},{-gv("FLA"),gv("Public")}},
       {{-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Public")},
        {gv("Change"),-gv("FLA"),-gv("Union")},
        {-gv("FLA"),gv("NGO")},{-gv("FLA"),gv("Public")},
        {gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")}},
       {{-gv("Change"),gv("FLA"),-gv("NGO"),-gv("Union")},
        {gv("Change"),-gv("FLA"),-gv("Union")},
        {-gv("FLA"),gv("NGO")},{-gv("FLA"),gv("Public")},
        {gv("FLA"),-gv("NGO"),-gv("Public"),gv("Union")}}]
       

Definition in file Marx2008.hpp.