Measuring Cultural Diversity? a heuristic approach from science and technology policy Sussex Energy Group Andy Stirling, SPRU science and technology policy research presentation to meeting of the UNESCO Convention on Cultural Diversity on Measuring Cultural Diversity, Barcelona, 1 st December 2008
Presentation by Andy Stirling, STEPS Centre co-director and SPRU science director entitled 'Measuring Cultural Diversity? a heuristic approach from science and technology policy'. This was presented to a meeting of the UNESCO Convention on Cultural Diversity in Barcelona on 1 December 2008
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Measuring Cultural Diversity? a heuristic approach from science and technology policy
Sussex Energy Group
Andy Stirling, SPRUscience and technology policy research
presentation to meeting of the UNESCO Convention on Cultural Diversityon Measuring Cultural Diversity,
Barcelona, 1st December 2008
Sussex Energy Group
Measuring Cultural Diversity? a heuristic approach from science and technology policy
Andy Stirling, SPRUscience and technology policy research
presentation to meeting of the UN Convention on Cultural Diversityon Measuring Cultural Diversity,
Barcelona, 1st December 2008
• Diversity in Cultures, Economies and Societies
• Some Key Attributes of Diversity
• A Framework for Analysing Diversity
• An Illustrative Example in Policy-Making
Multiple Rationales for Diversity
Many reasons for social / cultural / economic / technological diversity
reflect context diversity allows sensitivity to heterogeneous conditions
literature / music / film / art / theatre / dance / opera
genres / styles / provenances / languages / subjects
diversity can be increased in three different ways
What is Cultural Diversity? – many different disciplines converge
increasing diversity
varietynumber of genres in mix
What is Cultural Diversity?
widespread in economics and energy strategy, BUT
- partitioning of categories
eg: ‘popular music’ or “pop, rock, rap, techno, soul…”
- when to start counting?
eg: one record sale? one thousand? 1% of total sales?
- what about varying degrees of representation in cultural portfolio?
eg: “90% / 5% / 5%” or “33% / 33% / 33%” ?- what about the degree to which genres are different from each other?
eg: Italian / German / Russian orchestral vs orchestral / jazz / rock?
“Category counting”:
Existing Approaches to Diversity: Variety
varietynumber of genres in mix
increasing diversity
balanceevenness in allocations
varietynumber of elements in mix
What is Cultural Diversity?
balanceevenness in allocations
varietynumber of elements in mixincreasing
diversity
What is Cultural Diversity?
balanceevenness in allocations
Existing Approaches to Diversity: Balance
- addresses problem of when to start counting (partitioning)
eg: one record sale? one thousand?
- addresses varying degrees of allocation in total sales
eg: “90% / 5% / 5%” or “33% / 33% / 33%”
- still raise questions over ‘when is it one element and when two’?eg: “classic” / “opera / chamber /
orchestral”
- treats elements as if they are all equally different from each other
eg: “3 types of opera” / “rock, jazz, opera”
BUT:
Widespread in ecology & economics, more recently in energy policy
eg: Herfindahl ( i pi2 )
Shannon ( –i pi.ln pi )
increasing diversity
disparitydegree of differences
varietynumber of elements in mix
balanceevenness in contributions
What is Cultural Diversity?
increasing diversity
disparitydegree of differences
varietynumber of elements in mix
balanceevenness in contributions
What is Cultural Diversity?
disparitydegree of differences
Portfolio and taxonomic theories give elegant methods for representing disparity
- eg: Markowitz, Solow, Weitzman)
- represent particular parameters, taxonomies or geometries
BUT:
- do not accommodate contending parameters, taxonomies or geometries
- depend on multiple hidden variables (taxonomies, correlations, covariance, probability distributions)- do not address importance of variety and
balance
Existing Approaches to Diversity: Disparity
NEVERTHELESS: (whether explicit or acknowledged or not)
systematic transparent characterising of disparity is central to diversity measurement
1 Scaling of variety: where variety = 1, = 0
2 Monotonicity of variety: for equal B, D; rises monotonically with V
3 Monotonicity of balance: for given V, D; rises monotonically with B
4 Monotonicity of disparity: for given V, B; rises monotonically with D
5 Scaling of disparity: where aggregate difference = 0; = 0
6 Open Accommodation: is symmetric to any perspective on disparity
8 Parsimony of Form: has few components and simple structure
9 Explicit Aggregation: allows explicit weightings on V, B and D
7 Robust to Partitioning: is insensitive to aggregation on taxonomy
10 Ready Articulation: can be integrated with other priorities
Conditions for a General ‘Diversity Heuristic’
Start with disparity: for any particular perspective, any cultural portfolio can
be represented in multidimensional ‘disparity space’ (of attributes, properties)
Constructing a General Diversity Heuristic
applies equally to: literature
music
film
art
theatre
dance
opera
and diverse classical
critical perspectives: populist
avant garde
national bias
foreign bias
minority interest
Challenge of Objectivity:
This is intrinsic to any classification.
The task of a general diversity measure is to be symmetrical with respect to different classificatory schemes and yield transparent, definitive and comparable results across different taxonomies.
Distances between pairs of elements represent their mutual disparity (da,b )
a
b
c
Start with disparity: for any particular perspective, any diverse mix can
be represented in multidimensional ‘disparity space’ (of attributes, properties)
From Cultural Disparity to Cultural Diversity
Distances between pairs of elements represent their mutual disparity (da,b )
Disparity of a portfolio of elements is given as a function of these pairwise distances
a
b
c
da,b db,c
and…
Variety and balance can be captured by weighting this by the product of the proportional importance in the system of each element in the pair (pi.pj) = .pi.pj ij (ij) dij
Start with disparity: for any particular perspective, any diverse mix can
be represented in multidimensional ‘disparity space’ (of attributes, properties)
From Cultural Disparity to Cultural Diversity
easily shown to fulfill first six mathematical criteria:
= ij dij.pi .pj
Some Properties of the New Diversity Heuristic
1: if variety = 1; = 0
2: rises monotonically with variety
3: rises monotonically with balance unlike category
counting
4: rises monotonically with disparity unlike
Herfindahl/Shannon
5: if disparity = 0; = 0 unlike
Herfindahl/Shannon
6: generalises for any disparity attributes, dij unlike MVPA,
Weitzman
= ij dij.pi .pj
Easily shown to fulfill first six mathematical criteria
in addition: is robust to partitioning (criterion 7) unlike Shannon,
Herfindahl
Some Properties of the New Diversity Heuristic
PORTFOLIO A
= ij dij.pi .pj
Easily shown to fulfill first six mathematical criteria
disparity
in addition: is robust to partitioning (criterion 7) unlike Shannon,
Herfindahl
Some Properties of the New Diversity Heuristic
rock rap opera
PORTFOLIO A
= ij dij.pi .pj
Easily shown to fulfill first six mathematical criteria
Some Properties of the New Diversity Heuristic
disparity
in addition: is robust to partitioning (criterion 7) unlike Shannon,
Herfindahl
PORTFOLIO A
70% 5% 25%
= ij dij.pi .pj
Easily shown to fulfill first six mathematical criteria
Some Properties of the New Diversity Heuristic
disparity
in addition: is robust to partitioning (criterion 7) unlike Shannon,
Herfindahl
rock rap opera
PORTFOLIO A PORTFOLIO B
70% 5% 25% 70% 25% 5%
{ A } > { B }
in addition: is robust to partitioning (criterion 7) unlike Shannon,
Herfindahl
= ij dij.pi .pj
Easily shown to fulfill first six mathematical criteria
Some Properties of the New Diversity Heuristic
disparity
rock rap opera rock rap opera
= ij dij.pi .pj
Some Properties of the New Diversity Heuristic
allows exploring of weights on variety, balance, disparity (9) unique
in addition: is robust to partitioning (criterion 7)
Easily shown to fulfill first six mathematical criteria
´ = ij (dij) .(pi .pj)
= ij dij.pi .pj
Some Properties of the New Diversity Heuristic
allows exploring of weights on variety, balance, disparity (9) unique
in addition: is robust to partitioning (criterion 7)
Easily shown to fulfill first six mathematical criteria
´ = ij (dij) .(pi .pj)
0 0
´
ij dij0
diversity property
variety
= ij dij.pi .pj
Some Properties of the New Diversity Heuristic
in addition: is robust to partitioning (criterion 7)
Easily shown to fulfill first six mathematical criteria
allows exploring of weights on variety, balance, disparity (9) unique
´ = ij (dij) .(pi .pj)
0 0
0 1
´
ij dij0
ij pi.pj
diversity property
variety
balance
= ij dij.pi .pj
Some Properties of the New Diversity Heuristic
in addition: is robust to partitioning (criterion 7)
Easily shown to fulfill first six mathematical criteria
allows exploring of weights on variety, balance, disparity (9) unique
´ = ij (dij) .(pi .pj)
0 0
0 1
1 0
´
ij dij0
ij pi.pj
ij dij
diversity property
variety
balance
disparity
= ij dij.pi .pj
Some Properties of the New Diversity Heuristic
´ = ij (dij) .(pi .pj)
in addition: is robust to partitioning (criterion 7)
Easily shown to fulfill first six mathematical criteria
0 0
0 1
1 0
1 1
´
ij dij0
ij pi.pj
ij dij
ij dij.pi.pj
diversity property
variety
balance
disparity
diversity
allows exploring of weights on variety, balance, disparity (9) unique
Some Properties of the New Diversity Heuristic
New term, ij, allows heuristic attention to coherence (10) unique
ie: electricity portfolio interactions
= ij dij.ij.pi .pj
allows exploring different weights on variety, balance, disparity (9)
in addition: is robust to partitioning (criterion 7)
Easily shown to fulfill first six mathematical criteria
ij
PORTFOLIO A
gas wind75% 25%
Some Properties of the New Diversity Heuristic
PORTFOLIO A
= ij dij.ij.pi .pj
in addition: is robust to partitioning (criterion 7)
Easily shown to fulfill first six mathematical criteria
allows exploring different weights on variety, balance, disparity (9)
New term, ij, allows heuristic attention to coherence (10) unique
ie: electricity portfolio interactions `
+
+
gas wind75% 25%
Some Properties of the New Diversity Heuristic
+
+
75% nuclear 25% wind
PORTFOLIO B
value: { A } > value: { B }
= ij dij.ij.pi .pj
in addition: is robust to partitioning (criterion 7)
Easily shown to fulfill first six mathematical criteria
PORTFOLIO A
allows exploring different weights on variety, balance, disparity (9)
New term, ij, allows heuristic attention to coherence (10) unique