On the Measurement of Polarisation: A questionnaire study

1
On the Measurement of Polarisation A
questionnaire study

• Yoram Amiel, Frank Cowell, Xavi Ramos
• Ruppin Academic Center, Israel
• London School of Economics
• Universitat Autònoma de Barcelona
• May 2008
• http//darp.lse.ac.uk/polarisation/

2
Motivation

• Reasons for interest in polarisation
• concern with conflict and social division
• a link with inequality?
• Wolfson (Review of Income and Wealth 1997)
• Reasons for interest in measurement
• formalise intuition?
• do same job as in poverty inequality?
• Reasons for this approach
• do the formalisations make sense?
• do they really accord with intuitions?

3
Wolfson inequality and polarisation
4
The concept of polarisation

• Assumes the existence of poles
• normally two
• income levels
• Assumes agglomeration of at more than one pole.
• Need some of kind structure to give meaning to
  the concept
• also computable indices.
• Axiomatisation as in
• Esteban, J. and D. Ray (1994). On the measurement
  of polarization. Econometrica 62, 819-851.
• Chakravarty, S. R. and A. Majumdar (2001).
  Inequality, polarisation and welfare Theory and
  applications. Australian Economic Papers 40,
  1-13.
• Wang, Y.-Q. and K.-Y. Tsui (2000). Polarization
  orderings and new classes of polarization
  indices. Journal of Public Economic Theory 2,
  349-363.

5
Axiomatisation

• Some axioms used in polarisation are familiar
• similar to those used for inequality
• also social welfare and poverty
• Use these related fields
• Draw on methodology for attitudes to
  distributional comparisons
• compare empirical results with this literature
• But polarisation is a distinct concept
• requires a distinct axiomatisation

6
Esteban-Ray 1
p1
2p2

• Merging the masses x2 , x3 at geometric mean
  increases P

7
Esteban-Ray 2
p1
p3
p2

• Moving mass at x2 to the right increases P

8
Esteban-Ray 3, 4

• Moving mass from the middle outwards increases P

• Migration from a very small mass at low income to
  a moderately-sized high income does not reduce P

9
C M Increased spread

• P must increase if you decrease an income below
  the median or if you increase an income above the
  median

10
C M Increased bipolarity

• P must increase if you bunch incomes closer
  together
• within the group below the median
• within the group above the median
• Is it also related to Esteban-Ray Axiom 1?

11
Other axioms

• Population principle
• Scale Independence
• Translation Independence

12
Method

• Set up pairwise income-distribution comparisons
• Invite respondents which represents greater
  polarisation?
• purely ordinal approach
• Use collection of rankings on income-distribution
  pairs
• get insight on whether axiomatisation is
  appropriate
• are structures imposed consistent with people's
  perceptions of polarisation?
• Are respondents influenced by way questions are
  presented?
• Within a questionnaire pose questions both as
  numerical problems and in terms of principles
  expressed verbally.
• We used concurrently three forms of questionnaire
  that presented the numerical representation in
  different ways.

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Questionnaire introduction
14
Questionnaire no hints
15
Questionnaire hints
16
The pix version IS
17
The pix version IB
18
Verbal question IS
19
Verbal question IB
20
Axioms and Answers
Axiom Answers consistent with axiom ER Axiom
1 11B, 12B, 22B ER Axiom 2 6B, 18A ER Axiom
3 7B, 19A ER Axiom 4 8B, 20A Increased
Spread 1A, 7B, 9A, 10A, 13aC, 13bB,
21A Increased Bipolarity 2A, 14B Population
Principle 3AB, 15C Scale Independence 4AB, 5A,
16A, 17A Translation Independence 5AB, 4B, 17B,
16B
21
Finally

• Some personal questions

22
Sample

• Main study plus two follow-ups
• mixture of paper and Internet questionnaires
• Main
• 1263 respondents
• 550 Catalan
• 363 English
• 608 Spanish
• Follow-up 1
• 259 respondents
• special focus on polarisation versus inequality
  issue
• Follow-up 2
• 191 respondents
• special focus on ER1 versus IB issue

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Characteristics of main sample
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Main Study Increased Spread

• Q1 69 support this property
• verbal questions similar results
• 11a gets 69
• 11b gets 71
• Symmetry in the evaluation of (similar) changes
  when occurring at different ends (or halves) of
  the distribution
• People dont give more importance to a gap at the
  lower rather than the upper end of the
  distribution.

25
Main Study Increased Bipolarity

• Seems to be little support
• unfortunate because it provides a clear
  distinction between polarisation and inequality.
• Q2 Only 30.1
• Q14 Just 19.7
• Some respondents may consider that small changes
  make no difference
• Favoured option equalising transfer decreases
  polarisation.
• Result in Q2 could arise because the equalising
  transfer implies a loss in identification
• the pole at 10 loses one fourth of its mass,
• the movement does not generate another pole but
  creates a somewhat blurred picture at the bottom
  end of the distribution
• Respondents may be influenced by the notion of
  inequality
• Level of income of the poorest individual may
  have a large impact on individual's polarisation
  assessment

26
Main Study structure

• Population Principle Majority of the sample
  in line with this
• numerical 57
• verbal 83
• 69 of those who did not answer in line with the
  principle in the numerical question did so in the
  verbal one
• Scale Invariance Some support, especially in
  the verbal question
• only 28 for numerical question
• Translation Invariance Clear support
  dominates scale invariance
• numerical 61.5
• verbal 65
• cross-check 41 consistently respond in line
  with translation invariance in questions 5 and
  17.
• Verbal questions seem more persuasive than
  numerical
• Consistency between numerical and verbal
  questions
• both types of questions provide greater support
  for translation than for scale invariance

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Follow-up 1

• Do people really distinguish between I and P when
  they respond?
• FU1 used roughly equal numbers of
  I-questionnaires and P-questionnaires
• focus on cases where responses should differ
  between I and P
• numerical questions 2, 8, 9
• verbal questions 14, 20, 21
• Ambiguous results
• example Increased Bipolarity issue
• for numerical Q2 get similar responses
• for verbal Q14 get opposite responses

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Follow-up 2

• Lack of support for IB fatal for polarisation?
• Note this is not the same as ER1
• IB can be seen as a generalisation
• FU2 has explicit questions on both ER1 and IB
• ER1 questions (11, 12 and 22) are new
• IB questions (2 and 14) already in main study
• IB results much as before
• ER1 results more in line with orthodoxy
• but still not a majority
• But ER1 provides a nice discrimination
• I and P results clearly differ

29
Follow-up 2 a version of ER1
30
Follow-up 2 another version of ER1
31
Follow-up 2 P and I
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Questionnaire type?

• Necessarily complex
• Does it matter if we point people in the right
  direction?
• We have an automatic check because of
  questionnaire formats
• numerical hints
• pictures
• Numerical hints dont do much
• often respondents support principle more without
  hints!
• for example IS and IB
• Pictures sometimes help
• for example on structural questions
• also for IB

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Personal characteristics?

• Use multinomial logit
• examine effect of characteristics on response
  pattern
• consider two examples of this
• More likely to be heterodox on Q1 (IS)?
• older
• employed
• not an economist
• right wing
• More likely to be orthodox on Q2 (IB)?
• social sciences (not economist)
• not low income background
• not low income prospects
• pictures

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Conclusions

• Only weak support for main polarisation axiom
• more support for ER1 than for IB
• overall support for P indices very low
• Polarisation clearly distinguished from
  inequality?
• holds for ER1
• but not true for IB
• Consistency across component subsamples
• Translation invariance characterises comparisons
• contrast scale invariance for inequality
• Numerical hints dont do much
• Pictures sometimes help