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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/ Motivation Reasons for interest in polarisation

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On the measurement of polarisation a questionnaire study l.jpg

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


Motivation l.jpg

  • 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?

The concept of polarisation l.jpg
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.

Axiomatisation l.jpg

  • 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

Esteban ray 1 l.jpg







Esteban-Ray 1



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

Esteban ray 2 l.jpg





Esteban-Ray 2




  • Moving mass at x2 to the right increases P

Esteban ray 3 4 l.jpg
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

C m increased spread l.jpg
C & M: Increased spread

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

C m increased bipolarity l.jpg
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?

Other axioms l.jpg
Other axioms

  • Population principle

  • Scale Independence

  • Translation Independence

Method l.jpg

  • 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.

The pix version is l.jpg

1: A=(5,10,10,10,10,50,50,50,50,50)





























A is more polarised

Please check (






B is more polarised


polarisation is the same in A and B

The pix version: IS

The pix version ib l.jpg

2: A=(7,8,10,10,10,50,50,50,50,50)





















A is more polarised

Please check (






B is more polarised


polarisation is the same in A and B

The pix version: IB

Axioms and answers l.jpg
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

Finally l.jpg

  • Some personal questions:

Sample l.jpg

  • 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

Main study increased spread l.jpg
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 don’t give more importance to a gap at the lower rather than the upper end of the distribution.

Main study increased bipolarity l.jpg
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

Main study structure l.jpg
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

Follow up 1 l.jpg
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

Follow up 2 l.jpg
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

Questionnaire type l.jpg
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 don’t 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

Personal characteristics l.jpg
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

Conclusions l.jpg

  • 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 don’t do much

  • Pictures sometimes help