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Index of Inequality-Adjusted Happiness (IAH) Improved: A Research Note

Abstract

Eight years ago we proposed a new measure of happiness in nations, called Inequality-Adjusted Happiness (IAH). This measure indicates how successful nations are in combining a high level of happiness and a low degree of inequality in happiness among citizens. The index gives equal weight to the level of happiness measured using the mean and inequality of happiness measured using the standard deviation. Scores on this index are now available for 139 nations. In this paper we present a technical improvement for the method to calculate IAH.

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Fig. 1

Notes

  1. Questions on happiness can be phrased in more ways, using different key words. An overview of questions that fit the concept of ‘the subjective appreciation of one’s life as-a-whole is available in Veenhoven (2011b). The method described in this paper applies to all measures.

  2. In an earlier paper in this journal we argued that the standard deviation is a proper statistic for measuring inequality in happiness (Kalmijn and Veenhoven 2005). Recently, Delhey and Kohler (2011) proposed an adjustment to that method. We advised against that adjustment in Kalmijn (2012) and Veenhoven (2012) to which Delhey and Kohler (2012) replied.

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Acknowledgments

The authors wish to thank Dr. Jan Koster (Erasmus University Rotterdam) for his suggestion to apply the skew projection method.

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Correspondence to Ruut Veenhoven.

Appendices

Appendix 1: Improved IAH by the Application of Skew Projection

Let in Fig. 1 the point M be the centre of the semicircle with radius LM = r. If L is adopted as the origin, a nation N can be represented by its mean happiness value m = LG as its abscissa and its internal standard deviation s = NG as its ordinate.

Let W represent the compromise for the worst conceivable situation and WZ be the tangent through W to the semicircle. The skew projection U of N onto the IAH-axis WH is obtained as the intersection of WH with the line segment ND through N parallel to WZ.

In that case, the IAH-value of N equals the ratio (UW/HW) × 100.

From the parallelism of WZ and UD follows the proportionality

$$ \underline{UW} /\underline{HW} = \underline{ZD} /\underline{ZH} . $$

The angles ZMW and DNG are equal; let their value be 2φ, where φ: = angle(WHL). The value of 2φ equals [w E/(w E + w U)](π/2), where w E and w U are the weights assigned to the egalitarian and utilitarian views respectively. Since

$$ \begin{aligned} \underline{ZD} & = \underline{ZG} - \underline{DG} = \underline{ZL} + \underline{LG} - \underline{DG} = \underline{ZM} - \underline{ML} + \underline{LG} - \underline{DG} \\ & = r/\cos 2\varphi - r + m - s\,\tan 2\varphi \quad{\text{and}} \\ \underline{ZH} & = \underline{ZM} + \underline{MH} = r/\cos 2\varphi + r, \\ \end{aligned} $$

the IAH-value of the nation represented by the point N (m,s) equals

$$ \frac{{\frac{r}{\cos \,2\varphi } - r + m - s\,\tan \,2\varphi }}{{\frac{r}{\cos \,2\varphi } + r}} \times 100 $$

This result can also be written as

$$ IAH = \frac{(m - r)\cos \,2\varphi + r - s\,\sin \,2\varphi }{r + r\,\cos \,2\varphi } \times 100 $$

In the case of equal weights w E = w U and 2φ = π/4; when happiness is quantified on a [0, 10] scale, then r = 5 and in this particular case this formula can be simplified to IAH ≈ 8.28(m − s) +17.2.

Appendix 2: Inequality-Adjusted Happiness (IAH) in 15 Nations 2003–2009

IAH-values in modified and previous version.

.

Nation Happiness Inequality-Adjusted Happiness
Average SD IAH (new) IAH (old)
Denmark 8.03 1.53 71 (75)
Iceland 7.87 1.66 69 (73)
Switzerland 7.74 1.58 68 (72)
Finland 7.61 1.56 67 (71)
Netherlands 7.33 1.37 67 (69)
Japan 6.35 1.91 54 (57)
France 6.45 2.11 53 (58)
Indonesia 6.16 2.05 51 (55)
Poland 6.26 2.29 50 (55)
China 6.14 2.45 48 (53)
Macedonia 4.68 2.57 35 (39)
Bulgaria 4.46 2.41 34 (37)
Mali 4.73 2.77 33 (38)
Zimbabwe 3.23 2.28 25 (26)
Tanzania 3.03 2.76 19 (22)
  1. Source: Veenhoven (2011a, 2013a)

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Kalmijn, W., Veenhoven, R. Index of Inequality-Adjusted Happiness (IAH) Improved: A Research Note. J Happiness Stud 15, 1259–1265 (2014). https://doi.org/10.1007/s10902-013-9474-3

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Keywords

  • Happiness
  • Inequality
  • Inequality-Adjusted Happiness (IAH)