What If Well-Being Measurements Are Non-Linear?

ABSTRACT

Well-being measurements are frequently used to support conclusions about a range of philosophically important issues. This is a problem, because we know too little about the intervals of the relevant scales. I argue that it is plausible that well-being measurements are non-linear, and that common beliefs that they are linear are not truth-tracking, so we are not justified in believing that well-being scales are linear. I then argue that this undermines common appeals to both hypothetical and actual well-being measurements; I first focus on the philosophical literature on prioritarianism and then discuss Kahneman's Peak-End Rule as a systematic bias. Finally, I discuss general implications for research on well-being, and suggest a better way of representing scales.

KEYWORDS:

• wellbeing
• welfare
• well-being measurement
• Kahneman
• prioritarianism
• psychological measurement
• scales

Notes

¹ I am striving to be neutral between different conceptions of well-being. I leave open whether my arguments extend to measuring non-subjective components of well-being.

² This differs from Dyke's [2014: 14] use of the same term to refer ‘to a general philosophical tendency to place too much emphasis on language when doing ontology’.

³ There are plenty of threads and columns about such mistakes online. For instance, Larry Scheckel's 22 January 2014 ‘Ask Your Science Teacher’ column, on The Tomah Journal, described ‘What temperature is twice as hot as zero degrees?’ as a ‘tricky question’.

⁴ I would like to thank an anonymous referee for pushing me on this point.

⁵ I would like to thank an anonymous referee and editor for pushing me to clarify this.

⁶ This step in the argument could be defended on the basis of modal conditions, such as versions of the Sensitivity principle (see Nozick [1981: 179]), or non-modal explanatory conditions (see, e.g., Shafer [2014]). It is often thought that such conditions on knowledge can extend to conditions for justified belief (see, e.g., Setiya [2012: 139]). I am grateful to an anonymous referee for pushing me to clarify the relevant epistemic standard.

⁷ I am grateful to an anonymous referee for drawing my attention to this.

⁸ See, inter alia, Beardman [2000], Kelman [2005], Alexandrova [2008, 2012], Barrotta [2008], Feldman [2010: ch. 3], Hausman [2010], and Angner [2011b].

⁹ See Kahneman [1997: 386]. This is in line with by Kahneman's method of ‘confirming judgmental biases’ via ‘comparisons of subjective happiness to independent assessments of objective happiness’ [1999: 22, 19 and references therein].

¹⁰ This explanation of the methodology, from Kahneman [1999: 4], omits and simplifies some details from Redelmeier and Kahneman [1996: 4]. Nothing hangs on this.

¹¹ See Redelmeier and Kahneman [1996: 4] and Kahneman [1999: 4, 2011: 379]. I have combined his two graphs into one that is easier to read.

¹² Interestingly, Kahneman's [1999: 6] view suggests a different answer: the profiles differ in ‘length’, and ‘the average height’ for A is higher than for B.

¹³ There is further evidence that Kahneman assumes linearity. Redelmeier and Kahneman [1996: 5] report mean values for pain—e.g. ‘Average Pain’ (3.1)—in the same way as they report mean values for duration in minutes [ibid.: 23]. Kahneman [2011: 380] appeals to the ‘average of the level of pain reported at the worst moment of the experience and at its end’ (‘Peak-End Rule’), which would be identical for A and C (7.5).

¹⁴ Redelmeier and Kahneman [1996: 4] use parametric Pearson correlation statistics.

¹⁵ Notably, Kahneman et al. [1997: 393] provide a representation theorem that shows that if certain axioms obtain, there is ‘a suitable monotonic transformation of instant utility (and disutility) to ratio scales … with the same zero point.’ But the representation theorem does not tell us whether the axioms hold for (say) Patient C, or what the appropriate monotonic transformation of C's utility scores would be. We need empirical evidence to rescale C's original profile: hence the procedure in Kahneman [1999].

¹⁶ I am grateful to Ralf Bader for raising this in personal communication.

¹⁷ A similar concern applies to the use of verbal labels for intervals on Likert scales. See Wu and Leung [2017] for discussion of whether such scales can be treated as linear.

¹⁸ See O'Shaughnessy [1987: 150] on the logarithmic mel scale for pitch.

¹⁹ Thanks to Ralf Bader, Guy Fletcher, Gil Hersch, Ben Jantzen, Lydia Patton, Govind Persad, Kelly Trogdon, participants at Georgetown University's Workshop on Methodology in Applied Ethics, and two anonymous referees.