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Einhorn’s Theory of Happiness

The statistical mind looks beyond pleasure and pain.

Key points

  • An assessment of happiness requires us to look at nonevents as well.
  • Behavioral decision theory is relevant for the study of happiness.
J. Krueger
3 cookies of happniess
Source: J. Krueger

Don’t think about all the things that you want that you don’t have. Think of all the things that you don’t want that you don’t have. – Fortune cookie wisdom

Hillel Einhorn, one of the godfathers of behavioral decision theory (see Hogarth & Klayman, 1988, for a loving obituary), once found this epigraphic piece of wisdom in a fortune cookie, which got him thinking about the things he did not want and did not have (see here). Einhorn caught a glimpse of a statistical theory of happiness. Once we distinguish, he said, the things we want from the things we don’t want and the things we have from the things we don’t have, we can behold a 2 by 2 frequency table. Let’s call the things we want and have A, the things we want and don’t have B, the things we don’t want and have C, and the things we neither want nor have D. We can now estimate the correlation between (not) wanting and (not) having. A positive correlation would indicate happiness.

David Grüning
Einhorn's 2 x 2 of happiness
Source: David Grüning

Let’s call the conjunction of wants and haves pleasure (cell A, at the top left of the matrix in the figure). The conjunction of wants and not-haves, that is, cell B, might be called desire, and specifically unmet desire. The conjunction of not-wants and haves, cell C, might be called pain. Finally, Einhorn’s fortune cookie cell, D, is the conjunction of not-wants and not-haves.’ In the matrix, cells A and D are shaded green to indicate positive value, whereas cells B and C are shaded pink for negative value. The correlation between rows and columns is Φ = (AD-BC) / √(A+B)(C+D)(A+C)(B+D).

Let’s put some numbers into the cells to see how the Φ coefficient behaves and what lessons it can teach about happiness. There are several Φ calculators available online. For this exploration, let’s use the Statology site. We begin by generating numbers using two simple assumptions. First, suppose things are going well in that there are many pleasures that come to mind but few desires or pains. Second, Einhorn’s fortune cookie events, since they are nonevents, are hard to think of. Taking A = 10, B = 5, C = 5, and D = 0 as a start, we find that Φ = -.333. This is an unhappy result, although there are as many pleasures as there are unfulfilled desires and pains combined. We might even count our blessings and get the number of pleasures up to 100. The correlation is reduced in strength, but it remains negative with Φ = -.048. No positive number of pleasures yields a positive correlation if the three other numbers remain the same. Entering Einhorn with just 3 instance in cell D, however, turns the correlation into a positive Φ = .04. When, as is reasonable to assume, few unwanted non-events readily come to mind, just being able to think of a few more such non-event has a stronger salutary effect on the overall association than does adding more blessings to those already counted.

We may wonder if the Φ coefficient represents a psychological reality. A skeptic might argue that there is nothing but transitory psychological states. As we dwell on one of the 4 cells in our scheme, we represent either pleasures or pains, unmet desires, or misfortunes escaped, and we feel accordingly. A radical version of this argument is that we cannot integrate these states or aggregate them as the result would not correspond to any experiential state. A more forgiving form of skepticism says we may add up the positive entries (A + D) and subtract the negative ones (B + D); we just can’t compute a correlation. This approach has some appeal. It uses all available information and a difference of sums is always computable. In contrast, the Φ coefficient is not defined if there are no entries in one row or in one column. Moreover, the (A + D) – (B + C) index will be positively correlated with the Φ coefficient over cases when both indices can be computed. Yet, interesting differences remain. As noted above, when we start with a distribution such as A = 10, B = 5, C = 5, D = 0, increasing A or increasing D by the same amount will increase the difference score by the same amount. By contrast, the Φ coefficient becomes more positive more strongly when the smaller cell of the two is increased. Either way, we should not worry too much that an index integrating all 4 cells has no psychological meaning. At least we’d be in the good company of all those psychologists who ask questions such as “All things considered, how happy are you?” Such questions assume that respondents can take stock of relevant experiences, sample them from memory, and make a judgment of their overall drift.

That being so, and this is a lesson we learn from Einhorn, we can ask what happens when respondents consider only part of the accessible information — that is, if they fail to look at all four cells of the scheme. Ordinary respondents are not alone in their partiality. Some ‘positive‘ psychologists advise us to count our blessings — that is, to focus on the pleasures in cell A. Others, of the school of hedonism, ask about the relative preponderance of pleasures over pains (i.e., A – C). Still others, of the school of desire-satisfaction, ask about the relative preponderance of desires met over desires foiled (A – B). Einhorn’s insight was that all these efforts come with a unique blind spot, and all share the blind spot of considering that which we don’t have but also don’t want. Thus, on conceptual and statistical grounds, cell D matters.

Yet, as the conjunction of two negatives (don’t want & don’t have), cell D is ghostlike. It is easily overlooked, but when we confront it unwittingly, it is apt to spook us. On a good day, contemplation of cell D can beget humor, insight, and wisdom. Diagoras of Melos is said to have visited a shrine to the sea god who protected sailors. When his host delighted in the many votive offerings made by sailors who had returned safely to shore, Diagoras noted that there would be many more offerings had the drowned sailors also had the opportunity to thank the gods (Pettigrew, 1998). Another tale from antiquity makes the point more directly. In De Rerum Natura, the poet Lucretius muses ‘How lovely it is, when the winds lash the great sea into huge waves that beset sailors, to gaze out from dry land at the tribulations of others . . . [opening verse of Book II; Suave, mari magno turbantibus . . .] (Slavitt, 2008; see also Krueger, 2021). That’s cell D! Of course, cell D can be contemplated without beholding the suffering of others. It is a less nasty attitude, and it won’t bring survivor’s guilt in its wake.

Einhorn’s scheme is a general one. It can be applied to any domain of life. Robyn Dawes (2006), an eminent cognitive psychologist, a critic of clinical psychology, and a contemporary of Einhorn, captured the issue in his work on the structural availability bias. Clinical psychologists, Dawes argued, are liable to suffer an illusion of validity because they have no knowledge of the individuals whom they did not treat but who got better (this might be cell B). Then again, these psychologists also lack knowledge of those whom they did not treat and who did not get better (cell D). Thinking of those cases might help these psychologists to soften the blow of Dawes’s critique.

As a blogger, I (JK) can think about all the cool posts I have written. I can also think about the good ones I haven’t been able to write and the ones that turned out bad or were rudely criticized by commenters (when the site still allowed comments). Following Einhorn, I will now sit and meditate on the posts I never wanted to write and never wrote. It will make me feel better.

Note: I wrote this essay with David J Grüning, Heidelberg University


Dawes, R. M. (2006). An analysis of structural availability biases, and a brief study. In K. Fiedler & P. Juslin (Eds.) Information sampling and adaptive cognition (pp. 147-152). Cambridge University Press.

Hogarth, R. M., & Klayman, J. (1988). Hillel J. Einhorn (1941–1987). American Psychologist, 43(8), 656.

Krueger, J. I. (2021). Happiness made simple. Psychology Today Online.

Pettigrew, M. (1998). Diagoras of Melos (500 BC): an early analyst of publication bias. The Lancet, 352, 9139.

Slavitt, D. R. (2008). Lucretius – De rerum natura: The nature of things. University of California Press.