# Quasi-delusions and inequality aversion

Patient M: It’s impossible —- no one could urinate into that bottle -— at least no woman could. I’m furious with her [these are the patient’s emphases] and I’m damned if I am going to do it unless she gives me another kind of bottle. It’s just impossible to use that little thing.

Analyst: It sounds as if a few minutes of communication with the nurse could clear up the realistic part of the difficulty—is there some need to be angry with the nurse and keep the feeling that she has done something to you?

Patient M: The ‘impossibility’ of using the bottle could be gotten over by using another—or I could use a funnel or a plastic cup and pour it into the bottle. But I just won’t. It makes me so mad. If she wants that sample, she is going to have to solve that problem. [Sheepishly] I know how irrational all this is. The nurse is really a very nice person. I could easily talk to her about this, and/or just bring in my own container. But I am really so furious about it that I put all my logic and knowledge aside and I feel stubborn—I just won’t do it. She [back to the emphasis] can’t make me use that bottle. She gave it to me and it’s up to her to solve the problem.

The above is an excerpt from a session between psychoanalyst Leonard Shengold (1988) and his patient. The focus is on the contrast between M’s awareness of her delusion, and yet her continued anger and frustration. Rationally and consciously she knows that there is no reason to be angry at the nurse, but yet some unconscious, emotional impulse pushes her to feel externalities that produce a behavior that she can recognize as irrational. This is a quasi-delusion.

Marcel presented a specific type of quasi-delusion in an earlier post on quasi-magical thinking. This is a mistake of inference, where an agent realizes that their action cannot change the (often simultaneous) action of another agent, and yet they act in a way that is not-consistent with this view. They act as if their action will alter the choice made by their partner. I formalized Marcel’s discussion in the context of learning in our objective versus subjective rationality framework. The goal of this post is to do the same with quasi(mis)representations of the objective game.

We consider agents interact with each other in an objective one-shot, cooperate-defect game given by the payoff matrix $\begin{pmatrix} 1 & X \\ Y & 0 \end{pmatrix}$ (with $Y \geq X$). Suppose that the agent is aware of the game, but exhibits inequality or fairness biases (Fehr & Schmidt, 1999). If the agent is sensitive to advantageous and disadvantageous inequality with strength $\alpha$ and $\beta$ then, they will act as if the game is $\begin{pmatrix} 1 & U \\ V & 0 \end{pmatrix}$, where;

$U = X - \alpha(Y - X)$ and $V = Y - \beta(Y - X)$

Which means if we know their behavior and the objective game, then we can infer the inequality biases $\alpha$ and $\beta$ as:

$\alpha = \frac{X - U}{Y - X}$ and $\beta = \frac{Y - V}{Y - X}$

The best part about these inequality biases is that they are directly observable in humans, and monkeys! My favorite example is Bronson & de Waal’s (2003) experiment with capuchin monkeys. These monkeys eat both cucumber slices and grapes as snacks, but strongly prefer grapes over cucumbers. When a monkey is given a cucumber as a reward for an easy task, he happily gobbles it up. However, after seeing his friend receive a better reward — a grape! — for the same task, the monkey becomes angry. The next time he performs the task and receives a cucumber, he is extremely unhappy and rejects the treat. It is best to watch it for yourself (excerpt from a TED talk with Frans de Waal narrating):

In humans, Tricomi et al. (2010) directly observed both advantageous and disadvantageous inequality aversion with fMRI. Although human inequality aversion might not be innate or universal, children lack it at age 3-4 but develop an ethnocentric version of inequality aversion by age 7-8 (Fehr et al., 2008). In these experimental studies, unfortunately, both the monkeys and humans were not playing a game against each other, but receiving fixed rewards from the experimentalist. To gain direct experimental insights into inequality aversion in games, we have to turn to the economics literature where the results are much more mixed. This quasi-delusion is observed by some (Anderson et al., 2008) and not other (Sadrieh et al., 2006; Hofmeyr, 2007) studies, depending on the specifics of the public-goods game in consideration. hopefully, careful computational modeling of this can help us understand this literature better.

### References

Anderson, L. R., Mellor, J. M., & Milyo, J. (2008). Inequality and public good provision: An experimental analysis. The Journal of Socio-Economics, 37(3), 1010-1028.

Brosnan, S. F. & de Waal, F. B. M. (2003). Monkeys reject unequal pay. Nature, 425: 297-299.

Fehr, E., & Schmidt, K. (1999). A Theory of Fairness, Competition, and Cooperation The Quarterly Journal of Economics, 114 (3), 817-868 DOI: 10.1162/003355399556151

Fehr, E., Bernhard, H., & Rockenbach, B. (2008). Egalitarianism in young children. Nature, 454(7208), 1079-1083.

Hofmeyr, A., Burns, J., & Visser, M. (2007). Income inequality, reciprocity and public good provision: an experimental analysis. South African Journal of Economics, 75(3), 508-520.

Sadrieh, A., & Verbon, H. A. (2006). Inequality, cooperation, and growth: An experimental study. European Economic Review, 50(5), 1197-1222.

Shengold, L. (1988). Quasi-delusions: a brief communication. International journal of Psychoanalysis, 69(4): 471-473. [full text]

Tricomi, E., Rangel, A., Camerer, C. F., & O’Doherty, J. P. (2010). Neural evidence for inequality-averse social preferences. Nature, 463(7284), 1089-1091.

From the Department of Computer Science at Oxford University and Department of Translational Hematology & Oncology Research at Cleveland Clinic, I marvel at the world through algorithmic lenses. My mind is drawn to evolutionary dynamics, theoretical computer science, mathematical oncology, computational learning theory, and philosophy of science. Previously I was at the Department of Integrated Mathematical Oncology at Moffitt Cancer Center, and the School of Computer Science and Department of Psychology at McGill University. In a past life, I worried about quantum queries at the Institute for Quantum Computing and Department of Combinatorics & Optimization at University of Waterloo and as a visitor to the Centre for Quantum Technologies at National University of Singapore. Meander with me on Google+ and Twitter.

### 6 Responses to Quasi-delusions and inequality aversion

1. Saville says:

The behaviour shown by the monkey could easily be the result of operant conditioning, as is all too common in animal research that is not appropriately blinded. Without fuller context such videos are the worst in pulp science.

See the horse Clever Hans and many other examples of accidental and deliberate fraud in animal psychology.

• That is a very general comment that you could use against almost any animal behavior study. Is there any reason to believe that Frans de Waal made such basic mistakes in his study design? I am not an experimentalist, so I am not equipped to judge this, but I was under the impression that de Waal’s group produces very sound studies. If you have further insights into why these specific experiments are flawed then I’d love to read it!

The video is included not to convince you of something (for that the paper reference is given) but to share cute and funny monkeys.

2. Kate Zen says:

Hooray for cute and funny monkeys!

Just to troll you: why did you use the word “externalities” in that way? As I understand it, it’s economic jargon to signify costs that aren’t included in a market model, such as environmental costs and information asymmetries – not exactly an “emotional impulse” to be “felt,” except in a very very metaphorical way.

• Sorry for the (extremely) slow response.

I used ‘externalities’ here specifically to play with the economic jargon. This post is part of a bigger ongoing project on EGT models of objective-versus-subjective rationality. One of the contrasts I draw in that work is the tension between the experimentalist’s ‘objective’ assessment of the fitness effects of the interaction between agents and the ‘subjective’ assessment by the agents themselves which happens to encode inclusive fitness instead of individual fitness. These inclusive fitness effects are ‘external’ to the reductionist view of the (straw-man) experimentalist in much the same way as the environmental costs or information asymmetry are external to the perspective of the (straw-man) economist.

The bigger tension in that project (and maybe economics, too) is between reductionist and holistic definitions of fitness (utility, for the economist). Recently, this tension has re-appeared in my thinking about cancer and operationalizing fitness. There is something bigger looming under the surface here, and maybe I should write a whole post on mereology to uncover this.

So, thank you for trolling me. It is very helpful.

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