Natural Rationality | decision-making in the economy of nature
Showing posts with label marginal utility. Show all posts
Showing posts with label marginal utility. Show all posts

9/29/07

How is (internal) irrationality possible?

Much unhappiness (...) has less to do with not getting what we want, and more to do with not wanting what we like.(Gilbert & Wilson, 2000)

Yes, we should make choices by multiplying probabilities and utilities, but how can we possibly do this if we can’t estimate those utilities beforehand? (Gilbert, 2006)

When we preview the future and prefeel its consequences, we are soliciting advice from our ancestors. This method is ingenious but imperfect. (Gilbert, et al. 2007)


Although we easily and intuitively assess each other’s behavior, speech, or character as irrational, providing a non-trivial account of irrationality might be tricky (something we philosophers like to deal with!) Let’s distinguish internal and external assessment of rationality: an internal (or subjective) assessment of rationality is an evaluation of the coherence of intentions, actions and plans. An external (or objective) assessment of rationality is an evaluation of the effectiveness of a rule or procedure. It assesses the optimality of a rule for achieving a certain goal. An action can be rational from the first perspective but not from the second one, and vice versa. Hence subjects’ poor performance in probabilistic reasoning can be internally rational without being externally rational: the Gambler’s fallacy is and will always be a fallacy: it is possible, however, that fallacious reasoners follow rational rules, maximizing an unorthodox utility function. Consequently, it is easy to understand how one can be externally irrational, but less easy to make sense of internal irrationality.

An interesting suggestion comes from hedonic psychology, and mostly Dan Gilbert’s research: irrationality is possible if agents fail to want things they like. Gilbert research focuses on Affective Forecasting, i.e., the forecasting of one's affect (emotional state) in the future (Gilbert, 2006; Wilson & Gilbert, 2003): anticipating the affective valence, intensity, duration and nature of specific emotions. Just like Tversky and Kahneman studied biases in probabilistic reasoning, he and his collaborator study biases in hedonistic reasoning.

In many cases, for instance, people do not like or dislike an event as much as they thought they would. They want things that do not promote welfare, and not want things that would promote their welfare. This what Gilbert call “miswanting”. We miswant, explain Gilbert, because of affective forecasting biases.

Take for instance impact biases: subject overestimate the length (durability bias) or intensity (intensity bias) of future emotive states (Gilbert et al., 1998):

“Research suggests that people routinely overestimate the emotional impact of negative events ranging from professional failures and romantic breakups to electoral losses, sports defeats, and medical setbacks”. (Gilbert et al., 2004).

They also underestimate the emotional impact of positive events such as winning a lottery (Brickman et al., 1978): newly rich lottery winners rated their happiness at this stage of their life as only 4.0, (on a 6-point scale, 0 to 5) which does not differ significantly from the rating of the control subjects. Also surprising to many people is the fact that paraplegics and quadriplegics rated their lives at 3.0, which is above the midpoint of the scale (2.5). In another study, Boyd et al., (1990) solicited the utility of life with a colostomy from several different groups: patients who had rectal cancer and who had been treated by radiation, patients who had rectal cancer and who had been treated by a colostomy, physicians who had experience treating patients with gastrointestinal malignancies, and two groups of healthy individuals. The patients with a colostomy and the physicians rated life with a colostomy significantly higher than did the other three groups. Another bias is the Empathy gap: humans fail to empathize or predict correctly how they will feel in the future, i.e. what kind of emotional state they will be in. Sometimes, we fail to take into account how much our psychological “immune system” will ameliorate reactions to negative events. People do not realize how they will rationalize negative outcomes once they occur (the Immune neglect). People also often mispredict regret (Gilbert et al., 2004b):
the top six biggest regrets in life center on (in descending order) education, career, romance, parenting, the self, and leisure. (…) people's biggest regrets are a reflection of where in life they see their largest opportunities; that is, where they see tangible prospects for change, growth, and renewal. (Roese & Summerville, 2005).
So a perfectly rational agent, at time t, would choose to do X at t+1 given what she expects her future valuation of X to be. As studies showed, however, we are bad predictors of our own future subjective appreciation. The person we are at t+1 may not totally agree with the person we were at t. So, in one sense, this gives a non-trivial meaning to internal irrationality: since our affective forecasting competence is biased, we may not always choose what we like or like what we choose. Hedonic psychology might have identified incoherence between intentions, actions and plans, an internal failure in our practical rationality.

Recommended reading:



References

  • Berns, G. S., Chappelow, J., Cekic, M., Zink, C. F., Pagnoni, G., & Martin-Skurski, M. E. (2006). Neurobiological Substrates of Dread. Science, 312(5774), 754-758.
  • Boyd, N. F., Sutherland, H. J., Heasman, K. Z., Tritchler, D. L., & Cummings, B. J. (1990). Whose Utilities for Decision Analysis? Med Decis Making, 10(1), 58-67.
  • Brickman, P., Coates, D., & Janoff-Bulman, R. (1978). Lottery Winners and Accident Victims: Is Happiness Relative? J Pers Soc Psychol, 36(8), 917-927.
  • Gilbert, D. T. (2006). Stumbling on Happiness (1st ed.). New York: A.A. Knopf.
  • Gilbert, D. T., & Ebert, J. E. J. (2002). Decisions and Revisions: The Affective Forecasting of Changeable Outcomes. Journal of Personality and Social Psychology, 82(4), 503–514.
  • Gilbert, D. T., Lieberman, M. D., Morewedge, C. K., & Wilson, T. D. (2004a). The Peculiar Longevity of Things Not So Bad. Psychological Science, 15(1), 14-19.
  • Gilbert, D. T., Morewedge, C. K., Risen, J. L., & Wilson, T. D. (2004b). Looking Forward to Looking Backward. The Misprediction of Regret. Psychological Science, 15(5), 346-350.
  • Gilbert, D. T., Pinel, E. C., Wilson, T. D., Blumberg, S. J., & Wheatley, T. P. (1998). Immune Neglect: A Source of Durability Bias in Affective Forecasting. J Pers Soc Psychol, 75(3), 617-638.
  • Gilbert, D. T., & Wilson, T. D. (2000). Miswanting: Some Problems in the Forecasting of Future Affective States. Feeling and thinking: The role of affect in social cognition, 178–197.
  • Kermer, D. A., Driver-Linn, E., Wilson, T. D., & Gilbert, D. T. (2006). Loss Aversion Is an Affective Forecasting Error. Psychological Science, 17(8), 649-653.
  • Loomes, G., & Sugden, R. (1982). Regret Theory: An Alternative Theory of Rational Choice under Uncertainty. The Economic Journal, 92(368), 805-824.
  • Roese, N. J., & Summerville, A. (2005). What We Regret Most... And Why. Personality and Social Psychology Bulletin, 31(9), 1273.
  • Seidl, C. (2002). Preference Reversal. Journal of Economic Surveys, 16(5), 621-655.
  • Slovic, P., Finucane, M., Peters, E., & MacGregor, D. G. (2002). Rational Actors or Rational Fools: Implications of the Affect Heuristic for Behavioral Economics. Journal of Socio-Economics, 31(4), 329-342.
  • Srivastava, A., Locke, E. A., & Bartol, K. M. (2001). Money and Subjective Well-Being: It's Not the Money, It's the Motives. J Pers Soc Psychol, 80(6), 959-971.
  • Thaler, A., & Tversky, R. H. (1990). Anomalies: Preference Reversals. Journal of Economic Perspectives, 4, 201-211.
  • Wilson, T. D., & Gilbert, D. T. (2003). Affective Forecasting. Advances in experimental social psychology, 35, 345-411.



4/22/07

marginal utility, value and the brain

Economics assumes the principle of diminishing marginal utility, i.e. the utility of a good increases more and more slowly as the quantity consumed increases (Wikipedia). Mathematically, it means that the value of a monetary gain is not a linear function of the monetary value. Before Bernouilli St-Petersburg Paradox (1738]1954), the expected value of a possible gamble was construed as the product of the objective (for instance, monetary) value of its outcomes and its probability. Suppose, then, a gambler is offered the following lottery:

A fair coin is tossed. If the outcome is heads, the lottery ends and you win 2$. If the outcome is tail, toss the coin again. It the outcome is heads, the lottery ends and you win 4$, etc. If the nth outcome is heads, you win 2n.

Summing the products of probability and value leads to an infinite expected value:

(0.5 x 2) + (0.25 x 4) + (0.125 x 8)…. =
1+1+1 …

After 30 tosses, the gambler could win more than 1 billion $. How much would it be worth paying for a ticket? If a rational agent maximizes expected value, he or she must be willing to buy a ticket for this lottery at any finite price, considering that the expected value of this prospect if infinite. But, as Hacking pointed out, “few of us would pay even $25 to enter such a game” (Hacking, 1980). When Bernoulli offered scholars in St-Petersburg to play this lottery, nobody was interested in it. Bernoulli concluded that the utility function is not linear, but logarithmic. Hence the subjective value of 10$ is different, depending whether you are Bill Gates or a homeless. Bernoulli’s discussion of the St-Petersburg paradox is often considered as one of the first economic experiment (Roth, 1993, p. 3).

A new study in neuroeconomics (Tobler et al.) indicates that the brain's valuation mechanisms follow this principle. Subjects in the experiments had to learn whether a particular abstract shape--shown on a computer screen--predicts a monetary reward (a picture of a 20 pence coin) or not (scrambled picture of the coin). If the utility of money has a diminishing marginal value, then money should be more important for poorer people than for richer. "More important" meaning that the former would learn reward prediction partterns faster and would display more activity in reward-related area. Bingo! That's exactly what happened. Midbain dopaminergic regions were more solicited in the poorer. The valuation mechanisms obey diminishing marginal utility.

This suggest that midbain dopaminergic systems (about which I blogged earlier; see also references at the end of this post) are the seat of our natural rationality, or at least one of its major component. These systems compute utility, stimulate motivation and attention, send reward-prediction error signals, learn from these signals and devise behavioral policies. They do not encode anticipated or experienced utility (other zones are recruited for these: the amygdala and nucleus accumbens for experienced utility, the OFC for anticipated utility, etc.), but decision utility, the cost/benefits analysis of a possible decision.


References

  • Bernoulli, D. (1738]1954). Exposition of a new theory on the measurement of risk. Econometrica, 22, 23-36.
  • Hacking, I. (1980). Strange expectations. Philosophy of Science, 47, 562-567.
  • Roth, A. E. (1993). On the early history of experimental economics. Journal of the History of Economic Thought, 15, 184-209.
  • Tobler, P. N., Fletcher, P. C., Bullmore, E. T., & Schultz, W. (2007). Learning-related human brain activations reflecting individual finances. Neuron, 54(1), 167-175.
On dopaminergic systems:
  • Ahmed, S. H. (2004). Neuroscience. Addiction as compulsive reward prediction. Science, 306(5703), 1901-1902.
  • Bayer, H. M., & Glimcher, P. W. (2005). Midbrain dopamine neurons encode a quantitative reward prediction error signal. Neuron, 47(1), 129.
  • Berridge, K. C. (2003). Pleasures of the brain. Brain and Cognition, 52(1), 106.
  • Berridge, K. C., & Robinson, T. E. (1998). What is the role of dopamine in reward: Hedonic impact, reward learning, or incentive salience? Brain Res Brain Res Rev, 28(3), 309-369.
  • Cohen, J. D., & Blum, K. I. (2002). Reward and decision. Neuron, 36(2), 193-198.
  • Daw, N. D., & Doya, K. (2006). The computational neurobiology of learning and reward. Curr Opin Neurobiol, 16(2), 199-204.
  • Daw, N. D., & Touretzky, D. S. (2002). Long-term reward prediction in td models of the dopamine system. Neural Comput, 14(11), 2567-2583.
  • Dayan, P., & Balleine, B. W. (2002). Reward, motivation, and reinforcement learning. Neuron, 36(2), 285-298.
  • Di Chiara, G., & Bassareo, V. (2007). Reward system and addiction: What dopamine does and doesn't do. Curr Opin Pharmacol, 7(1), 69-76.
  • Egelman, D. M., Person, C., & Montague, P. R. (1998). A computational role for dopamine delivery in human decision-making. J Cogn Neurosci, 10(5), 623-630.
  • Floresco, S. B., & Magyar, O. (2006). Mesocortical dopamine modulation of executive functions: Beyond working memory. Psychopharmacology (Berl), 188(4), 567-585.
  • Frank, M. J., Seeberger, L. C., & O'Reilly, R. C. (2004). By carrot or by stick: Cognitive reinforcement learning in parkinsonism. Science, 306(5703), 1940-1943.
  • Joel, D., Niv, Y., & Ruppin, E. (2002). Actor-critic models of the basal ganglia: New anatomical and computational perspectives. Neural Netw, 15(4-6), 535-547.
  • Kakade, S., & Dayan, P. (2002). Dopamine: Generalization and bonuses. Neural Netw, 15(4-6), 549-559.
  • McCoy, A. N., & Platt, M. L. (2004). Expectations and outcomes: Decision-making in the primate brain. J Comp Physiol A Neuroethol Sens Neural Behav Physiol.
  • Montague, P. R., Hyman, S. E., & Cohen, J. D. (2004). Computational roles for dopamine in behavioural control. Nature, 431(7010), 760.
  • Morris, G., Nevet, A., Arkadir, D., Vaadia, E., & Bergman, H. (2006). Midbrain dopamine neurons encode decisions for future action. Nat Neurosci, 9(8), 1057-1063.
  • Nakahara, H., Itoh, H., Kawagoe, R., Takikawa, Y., & Hikosaka, O. (2004). Dopamine neurons can represent context-dependent prediction error. Neuron, 41(2), 269-280.
  • Nieoullon, A. (2002). Dopamine and the regulation of cognition and attention. Progress in Neurobiology, 67(1), 53.
  • Niv, Y., Daw, N. D., & Dayan, P. (2006). Choice values. Nat Neurosci, 9(8), 987-988.
  • Niv, Y., Duff, M. O., & Dayan, P. (2005). Dopamine, uncertainty and td learning. Behav Brain Funct, 1, 6.
  • Redish, A. D. (2004). Addiction as a computational process gone awry. Science, 306(5703), 1944-1947.
  • Schultz, W. (1999). The reward signal of midbrain dopamine neurons. News Physiol Sci, 14(6), 249-255.
  • Schultz, W., Dayan, P., & Montague, P. R. (1997). A neural substrate of prediction and reward. Science, 275(5306), 1593-1599.
  • Schultz, W., & Dickinson, A. (2000). Neuronal coding of prediction errors. Annu Rev Neurosci, 23, 473-500.
  • Self, D. (2003). Neurobiology: Dopamine as chicken and egg. Nature, 422(6932), 573-574.
  • Suri, R. E. (2002). Td models of reward predictive responses in dopamine neurons. Neural Netw, 15(4-6), 523-533.
  • Tom, S. M., Fox, C. R., Trepel, C., & Poldrack, R. A. (2007). The neural basis of loss aversion in decision-making under risk. Science, 315(5811), 515-518.
  • Ungless, M. A. (2004). Dopamine: The salient issue. Trends Neurosci, 27(12), 706.