Utility and consistency

1. Social foundations of consistent preferences: philosophical and neural learning background, and an experiment on a breakdown George Etheredge1, Glenn Harrison2, Andre Hofmeyr1, Harold Kincaid1, Daniel Munene1, Don Ross1,2 1 – School of Economics, University of Cape Town 2 – Center for Economic Analysis of Risk, Georgia State University

2. Utility and consistency • Risk-averse and risk-loving choice doesn’t maximize expected monetary gain. This is part of the reason why we define preferences over the abstract construct of utility. • Contrary to myth, economists do not assume that any person is perfectly consistent in their choices. However, extreme inconsistency in choice makes it difficult for someone to maintain or grow their personal wealth, especially if they are interacting with others who are more consistent than they are. Furthermore, some level of consistency in choice is a pre-condition on our being able to say that a person has preferences at all. As an application of this logic, we expect some level of consistency with respect to risk preferences. In experiments conducted all over the world with subjects making risky choices, we find very strong stability in these preferences. But South African community samples seem to be an exception.

3. Where do consistent preferences come from? • Economists – and philosophers – have often assumed that consistent preferences are the natural default, and that special explanations in terms of cognitive architecture, limited information-processing capacities, differences between the EEA and civilization, etc, are needed to explain and structure inconsistent preferences. • I think this is wrong on (at least) two dimensions: (1) Preferences don’t exist except from the intentional stance, which relates an agent to a space of ecologically distinguished options; and for humans that space is socially partitioned and scaffolded; and (2) comparative valuations in the brain don’t aggregate onto an economic preference scale. I’ll say a bit about (2) first.

4. Valuation in the brain (neuroeconomics) • A surprising discovery about neural computation of comparative option values in games is that neural groups learn mixed-strategy equilibria more reliably than they learn pure-strategy equilibria (Doris & Glimcher; Lee & Wang). • This is because brains are statistical processors: they rely on drift diffusion across very large numbers of simple units that are trained by conditioning. So they stochastically respond to distributions of (approximate) expected reward values. • This processing isn’t directly accessible to deliberation or linguistically structured self-representation. • The relevant statistics may be quantum rather than classical (Pothos & Busemeyer).

5. Preferences as social coordination devices • Developing people are socially recruited into agency. This means that they create, through trial and error under social judgment, distinctive characters for themselves that are defined by reference to matrices of preferences and expressive styles. The point of this is consistency: people need to be able to form tolerably reliable expectations about one another’s behavior under hypothetical circumstances in order to coordinate their joint projects and maintain complementary investment schedules based on specialization of information. • Consistency is not something that is or could be managed by people’s brains alone; a person and the members of her social network fill her environment with records and cues that support the maintenance of agency.

6. Flipping the person • On this picture, reward valuation systems in the brain are on all fours with external incentives to choice: responses in ventral striatum and related areas sometimes interfere with personal consistency and sometimes support it. Addiction is one kind of systematic subversion of personal consistency by the brain’s reward processing dynamics. • Can we identify pathologies on the other side of the relationship? Arguable cases are sexually abused children creating alternative selves who stand apart from the trauma; or Soviet citizens terrorized into atomism under Stalin who experienced hysterical grief on his death. But we don’t best scientifically investigate a phenomenon by considering extreme idiosyncratic instances. Also, we want to look for socially induced inconsistency we can econometrically measure. • I’ll now report on an experiment in progress.

7. Measuring risk preferences We measure people’s risk preferences by presenting them with choices between pairs of lotteries that vary systematically in ratios of risk between the members of the pairs. To understand the problem we’re investigating in South Africa, and our methodology for studying it, we must explain the experimental procedure.

9. Eliciting risk preferences Option A is the safe choice and Option B is the risky choice

10. Eliciting risk preferences: consistency It is inconsistent, regardless of risk attitude, to switch from choosing Option A to Option B and then back again to Option A.

11. Eliciting risk preferences: Attitude towards risk

12. Eliciting risk preferences: How do we now link this to a utility function? • All that we have done up to this point is elicit data on attitudes towards risk. • We now need to use the subject’s choice data to pin down the parameters of a utility function. We have various options here. It is common to impose the assumption that everyone in a population shares a common utility function. We don’t impose this assumption.

13. The CRRA utility function • The most commonly used utility function in applied risk preference research is the constant relative risk aversion (CRRA) utility function: • CRRA is a good starting point because it implies that your aversion to risk is constant and relative to your wealth => DARA. • But we use mixture specifications to allow us to empirically estimate a distribution of different utility functions in sub-sets of a given population. (We don’t assume that people are all alike.)

14. Example: estimating rgiven a CRRA function • Note that the value of r represents a person’s attitude towards risk: r < 0 => risk loving r = 0 => risk neutral r > 0 => risk averse

15. CRRA utility function: estimating r • Recall: switch to B before row 5 => risk loving switch to B in row 5 => risk neutral switch to B after row 5 => risk averse • The basic logic is that when someone switches from the safe to the risk lottery they implicitly select an interval of relative risk aversion.

16. CRRA utility function: estimating r • The variable r is the CRRA coefficient and we need to compute it from the subject’s choices • Let’s focus on row 4 of the table • Now, what we need to do is calculate the value of r that will make the expected utility of these two lotteries equal.

17. CRRA utility function: estimating r • Here are the results:

18. What we find in most populations If we use a mixture specification that allows us to estimate a distribution of different utility functions in a given population, we can find relatively stable r-values for the overwhelming majority of subjects. This includes populations sampled in rich countries and poor ones, across all levels of education, literacy and “numeracy”.

19. Which populations, exactly? • US, Danish and Cape Town university students (who show crazy time preferences but not crazy risk preferences); • hundreds of thousands of randomly selected Danish adults; • Ethiopian subsistence farmers (most illiterate); • Ghanianfisherpeople; • long-term inhabitants of refugee camps in East Timor; • adults in several rural Indian villages • adults in several rural Ugandan villages

20. What tends to be found in South African* community samples • Large sub-sets of samples – often majorities – switch multiple times in MPLs. In consequence, stable utility functions, and stable values of r, can’t be identified. • The observations are puzzling. Should someone publish a paper called “South Africans don’t care about money”? • *Also reported by some groups who’ve sought to estimate risk preferences in poor communities in Guatemala.

21. Hypotheses • Many poor South Africans – unlike poor Ethiopians or poor Ghanaians or poor East Timorese – don’t operate budgets over time; they instead get highly variable and opportunistic income and spend each installment all at once. In consequence, they frame the lottery choice sequence in an unknown way we would associate, in our ignorance, with some exotic form of “error”. • The culture inherited and reinforced by experience among poor South Africans encourages a view that the environment is globally malignant. In consequence, one should systematically hide one’s utility function from the world by randomizing choices even in non-strategic situations (playing mixed strategies against Nature).

22. Philosophy underlying hypothesis (2) • Since brains naturally approximate randomization, one way of hiding preferences is to simply hand over control to the myopic equilibrium-finding processes in the striatal reward system. Because it learns by conditioning, it would require thousands of actual outcomes (rewarded trials) before it converged on relative EVs. • In terms of the philosophical theory of the self / agent presented at the outset, this amounts to avoiding agency with respect to domains that are perceived as uncontrollably dangerous.

23. Our experiment • Step 1a: Collect observations of lottery choices in samples of poor South Africans, and model differences between sub-sets who choose consistently and subjects who don’t. • Step 1b: Have these same subjects make choices in which randomized choice and consistent choice are equally likely to maximize monetary returns unless the universe is malignant. (Have them play the game “Matching Pennies” against Nature.) Use these data to estimate quantal response equilibria for the population. This amounts to estimation of sensitivity to different conjectures about others’ choice patterns. • Step 2: Have subjects play strategic games in which non-randomized choice yields better expected returns, on average, for all, but in which randomized play by all is still an equilibrium that yields positive returns. Impute the quantal responses from step 1b to this different but matched group of subjects.

24. The story so far • We have conducted steps 1a and 1b with 400 participant subjects drawn randomly from the population of first-language isiXhosa speakers in Cape Town. We’ve done preliminary analysis on their lottery choices but haven’t yet analyzed their quantal response equilibria. • Each subject worked through 4 sets of 10 pairs of lottery options. They saw one choice at a time, to make portfolio construction difficult. Each subject was paid out on one chosen lottery, determined by dice rolling they did themselves. Subjects were brought to UCT in busloads of 20 at a time, and chose lotteries from pairs on workstations behind partitions. Choices followed extensive, piloted instructions and practice exercises. Participants also completed questionnaires on demographics, employment history, life events, and trust in their environment, which had been translated (with back-translation) into isiXhosa. isiXhosa-speaking RAs answered questions.

25. Key Summary Statistics • Data from 384 participants were included in the analysis. 27 participants were not included due to undetermined identity matching. • Population: • random sample of first-language isiXhosa speakers from greater Cape Town metropole • Age: • average 33 years • range 18-67 years. • Education: • average 12 years • 25 with zero years of schooling • 103 with Grade 12 qualification • 76 with post Grade 12 qualification (Certificate, Diploma &Degree) • Sex • Male 176 (46%)

26. Switching Categories • 0,1,3 switches with no choice of dominated lottery = consistent • 2 or 4 switches with no choice of dominated lottery = inconsistent 1 • 4 - 9 switches with no choice of dominated lottery = inconsistent 2 • chose dominated lottery = non-monotonic

27. Graph of switching Pattern

28. Transmission Matrix over 4 choice sets

29. Two probit models For a preliminary view of the data, we carried out 2 probit regressions with • Dependant variable 1 (Dep1) • 0 if consistent • 1 otherwise • Dependant variable 2 (Dep2) • 0 if consistent or inconsistent 1 • 1 otherwise

30. Covariates • Sex • 0-male • 1-female • Education • ranges from 0 (no schooling) to 21 (tertiary degree) • Financial shape: Participant’s impression of their current financial situation • 0- very good • 1- good • 2- neither • 3- bad • 4 - broke • Trust : To question “Most people will try to take advantage of you if they get the chance” • 0 - strongly agree • 1 - agree • 2 - neither • 3 - disagree • 4 - strongly disagree

31. Covariates, continued • Alcohol: how often participant drinks • 0-never • 1-once/twice • 2-monthly • 3-weekly • 4-daily • Impulsivity • Baratt Impulsivity index scale/scores. • Perceived social support from Family and Friends: • Friend and family index scales/scores: 0 (low) to 20 (high) • High Stakes • 0 if high right lottery payoff was 100 or 110 • 1 if high right lottery payoff was 300 or 400. • Order of Set : • 0 if the set ordering of lotteries (see below) was 0, 1, 2, 3 • 1 if the set ordering was 3, 2, 1, 0 • Set 0 – 25; 100 • Set 1 – 10; 110 • Set 2 – 40; 400 • Set 3 – 50; 300

32. Model 1: Stringent construction of consistency

33. Model 2:Liberal construction of consistency

34. Preliminary impressions • Female gender is the overwhelmingly dominant predictor of inconsistency and non-monotonicity in the preliminary models. Given the power imbalance and rates of domestic violence and rape in SA, this is suggestive for Hypothesis 2. • Trust and perceived support from family are significant predictors of consistency. This is suggestive for Hypothesis 2. • Perceived support from friends predicts inconsistency. This reversal with respect to perceived support from family needs investigation. • Most moderately inconsistent participants appear to have learned to choose more consistently over the course of the task. 70% of non-monotonic participants in choice set 1 remained non-monotonic choosers in choice set 4. This is suggestive for Hypothesis 2. • No significant order effects are observed.

35. Reflections • The better educated subjects with more experience of budget management but subject to extreme and pervasive risk from other people make choices that can’t be rationalized by the assumption that people prefer more money to less. • We suggest that this is evidence of a breakdown in the social maintenance of consistent agency.

36. Acknowledgments • Support from the National Research Foundation of South Africa and the Center for Economic Analysis of Risk, Georgia State University, is gratefully acknowledged. • Thanks also to our lab team, to the taxi mafias who told their soldiers not to shoot at our buses, and to the bus drivers who believed them.