Risk Preference — Eckel-Grossman

A simplified risk elicitation method in which respondents choose once among five gambles with identical expected values but increasing variance — the chosen gamble identifies their risk preference category.

What it is

The Eckel-Grossman (EG) method elicits risk preferences through a single choice rather than a sequence of binary decisions (Eckel & Grossman, 2002). A respondent is presented with five gambles: gamble 1 is a sure payment (degenerate lottery), and gambles 2–5 are 50/50 lotteries between a low and a high payoff. Across the five gambles, both expected value and variance rise monotonically — gamble 5 has the highest expected value but also the highest variance. A risk-neutral respondent (or anyone seeking only to maximise expected value) chooses gamble 5; risk-averse respondents accept lower expected value to reduce variance and choose lower-numbered gambles.

Two practical advantages over the Holt-Laury MPL. First, cognitive simplicity: one choice rather than ten, no probabilities to track across rows, no switching point, no sequential reasoning. Second, no probability-weighting confound: all gambles use a fixed 50/50 probability, so the elicited CRRA is not contaminated by probability weighting under cumulative prospect theory (Andersen, Harrison, Lau & Rutström, 2008; Harrison & Rutström, 2008). The cost is coarser classification — EG produces a 5- or 6-category outcome rather than a finer ordinal scale.

When to use it

The EG method is appropriate when risk aversion is a secondary variable — a control or heterogeneity moderator — rather than the primary outcome of interest, and when the respondent population has limited numeracy or attention bandwidth for multi-row tasks.

It is used across development economics, behavioural finance, and consumer research as a quick baseline measure of risk attitudes — often alongside time preference and trust measures in a short behavioural battery. The canonical comparison with Holt-Laury is Dave, Eckel, Johnson and Rojas (2010), who show that for low-numeracy respondents the simpler EG method yields better out-of-sample predictive validity than the more demanding Holt-Laury MPL; Crosetto and Filippin (2016) extend the comparison to four risk-elicitation methods, and Holzmeister and Stefan (2021) is the most recent across-method consistency study. Binswanger (1980) used a precursor design with eight gambles in rural India varying stakes across sessions — EG is a simplification of that earlier framework, not the other way around. Field implementations in sub-Saharan Africa and South Asia routinely use a row of coloured balls or stacked coin representations (Brick, Visser & Burns, 2012 in South Africa; Charness & Viceisza, 2016 in Senegal; Tanaka, Camerer & Nguyen, 2010 in Vietnam).

The method is less suited to research questions that require precise discrimination within a narrow risk-preference range. For finer resolution use Holt-Laury — but accept the probability-weighting confound and the higher comprehension burden. For very large surveys without incentivised tasks, the Dohmen et al. (2011) single-item or the Global Preference Survey short form (Falk et al., 2018) are the validated alternatives.

How it works

The standard five-gamble design from Eckel and Grossman (2002) uses payoffs in fractions of an experimental endowment:

Gamble	Low payoff	High payoff	Expected value	Std. deviation
1	16	16	16	0
2	12	24	18	6
3	8	32	20	12
4	4	40	22	18
5	0	48	24	24

(Original Eckel-Grossman 2002 design, in monetary units of the endowment. Scale to local currency for field use; the high payoff in gamble 5 should equal roughly one to three days’ wages in the study context.)

Gambles 2–5 are resolved with a 50/50 coin flip; gamble 1 is a sure payment. EV rises by 2 per step, SD by 6 per step — the marginal cost of one variance unit (in expected value) is the same across all transitions, making the design symmetric.

The chosen gamble maps to a CRRA range under expected utility with a power utility function. From Eckel and Grossman (2002, Table 1):

Chosen gamble	Classification	CRRA range
1	Highly risk-averse	r > 3.46
2	Very risk-averse	1.16 < r < 3.46
3	Risk-averse	0.71 < r < 1.16
4	Moderately risk-averse	0.50 < r < 0.71
5	Risk-neutral to risk-loving	r < 0.50 (a risk-neutral respondent chooses gamble 5)

The boundaries are exact under the CRRA functional form. They shift when the payoff structure is rescaled non-proportionally, so recompute them for any non-original payoff design (the indifference conditions are tractable in closed form).

The 6-gamble Eckel-Grossman (2008) version adds a dominated attention check. Gamble 6 has the same SD as gamble 5 but a lower expected value — it is strictly dominated by gamble 5. Respondents who choose gamble 6 reveal inattention or a misunderstanding of the task and should be flagged for sensitivity analysis. This is the standard modern implementation and the one we recommend.

Gamble	Low payoff	High payoff	Expected value	Std. deviation	Use
6	0	48 → e.g. 44	22 (with high payoff 44)	22	Strictly dominated by gamble 5 — attention check

Dave, Eckel, Johnson and Rojas (2010) extend further to seven gambles to add granularity at the risk-averse end; use that variant when category coarseness at the low end is the binding constraint.

Identification assumptions. For the CRRA mapping to hold, four conditions must be met:

Expected utility maximisation over the gamble payoffs (no probability weighting needed — but EG, unlike Holt-Laury, does not contaminate utility curvature with probability weighting because the probability is held at 0.5).
CRRA functional form (power utility). Under CARA, expo-power, or HARA the bin boundaries shift.
Comprehension of the coin-flip mechanism and the gamble structure — failure shows up as concentration at gamble 1 (distrust of randomisation) or at gamble 6 (the dominated option).
Trust in the randomisation device — when respondents doubt the coin flip is genuine, they treat gamble 1 as a guaranteed cash payment vs gamble 5 as a “promise.”

Without (2), only the rank-order interpretation of the gamble choice survives, which is still informative for between-group comparisons.

Key decisions

Adapting payoffs to the local context. The original Eckel-Grossman payoffs are in US dollars and should be rescaled to local wage levels. The anchoring properties of the design depend on preserving the ratio structure — the step from gamble to gamble should represent a meaningful increase in variance relative to expected return. Amounts equivalent to one to three hours of daily wage for the high payoff in gamble 5 are a common reference point. Pilot testing with a small convenience sample before the main survey confirms that the highest gamble is genuinely tempting rather than trivially dominated.

Real vs hypothetical incentives. Holt and Laury (2002) and Harrison and Rutström (2008) document that hypothetical incentives systematically understate risk aversion — respondents act bolder when no money is at stake. Use real payments where feasible, even at modest scale. When payments must be hypothetical, frame as concretely as possible and expect categories to shift toward gambles 4–5; report sensitivity to this in writeups.

Immediate payment of gamble outcomes. Pay the realised gamble outcome on the spot or with minimum delay. Any payment delay introduces time-preference into a risk-preference elicitation: respondents who heavily discount the future shift their gamble choice as if they were more risk-averse, because the LL option (gamble 5’s high payoff via delay) is discounted more than the SS option (gamble 1’s certain immediate payment).

Visual presentation. Use a physical card or laminated sheet with the five gambles as coloured bars or chips rather than verbal description. The visual makes variance intuitive — a wider bar signals greater spread — and reduces recall burden during the choice. Field implementations routinely use a row of coloured balls (one colour per outcome) or stacked coin representations.

5-gamble vs 6-gamble vs 7-gamble. Use the 6-gamble version (Eckel & Grossman, 2008) as the default: the 6th dominated gamble adds an attention check at trivial respondent cost. The 7-gamble version (Dave et al., 2010) adds granularity at the risk-averse end and is appropriate when the population is concentrated there.

Embedding in a larger battery. When EG is administered alongside other incentivised tasks (trust games, time-preference tasks, Holt-Laury), use random-task selection at the end of the session to determine which task is played for real. This prevents wealth effects from earlier outcomes contaminating later choices. Random-task selection does not address framing effects — a high-variance outcome in an earlier task can shift framing of a later gamble. Randomise task order across respondents to neutralise framing effects to first order.

Sample size. For detecting a 0.3-category mean shift in a regression of gamble_choice on a binary treatment at 80% power, plan for N ≈ 350 per arm under typical field-sample category distributions. Cluster-randomised designs need a 1 + (m̄ − 1)ρ design-effect adjustment.

Caveats & common mistakes

Coarse classification. The 5- or 6-gamble design assigns respondents to one of 5–6 categories. In populations where most respondents are moderately risk-averse — common in low-income settings — many will cluster at gambles 2 or 3, limiting variance in the measure. When risk aversion is a primary outcome or a finely-graded moderator, use the 7-gamble Dave et al. (2010) extension or pair EG with a Holt-Laury MPL. Crosetto and Filippin (2016) compare the predictive validity of EG and HL and find them broadly similar in general-population samples — the “coarser identification” trade-off is real but less severe than the category count suggests.

The CRRA boundary interpretation. Interpreting gamble choices as CRRA coefficients requires expected-utility maximisation under power utility. The gamble choice is always a valid rank-order indicator of risk aversion; the CRRA range is the additional parametric layer that depends on the utility assumption. EG’s advantage over Holt-Laury here: because probability is held at 50/50 across gambles, the CRRA estimate is not contaminated by probability weighting under cumulative prospect theory (Andersen et al., 2008; Harrison & Rutström, 2008), which is a real concern for HL.

Anchoring on gamble 1. Presenting a certain payment as gamble 1 is by design, but it can attract respondents who prefer certainty for reasons unrelated to expected utility — loss aversion, distrust of randomisation, unfamiliarity with probabilistic payoffs. More than 25% concentration at gamble 1 in a non-extreme-poverty sample is a red flag for misunderstanding the coin-flip mechanic; pilot debrief and a practice round are appropriate responses.

Inattention via the dominated gamble (6-gamble version). Respondents who choose gamble 6 in the EG-2008 design have selected a strictly dominated option — lower EV at the same SD as gamble 5. Flag these respondents (gamble_choice == 6) and report results with and without them in a sensitivity analysis. Recommended default: drop in sensitivity, keep in main.

Gender differences and the elicitation method. Eckel and Grossman (2002) — the original paper specifically about gender — document that women systematically choose lower-variance gambles than men in lab samples; Croson and Gneezy (2009) review the broader gender-and-risk literature. However, Filippin and Crosetto (2016) show the gender gap is sensitive to elicitation method: robust in Holt-Laury, smaller and sometimes absent in EG. Include gender as a control where relevant, but interpret the gap as conditional on the elicitation method rather than as a context-free behavioural regularity.

Wealth vs framing effects in a battery. When EG is administered alongside other incentivised tasks, two distinct cross-task contamination effects arise. Wealth effects: an earlier task’s payout changes the respondent’s effective endowment for the next task. Framing effects: an earlier outcome reframes the next choice (a high-variance loss may make a 50/50 gamble feel safer). Random task selection at the end of the session removes wealth effects cleanly but does nothing for framing. Randomise task order across respondents to neutralise framing to first order; expect residual effects.

Domain specificity. Like Holt-Laury, EG measures risk aversion over monetary lotteries. Domain-specific risk-taking (health, agriculture, financial) does not always track the lab measure (Dohmen et al., 2011). If the research question concerns a specific behavioural domain, supplement EG with a domain-specific risk measure.

Analysis Guide

import pandas as pd
import statsmodels.formula.api as smf

# gamble_choice: integer 1-5 (5-gamble version) or 1-6 (6-gamble version with the
# dominated attention-check gamble 6). Convention used here: LOW gamble = HIGH risk
# aversion (gamble 1 = certain payment; gamble 5 = highest variance).

# 1. Inattention flag for the 6-gamble version — gamble 6 is strictly dominated by
#    gamble 5 (same SD, lower EV). Respondents who choose it reveal a misunderstanding
#    of the task; report results both including and excluding them
df['inattentive'] = (df['gamble_choice'] == 6).astype('Int64')
print('Inattentive share:', df['inattentive'].mean())

# 2. CRRA category labels — gamble 1 is the highest-risk-aversion choice; gamble 5
#    is the lowest. The label order matches the gamble order. Gamble 6 (if present)
#    is the inattention bin
df['crra_cat'] = pd.Categorical(
  df['gamble_choice'].map({
      1: 'Highly risk-averse',
      2: 'Very risk-averse',
      3: 'Risk-averse',
      4: 'Moderately risk-averse',
      5: 'Risk-neutral / risk-loving',
      6: 'Dominated (inattentive)'}),
  categories=['Highly risk-averse', 'Very risk-averse', 'Risk-averse',
              'Moderately risk-averse', 'Risk-neutral / risk-loving',
              'Dominated (inattentive)'],
  ordered=True)

# 3. Distribution of gamble choices — concentration at gamble 1 (>25%) flags
#    distrust of the coin flip; concentration at gamble 6 flags misunderstanding;
#    a spread across gambles 2-5 is the typical field pattern
print(df['gamble_choice'].value_counts(normalize=True).sort_index().mul(100).round(1))

# 4. Regress gamble choice on covariates — HIGHER gamble_choice = LOWER risk aversion.
#    A positive coefficient means the variable predicts choosing higher-variance
#    gambles (lower risk aversion); a negative coefficient means greater risk aversion.
#    For cluster-randomised designs use cov_type='cluster', cov_kwds={'groups': df['psu']}
fit = smf.ols('gamble_choice ~ age + female + log_hh_expenditure + treatment',
            data=df[df['inattentive'] == 0]).fit(cov_type='HC2')
print(fit.summary())

# 5. Ordered probit / logit for inference on the latent risk-aversion variable —
#    treats gamble_choice as a discrete ordinal outcome rather than continuous;
#    correct when category boundaries are not equally spaced in CRRA terms
from statsmodels.miscmodels.ordinal_model import OrderedModel
fit_ord = OrderedModel(df.loc[df['inattentive'] == 0, 'gamble_choice'],
                     df.loc[df['inattentive'] == 0,
                            ['age', 'female', 'log_hh_expenditure', 'treatment']],
                     distr='probit').fit(method='bfgs', disp=False)
print(fit_ord.summary())

# 6. Heterogeneous treatment effects by risk aversion — highly-risk-averse respondents
#    are those at gambles 1-2; less risk-averse are gambles 3-5. A positive interaction
#    means the treatment effect is larger among less risk-averse respondents
df['risk_averse_high'] = (df['gamble_choice'] <= 2).astype('Int64')
fit_het = smf.ols(
  'outcome ~ treatment * risk_averse_high + gamble_choice + age + female',
  data=df[df['inattentive'] == 0]).fit(cov_type='HC2')
print(fit_het.summary())

library(estimatr)   # lm_robust with HC2 robust SEs
library(MASS)       # polr for ordered logit; or use ordinal::clm

# gamble_choice: integer 1-5 (5-gamble version) or 1-6 (6-gamble version with the
# dominated attention-check gamble 6). LOW gamble = HIGH risk aversion.

# 1. Inattention flag — gamble 6 is strictly dominated by gamble 5; flag and run
#    sensitivity analyses including and excluding these respondents
df$inattentive <- as.integer(df$gamble_choice == 6)
mean(df$inattentive, na.rm = TRUE)

# 2. CRRA category labels — labels run from highly risk-averse (gamble 1) to risk-
#    neutral/risk-loving (gamble 5); gamble 6 is the inattention bin. The factor
#    levels run 1->6 so the label order MUST match
df$crra_cat <- factor(df$gamble_choice,
levels = 1:6,
labels = c("highly risk-averse", "very risk-averse", "risk-averse",
           "moderately risk-averse", "risk-neutral / risk-loving",
           "dominated (inattentive)"))

# 3. Distribution of gamble choices — concentration at gamble 1 above ~25% flags
#    distrust of the coin flip; concentration at gamble 6 flags misunderstanding
prop.table(table(df$gamble_choice)) * 100

# 4. Regress gamble choice on covariates — HIGHER gamble_choice = LOWER risk aversion.
#    Positive coefficient = predicts higher-variance choices (less risk-averse).
#    For cluster-randomised designs use clusters = ~ psu, se_type = "CR1"
fit <- lm_robust(gamble_choice ~ age + female + log_hh_expenditure + treatment,
               data    = df[df$inattentive == 0, ],
               se_type = "HC2")
summary(fit)

# 5. Ordered probit / logit for inference on the latent risk-aversion variable
fit_ord <- polr(factor(gamble_choice) ~ age + female + log_hh_expenditure + treatment,
              data = df[df$inattentive == 0, ], method = "probit", Hess = TRUE)
summary(fit_ord)

# 6. Heterogeneous treatment effects by risk aversion — high risk aversion =
#    gambles 1-2; low = gambles 3-5. Positive interaction = treatment effect
#    larger among less risk-averse respondents
df$risk_averse_high <- as.integer(df$gamble_choice <= 2)
df$treat_x_risk     <- df$treatment * df$risk_averse_high
fit_het <- lm_robust(outcome ~ treatment + treat_x_risk + gamble_choice +
                     age + female,
                   data = df[df$inattentive == 0, ], se_type = "HC2")
summary(fit_het)

XLSForm / SurveyCTO

Display the five (or six) gambles as a select_one question on a single screen, with a laminated visual aid card showing the low payoff, high payoff, and a visual representation of variance (wider bar or more chips for higher-variance options) for each. Question text: “Which of these options would you choose if we were actually going to flip a coin and pay you what it shows?”

Use the 6-gamble version with the dominated attention check. Respondents who select gamble 6 trigger a constraint_message follow-up confirming their choice; persist inattentive to the submission.

Random task selection at end of session when EG is administered alongside other incentivised tasks. The canonical SurveyCTO pattern, with k tasks indexed 1..k:

type            name           calculation
calculate       task_played    once(int(random() * ${k}) + 1)

For k = 4 tasks, this draws an integer in [1, 4]. The outer once() is critical — without it, the draw re-evaluates on every form recompute and the realised task changes mid-session. Reference ${task_played} downstream; never call random() a second time at payment.

Realised payoff calculation. When EG is the played task, draw the 50/50 coin flip and compute the realised payoff:

calculate       coin_flip       once(if(random() < 0.5, 0, 1))
calculate       gamble_payoff   if(${gamble_choice} = 1, ${pay_low_1},
                                if(${coin_flip} = 0, ${pay_low_n}, ${pay_high_n}))
note            payoff_display  Coin flip: ${coin_flip}. Your payment: ${gamble_payoff}.

Persist gamble_choice, coin_flip, gamble_payoff, and inattentive to the submission. Store the raw gamble number (1–6), not a pre-coded CRRA category — this allows flexible re-coding and the inattention diagnostic in analysis.

Reading the output

Convention reminder. gamble_choice runs from 1 (certain payment, highest risk aversion) to 5 (highest variance, lowest risk aversion / risk-neutral). In the 6-gamble version, gamble 6 is the strictly dominated attention-check option.
Distribution diagnostics. Field samples typically cluster at gambles 2–4. A mode at gamble 1 above ~25% in a non-extreme-poverty sample flags distrust of the randomisation device or misunderstanding of the coin-flip mechanic — pilot debrief and a practice round are appropriate responses. A mode at gamble 6 (in the 6-gamble version) flags misunderstanding of the dominance ordering.
CRRA mapping. Categories from Eckel-Grossman (2002, Table 1): gamble 1 = highly risk-averse (r > 3.46); gamble 2 = very risk-averse (1.16 < r < 3.46); gamble 3 = risk-averse (0.71 < r < 1.16); gamble 4 = moderately risk-averse (0.50 < r < 0.71); gamble 5 = risk-neutral to risk-loving (r < 0.50). The CRRA boundaries are valid under power utility only; report the functional form alongside CRRA categories.
Regression interpretation. A positive coefficient on gamble_choice means the variable predicts choosing higher-variance gambles, i.e., LOWER risk aversion. A negative coefficient means greater risk aversion. OLS treats the discrete ordinal outcome as continuous; ordered probit (step 5) is the formally correct estimator and should be reported as a robustness check.
Heterogeneous treatment effects. The risk_averse_high interaction tests whether treatment effects differ between respondents who chose gamble 1 or 2 (highly risk-averse) versus gambles 3–5 (less risk-averse). A positive interaction coefficient means the treatment effect is LARGER for the less risk-averse subgroup; a negative coefficient means larger for the risk-averse subgroup.
Inattention sensitivity. Report results both including and excluding gamble-6 respondents. Material differences indicate that misunderstanding is contaminating the estimates and the comprehension procedure should be reviewed.

References

Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2008). Eliciting risk and time preferences. Econometrica, 76(3), 583–618. https://doi.org/10.1111/j.1468-0262.2008.00848.x

Binswanger, H. P. (1980). Attitudes toward risk: Experimental measurement in rural India. American Journal of Agricultural Economics, 62(3), 395–407. https://doi.org/10.2307/1240194

Brick, K., Visser, M., & Burns, J. (2012). Risk aversion: Experimental evidence from South African fishing communities. American Journal of Agricultural Economics, 94(1), 133–152. https://doi.org/10.1093/ajae/aar120

Charness, G., Gneezy, U., & Imas, A. (2013). Experimental methods: Eliciting risk preferences. Journal of Economic Behavior & Organization, 87, 43–51. https://doi.org/10.1016/j.jebo.2012.12.023

Charness, G., & Viceisza, A. (2016). Three risk-elicitation methods in the field: Evidence from rural Senegal. Review of Behavioral Economics, 3(2), 145–171. https://doi.org/10.1561/105.00000046

Croson, R., & Gneezy, U. (2009). Gender differences in preferences. Journal of Economic Literature, 47(2), 448–474. https://doi.org/10.1257/jel.47.2.448

Crosetto, P., & Filippin, A. (2016). A theoretical and experimental appraisal of four risk elicitation methods. Experimental Economics, 19(3), 613–641. https://doi.org/10.1007/s10683-015-9457-9

Dave, C., Eckel, C. C., Johnson, C. A., & Rojas, C. (2010). Eliciting risk preferences: When is simple better? Journal of Risk and Uncertainty, 41(3), 219–243. https://doi.org/10.1007/s11166-010-9103-z

Dohmen, T., Falk, A., Huffman, D., Sunde, U., Schupp, J., & Wagner, G. G. (2011). Individual risk attitudes: Measurement, determinants, and behavioral consequences. Journal of the European Economic Association, 9(3), 522–550. https://doi.org/10.1111/j.1542-4774.2011.01015.x

Eckel, C. C., & Grossman, P. J. (2002). Sex differences and statistical stereotyping in attitudes toward financial risk. Evolution and Human Behavior, 23(4), 281–295. https://doi.org/10.1016/S1090-5138(02)00097-1

Eckel, C. C., & Grossman, P. J. (2008). Forecasting risk attitudes: An experimental study using actual and forecast gamble choices. Journal of Economic Behavior & Organization, 68(1), 1–17. https://doi.org/10.1016/j.jebo.2008.04.006

Falk, A., Becker, A., Dohmen, T., Enke, B., Huffman, D., & Sunde, U. (2018). Global evidence on economic preferences. Quarterly Journal of Economics, 133(4), 1645–1692. https://doi.org/10.1093/qje/qjy013

Filippin, A., & Crosetto, P. (2016). A reconsideration of gender differences in risk attitudes. Management Science, 62(11), 3138–3160. https://doi.org/10.1287/mnsc.2015.2294

Harrison, G. W., & Rutström, E. E. (2008). Risk aversion in the laboratory. Research in Experimental Economics, 12, 41–196. https://doi.org/10.1016/S0193-2306(08)00003-3

Holt, C. A., & Laury, S. K. (2002). Risk aversion and incentive effects. American Economic Review, 92(5), 1644–1655. https://doi.org/10.1257/000282802762024700

Holzmeister, F., & Stefan, M. (2021). The risk elicitation puzzle revisited: Across-methods (in)consistency? Experimental Economics, 24(2), 593–616. https://doi.org/10.1007/s10683-020-09674-8

Tanaka, T., Camerer, C. F., & Nguyen, Q. (2010). Risk and time preferences: Linking experimental and household survey data from Vietnam. American Economic Review, 100(1), 557–571. https://doi.org/10.1257/aer.100.1.557