Linking Social and Personal Preferences: Theory and Experiment

This paper asks whether an individual’s attitude toward risk in the personal domain (choices affecting only oneself) can be linked to that same individual’s attitude toward risk in the social domain (choices affecting both oneself and others). The authors provide a theoretical answer in the form of necessary and sufficient conditions, and then test those conditions experimentally.

The formal model posits a decision maker (DM) with a preference relation over lotteries on a set of social states, where a distinguished subset of states are personal (consequences for the DM alone). The authors assume preferences satisfy Completeness, Transitivity, Continuity, and State Monotonicity — the last being equivalent to respect for First-Order Stochastic Dominance (FOSD), a condition weaker than the Expected Utility Independence Axiom and satisfied by virtually all extant decision theories including Weighted Expected Utility, Rank-Dependent Utility, and Prospect Theory. The key theoretical result (Theorem 1) establishes that the full preference relation over all social lotteries can be uniquely deduced from the partial observations of (i) riskless social choices and (ii) risky personal choices if and only if the DM finds every social state indifferent to some personal state. When this condition fails, there exist social lotteries whose ranking cannot be recovered from the partial data.

For two empirically relevant preference types, this condition generates directly testable predictions: for selfish subjects (who allocate nothing to others in deterministic social choices), risky personal preferences must coincide with risky social preferences; for impartial subjects (who treat self and other symmetrically in deterministic social choices), riskless social preferences must coincide with risky social preferences.

The experiment was conducted at the University of Bergen and NHH Norwegian School of Economics with 276 undergraduate subjects. Each subject faced 50 budget-line choice problems in each of three domains: Personal Risk (equiprobable binary lotteries over own payoffs only), Social Choice (deterministic splits between self and an anonymous other), and Social Risk (equiprobable binary lotteries over symmetric payout pairs for self and other). The graphical interface of Choi et al. (2007b) was used throughout. One randomly selected decision per domain was paid out; each token was worth 1.2 NOK (approximately 0.2 USD), with average earnings of approximately 270 NOK.

Within-domain consistency, measured by the Critical Cost Efficiency Index (CCEI), is high: mean CCEIs are 0.959, 0.952, and 0.902 in the Personal Risk, Social Choice, and Social Risk domains respectively. At the CCEI > 0.90 threshold, 89.9%, 85.9%, and 69.9% of subjects pass in the three domains. Using a 0.95 share-to-self threshold, 103 subjects (37.3%) are classified as selfish; using revealed-preference criteria at the 5% significance level, 33 subjects (12.0%) are classified as impartial.

Testing is done via an individual-level nonparametric permutation test that draws 10,000 random data sets per subject and compares simulated CCEI distributions to actual cross-domain CCEIs, with Bonferroni correction. At the 1% significance level, the null that Personal Risk and Social Risk preferences coincide is rejected for only 5.9%–9.3% of selfish subjects (varying by classification threshold), compared with 14.7%–16.3% rejection rates for non-selfish subjects. For impartial subjects at the 1% level, the null that Social Choice and Social Risk preferences coincide is rejected for 0.0%–11.1%, compared with 19.8%–26.8% for non-impartial subjects. The theory’s predictions are thus supported for a large majority of both selfish and impartial subjects.

A theoretical extension (Theorem 2) shows that if one additionally observes comparisons between social states and personal lotteries, unique deduction of the full preference relation requires that preferences in both personal and social domains satisfy Expected Utility (Independence Axiom) and that every social state is indifferent to some personal lottery — a strictly stronger set of conditions.

Q: What is the central theoretical question and why does it matter? A: The paper asks whether preferences over risky social choices (lotteries over outcomes for self and others) can be deduced from observing only riskless social choices and risky personal choices. This matters because people frequently observe or predict the risky social choices of leaders and representatives, but may have access only to those leaders’ personal risk-taking behavior and their expressed social preferences under certainty.

Q: What is the main theoretical result (Theorem 1)? A: Under Completeness, Transitivity, Continuity, and State Monotonicity, the unique extension of the partial preference relation (over social states and personal lotteries) to the full domain of social lotteries exists if and only if every social state is indifferent to some personal state. When this condition is not met, multiple distinct preference relations can extend the partial observations, making deduction impossible.

Q: What is State Monotonicity and how does it relate to standard axioms? A: State Monotonicity requires that if each social state in one lottery dominates the corresponding state in another lottery, then the first lottery is weakly preferred. The paper shows this is equivalent to respect for First-Order Stochastic Dominance (FOSD) given the other axioms, and is strictly weaker than the von Neumann–Morgenstern Independence Axiom. It is satisfied by Weighted Expected Utility, Rank-Dependent Utility, and Prospect Theory, making it a broadly applicable assumption.

Q: What are the testable predictions for selfish subjects? A: Proposition 2 establishes that if a subject’s Social Choice preferences are selfish — meaning any bundle (x, y) is indifferent to (0, y), so the subject is indifferent between keeping x for self and giving it to other — then preferences in the Personal Risk domain must coincide with preferences in the Social Risk domain. In the experiment, selfish subjects are those allocating more than 95% of tokens to themselves in the Social Choice domain (103 of 276 subjects, or 37.3%).

Q: What are the testable predictions for impartial subjects? A: Proposition 3 establishes that if a subject’s Social Choice preferences are symmetric — meaning (x, y) is indifferent to (y, x) for all pairs — then preferences in the Social Choice domain must coincide with preferences in the Social Risk domain, implying risk neutrality toward social lotteries. The intuition is that such a subject treats self and other identically, so risky splits are evaluated by expected value alone. In the experiment, 33 subjects (12.0%) are classified as impartial by the revealed-preference criterion at the 5% significance level.

Q: How does the experiment measure within-domain rationality? A: Choices within each domain are evaluated using the Critical Cost Efficiency Index (CCEI, following Afriat 1967), which measures how much a budget constraint must be relaxed to remove all GARP violations. Mean CCEIs are 0.959 (Personal Risk), 0.952 (Social Choice), and 0.902 (Social Risk). At the CCEI > 0.90 threshold, 248 subjects (89.9%), 237 (85.9%), and 193 (69.9%) pass in the three domains respectively, compared to a simulated mean CCEI of only 0.585 for subjects randomizing uniformly.

Q: How does the cross-domain test work and why is it nonparametric? A: The test uses individual-level permutation inference: under the null that preferences in domains I and J are identical, any 50-element subset drawn from the pooled 100 choices should satisfy GARP as well as the actual domain-specific choices. For each subject, 10,000 such random draws are generated, their CCEI scores are computed, and the distribution is compared to the actual cross-domain CCEI with Bonferroni correction. The test makes no functional form assumptions about utility and accommodates the observed within-domain errors without parametric error modeling.

Q: What are the rejection rates for the selfish-subject prediction? A: At the 1% significance level, the null that Personal Risk and Social Risk preferences coincide is rejected for only 5.9%–9.3% of selfish subjects (range across four classification thresholds from 0.99 to 0.90 share-to-self), compared to 14.7%–16.3% for non-selfish subjects. At the 5% level, rejection rates rise to 20.4%–25.6% for selfish and 22.4%–31.8% for non-selfish subjects.

Q: What are the rejection rates for the impartial-subject prediction? A: At the 1% significance level, the null that Social Choice and Social Risk preferences coincide is rejected for 0.0%–11.1% of impartial subjects (range depending on threshold and classification method), compared to 19.8%–26.8% for non-impartial subjects. At the 5% and 10% levels, rejection rates for impartial subjects range from 0.0% to 22.2%.

Q: Does the theory predict how risk aversion should map across domains for non-selfish, non-impartial subjects? A: The theory does not directly produce testable cross-domain predictions for subjects who are neither selfish nor impartial without additional parametric assumptions, because the specific personal-state equivalent of each social state depends on the form of preferences. The paper restricts its nonparametric tests to the two polar cases where the equivalence mapping is determinate from social choice behavior alone.

Q: What is the extended result (Theorem 2) and what stronger conditions does it require? A: When one additionally observes comparisons between social states and personal lotteries (not just within each domain separately), unique deduction of the full preference relation is possible if and only if preferences in both the personal and social domains are consistent with an Expected Utility representation and every social state is indifferent to some personal lottery. This requires the Independence Axiom — a strictly stronger condition than State Monotonicity — highlighting that the main Theorem 1 result exploits the weaker observational structure.

Q: What is the distribution of social preferences in the sample? A: Of 276 subjects, 103 (37.3%) are classified as selfish at the 0.95 share-to-self threshold. Only 6 subjects (2.2%) kept fewer than 0.45 of tokens on average, making purely altruistic subjects rare. In the Personal Risk domain, 41 subjects (14.9%) allocated more than 95% to the cheaper account (consistent with risk neutrality), while 9 (3.3%) allocated fewer than 55% (consistent with infinite risk aversion). In the Social Risk domain, 30 subjects (10.9%) are consistent with utilitarianism in money and 9 (3.3%) with Rawlsianism in money.

Q: How does the Social Risk domain compare to the Personal Risk and Social Choice domains in terms of rationality scores? A: The Social Risk domain shows lower consistency than the other two: mean CCEI is 0.902 versus 0.959 and 0.952, and only 69.9% of subjects exceed the 0.90 threshold versus 89.9% and 85.9%. The CCEI distribution is shifted left for Social Risk, suggesting the novel combined dimension of social and risky choice introduces more decision complexity or error.

Q: What is the relationship to the prior experimental literature on social and risk preferences? A: The Personal Risk domain replicates the symmetric risk experiment of Choi et al. (2007a), and the Social Choice domain replicates the linear two-person dictator experiment of Fisman et al. (2007). The Social Risk domain is new to this paper. The theoretical framework connects to Saito (2013) on social preferences under risk, and to the preference extension literature of Grant et al. (1992) and Nishimura et al. (2017).

State Monotonicity: The axiom requiring that if each social state in one lottery weakly dominates the corresponding social state in another lottery, the first lottery is weakly preferred. The paper proves this is equivalent to respect for First-Order Stochastic Dominance given Completeness, Transitivity, and Continuity, and distinguishes it from the stronger Independence Axiom by noting that Independence compares lotteries over lotteries while State Monotonicity only compares lotteries over states.

Selfish preferences (in the paper’s sense): Preferences in the Social Choice domain such that (x, y) is indifferent to (0, y) for all bundles — the subject is indifferent between receiving x themselves versus giving x to the other person. Operationally measured as allocating more than a threshold share (e.g., 95%) of tokens to self across Social Choice decisions.

Impartial preferences (in the paper’s sense): Preferences in the Social Choice domain such that (x, y) is indifferent to (y, x) for all bundles — the subject treats self and other symmetrically. Operationally identified by the revealed preference criterion that choices in the Social Choice domain satisfy GARP and are consistent with symmetric treatment.

Unique extension (deducibility): The property that there exists exactly one complete preference relation over all social lotteries that is consistent with the axioms and agrees with the observed partial relation over social states and personal lotteries. Theorem 1 identifies the necessary and sufficient condition for unique extension under State Monotonicity.

Personal state indifference condition: The condition that for every social state omega in Omega minus P, there exists some personal state in P to which the DM is indifferent. This is the necessary and sufficient condition in Theorem 1 for deducibility of the full preference relation. Interpreted as: for every proposed social allocation, there exists a “bribe” — a personal allocation with nothing for others — that the DM finds equally desirable.

Critical Cost Efficiency Index (CCEI): A measure of how much budget constraints must be scaled down to eliminate all GARP violations in a dataset of choices from budget lines (following Afriat 1967). A CCEI of 1 indicates perfect rationality; the paper uses 0.90 as a practical threshold. Mean values are 0.959, 0.952, and 0.902 in the Personal Risk, Social Choice, and Social Risk domains respectively.

Nonparametric permutation test: The individual-level test used to assess consistency across choice domains. Under the null that preferences are identical in domains I and J, any random 50-element draw from the pooled 100 choices should achieve CCEI scores no worse than the actual domain scores. The test draws 10,000 permuted datasets per subject and uses the Bonferroni correction for multiple comparisons, making no assumptions about the functional form of utility.