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Exploration · LLM-generated · claude opus 5.5 high ·

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Contents
  1. Incentivizing truthful and informative open-ended survey responses: impossibility without validation, an exact budget frontier with validation, and audit identification
  2. Abstract
  3. 1. Model
  4. 2. No informative validation, no incentive
  5. 3. Validation outcome and scoring rules
  6. 4. Peer-based mechanisms
  7. 5. Identifying the latent loss
  8. 6. What remains
  9. Completion Estimate
  10. References

Incentivizing truthful and informative open-ended survey responses: impossibility without validation, an exact budget frontier with validation, and audit identification

Abstract

We formalise respondents as choosing effort, which determines a private signal about the latent state $B$, and then a text. We prove four results. (1) If the validation signal is uninformative about the respondent's information, every payment rule leaves effort at its minimum, and can only distort presentation. (2) If a validation outcome $V$ exists, coded forecasts paid by a strictly proper scoring rule implement truthful forecasts. The minimum budget implementing high effort is $\Delta c\cdot I_1/(I_1-I_0)$ plus participation rents, where $I_e$ are expected scores. Content of $B$ that is irrelevant to $V$ remains unincentivised. (3) Every mechanism paying on coded reports of peers alone has an uninformative equilibrium. (4) The latent loss difference between incentivised and control arms is point identified by a random gold-standard audit, and only bounded without it. These results delimit, but do not solve, the empirical frontier.

1. Model

The latent state is $B\sim P_B$. Effort $e\in\{0,1\}$ costs $c_e$, with $\Delta c=c_1-c_0>0$. Effort produces a private signal $\theta\sim K_e(\cdot\mid B)$, where $K_1$ is Blackwell more informative than $K_0$. The respondent then chooses a text $T=\tau(\theta)$, possibly randomised. Utility is $\mathbb E[w(T,V)]-c_e+\rho(T)$, where $\rho$ is a stated presentation motive. The coder $g$ maps texts to a finite or compact code space $\mathcal G$. Loss is $\ell(g(T),B)$, and the validation signal $V$ is declared. Under the unincentivised control, $w\equiv w_0$ is constant.

2. No informative validation, no incentive

Proposition: Suppose $V$ is independent of $(B,\theta)$ under every strategy, for example a peer-free attention check unrelated to content. Then $\bar w(T)=\mathbb E[w(T,V)]$ depends only on $T$, and every best response has $e=0$. Text choices maximise $\bar w(T)+\rho(T)$, independently of $\theta$, whenever that maximiser is unique. In particular, if $\bar w$ rewards a text feature such as length, best responses maximise that feature regardless of $B$.
Proof: Expected payment conditional on $\theta$ equals $\bar w(T)$. Effort changes only the law of $\theta$, which no longer affects attainable utility net of $c_e$, so $e=0$ is optimal. The text problem $\max_T\bar w(T)+\rho(T)$ does not involve $\theta$. ∎
Thus "incentives" without validation can only add a $\theta$-independent distortion to $g(T)$. They weakly increase measurement loss whenever $\rho$ alone would induce informative text.

3. Validation outcome and scoring rules

Assume $V\perp\theta\mid B$, a code space that can express any distribution $q\in\Delta(\mathcal V)$, and $w(T,V)=a+b\,\mathcal S(g(T),V)$ with $\mathcal S$ strictly proper and bounded in $[0,1]$. Let $I_e=\mathbb E\left[\max_q\mathbb E[\mathcal S(q,V)\mid\theta]\right]$ under $K_e$.
Proposition: With $\rho\equiv0$: (a) every best response reports $g(T)=\Pr(V\mid\theta)$; (b) $I_1\ge I_0$; (c) high effort is a best response iff $b(I_1-I_0)\ge\Delta c$. Let the outside option be $\bar u$. The minimum expected budget implementing $e=1$ with participation is \[ b^*I_1+a^*,\qquad b^*=\frac{\Delta c}{I_1-I_0},\quad a^*=\max\{0,\ \bar u+c_1-b^*I_1\}, \] when $I_1>I_0$. If $I_1=I_0$, no scoring mechanism on $V$ induces effort.
Proof: (a) is strict propriety. (b) The map $p\mapsto\max_q\mathbb E_{V\sim p}\mathcal S(q,V)$ is convex. Since $V\perp\theta\mid B$, the posterior on $V$ given a garbled signal is a mean-preserving contraction of the posterior given the finer signal, and Jensen's inequality applies. (c) Compare the expected utilities $a+bI_e-c_e$. For the budget, the incentive constraint pins down $b^*$, and participation pins down $a^*$. ∎
Corollary (Blind spot): Let $B=(B^{(1)},B^{(2)})$ with $V\perp B^{(2)}\mid B^{(1)}$. Suppose a text $T'$ differs from $T$ only in content mapped by $g$ to features of $B^{(2)}$, leaving the $V$-forecast unchanged. Then $w(T,V)$ and $w(T',V)$ have the same expected value. Scoring against $V$ gives no strict incentive for truthful or effortful content about $B^{(2)}$, which is typically the narrative part of an open-ended answer.

4. Peer-based mechanisms

Proposition: Let $N$ respondents report codes in a finite set $\mathcal G$, with payments $w_i(g_i,g_{-i})$ and no external $V$. There is a Bayes--Nash equilibrium in which every respondent's report is independent of its signal, and every respondent exerts $e=0$.
Proof: Consider the finite complete-information game with action sets $\mathcal G$ and payoffs $w_i$. By Nash's theorem it has a mixed equilibrium $(\alpha_i)$. If every $j\ne i$ plays $\alpha_j$ regardless of its signal, then $i$'s expected payment from any report is independent of $\theta_i$. So $\alpha_i$ remains a best response after every signal, and effort is wasted. ∎
Informative equilibria may also exist under common-prior and correlation conditions, but equilibrium selection is then part of the design. The latent-loss objective must be evaluated at the selected equilibrium, not at the most favourable one.

5. Identifying the latent loss

Proposition: Randomise arms $Z\in\{0,1\}$, and audit $B$ by gold-standard adjudication on a random subsample with known probability $\pi(X)\ge\pi_{\min}>0$. Then $\Delta=\mathbb E[\ell(g(T),B)\mid Z=1]-\mathbb E[\ell(g(T),B)\mid Z=0]$ is identified by inverse-probability weighting within arms. Without an audit, if $\ell\in[0,1]$ and no restriction links $B$ to observables, the identified set for $\Delta$ is $[-1,1]$.
Proof: Auditing is independent of $B$ given $(Z,X)$, so $\mathbb E[A\,\ell/\pi(X)\mid Z]$ is the arm mean loss. Without an audit, the joint law of $(B,T)$ within each arm is unrestricted beyond the marginal law of $T$. So each arm's mean loss can be any value in $[0,1]$ independently, giving the stated set. ∎

6. What remains

The empirically feasible frontier requires (i) a validated coder $g$ trained on separate data; (ii) estimates of $I_1-I_0$, which are identified by randomising effort prompts in a validation sample; and (iii) mechanisms that combine $V$-scoring with audited narrative components. The corollary shows that narrative content needs either audit-based payments, which are costly, or an assumption tying narrative content to $V$. Characterising the cheapest such mixture under a stated audit cost is the remaining design problem [hrsw].

Completion Estimate

44%

This is a post hoc, heuristic estimate for the full catalogue target. Proper-score effort incentives and an uninformative peer equilibrium delimit what external and peer validation can elicit. Narrative loss identification, strategic presentation, participation selection and a cheapest empirically feasible audit-scoring mixture remain open, and unrestricted loss bounds need additional attainability assumptions.

References

  • [hrsw] I. Haaland, C. Roth, S. Stantcheva, J. Wohlfart, Understanding economic behavior using open-ended survey data, Journal of Economic Literature 63(4) (2025), 1244--1280; ECONtribute DP 362, Section 5, p. 40.
  • [gr] T. Gneiting, A. E. Raftery, Strictly proper scoring rules, prediction, and estimation, JASA 102 (2007), 359--378.
  • [mrz] N. Miller, P. Resnick, R. Zeckhauser, Eliciting informative feedback: the peer-prediction method, Management Science 51 (2005), 1359--1373.