Data pricing has been studied from several complementary directions. Query-based mechanisms price access to database views while avoiding arbitrage ([10]; [11]). Other models incorporate data quality, completeness, timeliness, or tuple-level characteristics into the valuation rule ([14]; [16]). Asset-valuation approaches extend conventional valuation concepts to data, while information-theoretic approaches use entropy or related measures to describe scarcity, uncertainty, or information content ([17]). These contributions clarify the technical side of data value but do not fully determine how much a specific individual must be compensated to supply privacy-sensitive data.

From an economic perspective, the provider’s reservation value is central. WTA is the minimum compensation that makes disclosure acceptable to the provider. In privacy settings, WTA need not equal a socially efficient price because individuals may face limited information about future data use, data may create externalities, and preferences may be context dependent ([2]; [1]). Nevertheless, WTA remains a useful supply-side concept because it makes explicit that privacy loss is a cost borne by the provider rather than a free input to the data buyer.

The present model therefore does not attempt to solve the full equilibrium of a data market. It constructs a reference price from the provider side. Buyer willingness to pay, platform bargaining power, downstream externalities, and competition would still be required to obtain a market-clearing transaction price. This narrower interpretation improves the economic meaning of the model: the output is a structured reservation-compensation benchmark conditioned on the informational contribution of the supplied data.

Let x j denote a category or state and P ( x j ) its empirical probability. Shannon self-information for a realized state is − log 2 P ( x j ) , while Shannon entropy is the probability-weighted expectation over possible states. The classic entropy form is:

Equation (1) provides the information-theoretic foundation, but the record-level quantity H i used later is deliberately narrower. Because the pricing exercise assigns value only to attributes that are present and disclosed in a profile, H i aggregates the present-state Shannon contribution − P ( x j ) log 2 P ( x j ) , weighted by category sensitivity and attribute count. It is therefore a sensitivity-weighted information-content term derived from Shannon entropy, not the full Shannon entropy of the complete binary vector. For a binary variable, the full entropy would additionally include the absent-state term − ( 1 − P ) log 2 ( 1 − P ) . This distinction is maintained throughout the revised model.

Personal information is heterogeneous. Identification data, financial records, medical information, location traces, preferences, communication-network information, and biometrics differ in both perceived sensitivity and economic consequences. The Information Security Technology—Personal Information Security Specification (GB/T 35273-2020) ([15]) provides a practical classification framework, and prior empirical work similarly distinguishes information categories when studying disclosure and privacy concern ([5]; [7]; [12]).

Table 1. Survey components and their role in the pricing framework.

Note: Privacy-compensation preference is distinguished from domain-general risk attitude to avoid overinterpreting the six survey items.

The survey used in this study combines attitudinal items concerning compensation and disclosure with a conjoint exercise. The attitudinal items are treated as indicators of privacy-compensation preference, not as a validated measure of general risk preference in the behavioral-economics sense. This terminology avoids equating willingness to disclose personal data with domain-general risk aversion. The conjoint component is used to derive normalized sensitivity weights for the seven information categories. These survey components and their analytical roles are summarized in Table 1.

To represent heterogeneous provider tolerance for privacy disclosure, the model uses three stylized compensation regimes. They are not estimated latent classes. Rather, they provide comparative pricing schedules for a relatively risk-tolerant provider, a benchmark provider, and a privacy-sensitive provider. Let S i denote the aggregate sensitivity of all information supplied by provider i , and let L denote the number of personal-information categories. In all calculations below, L = 7. The three compensation factors are:

Note. C1 represents the relatively risk-tolerant schedule, C₂ the benchmark schedule, and C₃ the privacy-sensitive schedule. The plotted functions use L= 7; at S_i = 10 they yield C₁ = 0.952, C₂ = 1.134, and C₃ = 1.316.

Figure 1.Stylized privacy-compensation schedules.

The benchmark compensation factor is the average of the relatively risk-tolerant and privacy-sensitive schedules. Aggregate sensitivity is calculated from the quantity of contributed information and the category-specific sensitivity coefficients:

These functions are dimensionless and monotone in aggregate sensitivity. Specifically, d C 1 / d S i = 2 / ( 1 + 2 S i ) 2 > 0 and d C 3 / d S i = 1000 / [ 7 ( 1000 S i + 1 ) ] > 0 ; because C 2 = ( C 1 + C 3 ) / 2 , d C 2 / d S i > 0 as well. The benchmark schedule is therefore exactly the midpoint between the two limiting schedules for every S i . For example, at S i = 10 , C₁ = 0.952, C₃ = 1.316, and C₂ = 1.134. The numerical illustration below calculates every benchmark factor from Equation (4), rather than assigning benchmark values independently (Figure 1).

The study used an online questionnaire administered through Wenjuanxing between March and May 2024. Participants were recruited by convenience sampling through WeChat and personal networks and through school and workplace channels, with limited onward sharing of the questionnaire link. Recruitment was geographically concentrated in Guangdong Province, primarily Guangzhou. Eligibility required respondents to be able to read Chinese, use Internet or mobile services, and complete the online questionnaire; the study did not impose an age-18 eligibility threshold. A total of 130 submissions were recorded. Data-quality screening excluded 27 cases: 12 were incomplete or missing key questionnaire/conjoint sections, 7 had completion times below one-third of the sample median, 5 showed clear straight-line responding or logical inconsistencies, and 3 were duplicate submissions identified from the platform record and response pattern. The final analytical sample therefore contained 103 respondents, a retained-response rate of 79.2%. Because recruitment was non-probability based, the sample is treated as a calibration sample rather than a population-representative survey.

Privacy-compensation preference was measured with six 5-point items (1 = strongly disagree, 5 = strongly agree). The three compensation-attitude items were: C1, “I should receive compensation when an organization collects or uses my personal information”; C2, “The more sensitive the personal information is, the higher the compensation should be”; and C3, “I would require higher compensation when more categories of my personal information are disclosed.” The three disclosure-willingness items were: D1, “I am willing to provide basic identity information when the compensation is adequate”; D2, “I am willing to provide location or behavioral information when the compensation is adequate”; and D3, “I am willing to provide highly sensitive information (e.g., financial, health, or biometric data) when the compensation is adequate.” C1-C3 were scored in the original direction and D1-D3 were reverse-coded so that higher values consistently indicated a stronger compensation requirement. The composite score was the mean of the six items after reverse coding. Internal consistency was Cronbach’s alpha = 0.81; the composite had M = 3.81 and SD = 0.52 in the 103 retained cases. The measure is interpreted specifically as privacy-compensation preference rather than as a domain-general risk-aversion scale.

Within the retained sample, men account for 52.43% and women 47.57%. The age distribution is concentrated in the 36 - 55 range: respondents aged 46 - 55 constitute 46.60% and those aged 36 - 45 constitute 30.10%. Bachelor’s degree holders are the largest education group at 33.98%, followed by associate-degree/junior-college respondents at 25.24%. Corporate employees account for 35.92% of the sample. Ninety-three respondents (90.29%) report that they regard privacy as very important. All sample counts and analytical inputs reported below were cross-checked against the archived questionnaire export, screening log, conjoint record, and calculation files before the revised model was recomputed. Detailed sample characteristics are reported in Table 2.

Table 2.Sample characteristics (N = 103).

Drawing on prior classifications and GB/T 35273-2020, the study organizes personal information into seven categories. The categories are broad enough to support a parsimonious pricing rule while retaining economically meaningful differences in privacy sensitivity. The seven personal-information categories and their illustrative content are presented in Table 3.

Table 3.Personal-information categories.

Note: Classification is based on the study’s original coding scheme and GB/T 35273-2020 ([15]).

The conjoint task treated each hypothetical data-sharing profile as a bundle of attributes. The compensation attribute had three levels-300, 1500, and 3000 yuan-and each of the seven personal-information categories was coded as present or absent. An orthogonal design reduced the full factorial space to 16 profiles. Every respondent evaluated all 16 profiles on a 5-point acceptance/disclosure-willingness rating scale (1 = very unwilling, 5 = very willing). The orthogonal profile set was fixed, while Wenjuanxing randomized the order in which profiles were presented to respondents to reduce systematic order effects.

The monetary amounts are experimental levels rather than externally validated transaction prices. Following standard additive conjoint practice ([9]; [13]), an additive conjoint model was estimated across the 16 ratings. For information category j, its utility range was calculated as r j = max ( u j l ) − min ( u j l ) across the present/absent levels; category sensitivity was then normalized as s j = r j / ∑ k = 1 7 r k , so that the seven information-category coefficients sum to one. The compensation attribute was estimated jointly in the conjoint model but was not included in this seven-category normalization. Model fit was Pearson’s R = 0.847 and Kendall’s tau = 0.712, indicating reasonably strong agreement between predicted and observed profile ordering within the sample. The conjoint attributes and levels are summarized in Table 4.

Table 4.Conjoint attributes and levels.

The empirical analysis has two linked purposes. First, the six-item privacy-compensation preference score is used in exploratory subgroup comparisons. Gender is tested with an independent-samples t test; age, education, and prior privacy-breach experience are examined with one-way ANOVA. Effect sizes are reported as Cohen’s d for gender and eta-squared for the ANOVAs. These subgroup tests describe heterogeneity but do not define the three stylized compensation regimes and are not inputs to Equations (2)-(8). Second, conjoint utility ranges are normalized across the seven information categories to obtain s j , after which the pricing model combines those category weights with profile-specific information quantities, empirically reconstructed entropy probabilities, and one of the three compensation schedules.

Before group comparisons, score distributions and residual plots were inspected and homogeneity of variance was checked with Levene tests; no material variance violation was detected (all p > 0.05). The six pre-specified age categories were retained rather than pooled post hoc, even though the 18 - 25 group contained only three respondents and three additional age cells contained seven respondents. Consequently, the age result is treated as exploratory and no pairwise claim is made from the sparse cells. The doctoral education group (n = 5) is handled similarly. The verified statistics are t(101) = −0.676, p = 0.501 for gender; F(5,97) = 3.884, p= 0.003 for age; F(4,98) = 2.396, p = 0.055 for education; and F(2,100) = 5.159, p = 0.007 for prior privacy-breach experience.

The verified subgroup comparisons are summarized in Table 5. Men (n = 54, M = 3.77, SD = 0.525) and women (n = 49, M = 3.84, SD = 0.525) differ only trivially, t(101) = −0.676, p = 0.501, d = −0.133. Across the six age groups, means increase from 3.35 (<18), 3.30 (18 - 25), 3.55 (26 - 35), and 3.72 (36 - 45) to 3.95 (46 - 55) and 4.10 (56+), with a common within-group SD of approximately 0.482; the omnibus difference is F(5,97) = 3.884, p = 0.003, eta-squared = 0.167. Education means are 3.60, 3.72, 3.86, 4.00, and 4.15 from the lowest to highest category (SD approximately 0.496), but the omnibus result does not reach the 5% threshold, F(4,98) = 2.396, p = 0.055, eta-squared = 0.089. Prior privacy-breach experience shows a significant difference: no breach (n = 58, M = 3.68), unsure/suspected (n = 18, M = 3.84), and yes (n = 27, M = 4.05), with SD approximately 0.497, F(2,100) = 5.159, p= 0.007, eta-squared = 0.094. These patterns support heterogeneity in privacy-compensation preference but do not justify mechanically assigning demographic groups to the model’s stylized compensation regimes.

Table 5.Exploratory group comparisons in privacy-compensation preference.

Note. All group counts, test statistics, and effect sizes were verified against the archived analysis. The six age categories and five education categories were retained as pre-specified groups; because some cells are small, no pairwise inference is based on the sparse groups.

The normalized information-category sensitivity coefficients derived from the conjoint utility ranges sum to one. Biometric information receives the largest weight (0.190), followed by financial information (0.141), medical and health information (0.140), basic identity information (0.140), preference information (0.136), location information (0.127), and communication-network information (0.126). These coefficients are sample-specific relative sensitivity weights: they indicate how strongly information categories differentiate disclosure utility within this conjoint calibration, not universal monetary values or legal damage weights. The resulting coefficients are reported in Table 6.

Table 6.Normalized personal-information sensitivity coefficients.

Note. Coefficients are normalized to sum to 1.000.

Let T i j denote the number of present attributes from category j in profile i, s j the normalized sensitivity coefficient for categoryj, and S i j = T i j s j the category-specific sensitivity contribution. Let P ( x i j ) denote the empirical presence probability for category j and C ( x i ) the compensation factor associated with the selected privacy-compensation regime. The model-specific sensitivity-weighted information-content term is H i = − ∑ j [ T i j s j P ( x i j ) log 2 P ( x i j ) ] , and the record-level pricing factor is F ( x i ) = C ( x i ) H i . H i is derived from the present-state Shannon entropy contribution; it is not the full binary Shannon entropy because absent states are intentionally excluded from the pricing index.

The record-level monetary reference price scales this factor by a baseline value V 0 ( x i ) :

Aggregating across n providers yields the dataset-level supply-side reference value:

Equations (6)-(8) make the units and economic structure explicit. H i and C ( x i ) are dimensionless, while the baseline V 0 ( x i ) carries the monetary unit; therefore V ( x i ) has the same currency unit as V 0 ( x i ) . In the verified numerical matrix below, P ( x i j ) is computed from the observed presence frequency of attributes in the same information category across the 12 profiles. Absent attributes do not enter T i j because the pricing rule values disclosed/present attributes only. Thus H i should be interpreted as a sensitivity-weighted information-content index, not as the entropy of the full 39-dimensional binary vector. The model is multiplicative: holding other terms fixed, a larger compensation factor, information-content term, or baseline raises the reference price proportionally.

First, holding the baseline price and information content fixed, a larger compensation factor increases the model-implied reference price proportionally. The three stylized regimes therefore create an explicit privacy-compensation wedge between otherwise identical data profiles. Second, holding the compensation regime fixed, information categories with larger sensitivity coefficients contribute more to the weighted information-content term. Third, because the baseline price enters multiplicatively, changing V₀ rescales all model-implied prices without changing the ranking of profiles, provided the same baseline is used for all observations.

These properties also clarify what the model does not measure. The Shannon-derived information-content term is not buyer willingness to pay, the sensitivity coefficient is not a legal damages schedule, and C ( x i ) is not a statistically estimated coefficient from a structural utility model. The framework is therefore best used as a transparent supply-side pricing rule or negotiation benchmark. A complete market model would additionally require demand-side value, bargaining, data externalities, platform competition, and transaction costs.

The numerical illustration uses a study-generated 12-profile binary attribute matrix rather than an external public dataset. The matrix contains 39 attributes grouped into seven categories: 9 basic-identity attributes, 3 communication-network attributes, 5 financial attributes, 14 preference attributes, 2 location attributes, 4 medical/health attributes, and 2 biometric attributes. The observation unit for the entropy frequencies is an attribute state within a profile. With 12 profiles and 39 attributes, the matrix contains 468 binary attribute opportunities. Across these opportunities, 304 attributes are present.

Category-specific presence probabilities are calculated directly from the 12-profile matrix: basic identity 87/108 = 0.8056; communication network 22/36 = 0.6111; financial 35/60 = 0.5833; preference 97/168 = 0.5774; location 15/24 = 0.6250; medical/health 28/48 = 0.5833; and biometric 20/24 = 0.8333. For each present attribute in category j, P ( x i j ) is set to the corresponding category probability. A common baseline V₀ = 1500 yuan is used for all 12 profiles. The profile count vector T i j is combined with the sensitivity coefficients reported in Table 6 to obtain S i and H i ; risk-tolerant profiles use C₁, benchmark profiles use C₂ = (C₁ + C₃)/2, and privacy-sensitive profiles use C₃. Supplementary Tables S1-S4 provide the complete 12 × 39 binary realization, category-frequency inputs, and reproducibility calculations. The profile-level information counts and assigned regimes are summarized in Table 7.

Table 7.Data profiles in the verified numerical illustration.

Note. The 12 rows form the study-generated 12 × 39 profile matrix used for the numerical illustration. Regime labels are scenario assignments for applying C₁, C₂, or C₃; they are not demographic classifications.

Table 8.Recomputed pricing results from the verified profile matrix (V₀ = 1500 yuan).

The information-content term and compensation factor are recomputed from the documented inputs, as shown in Table 8. The revision also corrects the earlier benchmark inconsistency: for profile 1, S i = 3.120 gives C₁ = 0.862 and C₃ = 1.149, so Equation (4) yields C₂ = 1.006. Using P ( x i j ) from the verified category frequencies and V₀ = 1500 yuan, the weighted information-content terms range from 0.898 to 1.775 and the resulting reference prices range from 1331.387 yuan (profile 3) to 3155.288 yuan (profile 5). Calculations use unrounded probabilities and compensation factors; displayed values are rounded for readability.

The central contribution of the framework is conceptual separation. Personal-data pricing contains at least three distinct objects that are often conflated: information content, privacy sensitivity, and provider reservation compensation. Shannon entropy supplies the information-theoretic foundation, while the model-specific H i is a sensitivity-weighted present-state information-content term; sensitivity weights capture the relative privacy importance of information categories; and the compensation factor represents the provider-side adjustment required under different privacy-tolerance regimes. Multiplying these components creates a tractable reference-pricing rule without claiming that H i is the full entropy of a binary record or that any single component is itself the market price.

This separation connects the paper to the broader economics of data markets. Prior research emphasizes that data have externalities and that individual disclosure can affect the information available about others ([1]; [6]). The present model does not solve those externalities, but it contributes a micro-level pricing primitive that can be embedded in richer market settings: the amount a platform would need to compensate a provider before demand-side value and external effects are considered. In that sense, the model is closer to a reservation-compensation schedule than to a complete theory of data-market equilibrium.

Behavioral evidence remains secondary to the pricing model but is now fully documented. The six-item measure has acceptable internal consistency, and the corrected age and privacy-breach ANOVAs indicate meaningful heterogeneity in privacy-compensation preference. At the same time, the very small age cells, the non-significant gender result, and the education result at p = 0.055 argue against demographic pricing rules. The three compensation regimes therefore remain transparent modeling scenarios rather than respondent classes inferred from age, education, gender, or breach history.

For data platforms, the model provides a transparent way to structure a posted compensation schedule. A platform could begin with a common baseline value, apply category-specific sensitivity weights, and then offer alternative compensation schedules reflecting consent conditions or privacy guarantees. The approach is especially useful when a platform lacks a long history of comparable transactions and therefore cannot estimate market prices directly.

The framework also illustrates why a single uniform price for all personal data is difficult to justify. Biometric and financial information receive higher sensitivity weights than communication-network and location information in the present calibration, and privacy-sensitive providers receive a larger compensation adjustment than risk-tolerant providers. Even if a platform ultimately uses a simpler commercial rule, these differences identify the dimensions along which a uniform price can undercompensate some providers and overcompensate others.

Policy applications require greater caution. The sensitivity coefficients in this study are sample-specific and should not be used as statutory compensation standards for data breaches. Legal damages depend on rights, harm, causation, and jurisdiction, whereas the present coefficients reflect relative disclosure sensitivity in a survey exercise. The model is therefore more appropriate for voluntary data exchange and platform pricing than for legal damage assessment.

Several limitations are important. First, the survey is a small non-probability convenience sample recruited primarily in Guangzhou and the wider Guangdong context. Although recruitment procedures and exclusions are now documented, the sample should not be treated as representative of the broader Chinese population. Replication with a larger probability-based sample would improve the stability and generalizability of subgroup and sensitivity estimates.

Second, the six-item privacy-compensation preference measure is study-specific. Its internal consistency is acceptable (alpha = 0.81), but it is not a validated domain-general risk-preference instrument. Future work should combine privacy-specific WTA items with established behavioral risk measures and test convergent, discriminant, and predictive validity.

Third, the conjoint task is hypothetical. Every respondent rated all 16 profiles and profile order was randomized, which improves internal consistency of administration, but hypothetical ratings may still differ from incentive-compatible disclosure choices. Future studies should use real or consequential compensation where feasible and test whether sensitivity weights replicate out of sample.

Fourth, the category probabilities used in the Shannon-derived information-content term are estimated from the study-generated 12 × 39 profile matrix rather than from the empirical distribution of a large external data market. This makes the calculation reproducible but still illustrative. Future research should estimate P ( x i j ) from a named external dataset and compare model-implied prices with actual negotiated prices, buyer willingness to pay, or experimentally elicited willingness to accept in a holdout sample.

Fifth, the framework is intentionally supply-side. It does not model informational externalities, bargaining, platform competition, repeated use of data, or the marginal value of data to a specific buyer. These mechanisms are central to welfare and equilibrium pricing in data markets ([1]; [6]). A natural extension is to embed the current reservation-compensation rule in a two-sided bargaining or mechanism-design model.

The numerical illustration is based on 12 profiles and 39 binary attribute indicators grouped into seven information categories. The model enters these data through category-level present counts T i j and category-specific probabilities P ( x i j ) . Accordingly, the identity of a particular indicator within a category is exchangeable for the calculation: any within-category permutation leaves T i j , P ( x i j ) , S i , H i , and the resulting reference price unchanged. Tables S1(a)-(c) provide the complete canonical 12 × 39 binary realization used for reproducibility, with 1 indicating a present/disclosed attribute and 0 indicating an absent attribute. The matrix exactly reproduces the verified category counts reported in the manuscript.

Table S1.(a) Binary matrix: basic identity and communication network; (b) Binary matrix: financial and preference indicators 1 - 7; (c) Binary matrix: preference indicators 8 - 14, location, medical/health, and biometric.

Note. Column codes identify binary indicators within each information category; only category membership and the present/absent state enter the pricing calculation.

Table S2 reproduces the category count vector T i j used in the main-text numerical illustration and verifies that each row of Tables S1(a)-(c) yields the same profile totals.

Table S2.Profile counts and compensation regimes.

For category j, the presence probability p j is the number of present binary states divided by the number of possible states across the 12 profiles. These probabilities supply the present-state Shannon contribution − p j log 2 ( p j ) used in H i .

Table S3.Frequency inputs used to calculate P ( x i j ) .

For a binary variable with presence probability p, full Shannon entropy is H B   ( p ) = − p log 2   ( p ) − ( 1 − p ) log 2   ( 1 − p ) . The pricing model does not use H B   ( p ) as the record-level quantity because the monetary rule is applied only to attributes that are present and disclosed in a profile. Instead, it uses the present-state entropy contribution − p log 2 ( p ) , multiplied by the number of present attributes T i j and the category sensitivity weight s_j. Thus H i = − ∑ j T i j s j p j log 2 ( p j ) . H i should therefore be read as a sensitivity-weighted information-content term derived from Shannon entropy, not as the full binary Shannon entropy of the 39-dimensional profile. This terminology change clarifies the information-theoretic interpretation without changing any calculation.

Table S4.Reproducibility check for profile-level pricing outputs.

Reproducibility note. Calculations in the manuscript use unrounded category probabilities and compensation factors; displayed values are rounded for readability. Because within-category indicators share the same s j and p j , within-category column permutations in Table S1 do not alter the reported H i or reference prices.