Surrogate Scoring Rules (1802.09158v7)

Abstract: Strictly proper scoring rules (SPSR) are incentive compatible for eliciting information about random variables from strategic agents when the principal can reward agents after the realization of the random variables. They also quantify the quality of elicited information, with more accurate predictions receiving higher scores in expectation. In this paper, we extend such scoring rules to settings where a principal elicits private probabilistic beliefs but only has access to agents' reports. We name our solution \emph{Surrogate Scoring Rules} (SSR). SSR build on a bias correction step and an error rate estimation procedure for a reference answer defined using agents' reports. We show that, with a single bit of information about the prior distribution of the random variables, SSR in a multi-task setting recover SPSR in expectation, as if having access to the ground truth. Therefore, a salient feature of SSR is that they quantify the quality of information despite the lack of ground truth, just as SPSR do for the setting \emph{with} ground truth. As a by-product, SSR induce \emph{dominant truthfulness} in reporting. Our method is verified both theoretically and empirically using data collected from real human forecasters.

• The paper introduces SSR to extend SPSR methods, enabling reliable scoring without direct truth verification by correcting bias and estimating error rates.
• It shows that SSR mechanisms can induce dominant truthfulness in multi-task scenarios by leveraging peer report analysis.
• Empirical tests on 14 real-world forecasting datasets confirm SSR’s robust performance in approximating true prediction scores.

Surrogate Scoring Rules: Extending Information Elicitation Without Verification

The paper "Surrogate Scoring Rules" introduces a novel mechanism for information elicitation when the truth is not verifiable, an area known as Information Elicitation Without Verification (IEWV). The paper's central contribution is the formulation of Surrogate Scoring Rules (SSR), an extension of Strictly Proper Scoring Rules (SPSR) commonly used in scenarios where the ground truth is accessible. The SSR framework is adept at quantifying information quality and incentivizing honesty in probabilistic belief reporting, even without direct truth verification.

Key Contributions

1. SPSR Extension to IEWV: The introduction of SSR provides a method to extend SPSR to situations where the truth cannot be directly verified. This is achieved through a bias correction approach and an error rate estimation from agents' reports. SSR thus quantifies information accuracy akin to SPSR, even without truth access.
2. Dominant Truthfulness Inducement: A salient feature of SSR is its ability to induce dominant truthfulness in reporting, a significant advancement for multi-task settings. The paper argues that with adequate task and agent numbers, SSR mechanisms can elicit truthful reporting reliably, overcoming the challenges imposed by traditional peer prediction mechanisms.
3. Empirical Validation: The theoretical contributions are bolstered by empirical validation. Using fourteen real-world human forecasting datasets, SSR mechanisms demonstrated strong correlation with true scores produced by SPSR with ground truth, outperforming traditional peer prediction methods.

Theoretical Framework

The paper builds upon the traditional SPSR, known for its incentive compatibility and its capacity to measure information accuracy accurately in scenarios with verifiable truths. SSR adapts this framework to IEWV by leveraging surrogate loss functions and indirect ground truth proxies derived from peer reports.

The mechanisms rely on estimating a "noisy" reference point from peer predictions and use this as the proxy truth. Under the assumption of task prior knowledge, specifically the prior probability that the event of interest holds a certain value, SSR can correct biases and estimate reporting errors accurately.

Results and Implications

The SSR mechanism recovers the expected score of the SPSR even in the absence of ground truth data. This result has profound implications for practical applications, such as crowdsourcing and collective intelligence systems, where truth verification is often impractical or impossible.

Furthermore, the empirical results from a variety of forecasting scenarios underscore SSR's robustness and reliability in practical settings. By more accurately reflecting true prediction quality, SSR can refine performance assessment and reward structures in prediction and decision-making environments.

Future Directions

The paper opens several avenues for future research. There is potential to refine bias correction and error estimation components further, improving efficiency for scenarios with limited samples. Additionally, research could explore SSR's applicability across diverse domains, such as financial forecasting and sensor networks, where grounding truth is often challenging.

In summary, "Surrogate Scoring Rules" presents a significant step forward in information elicitation methodology for unverifiable truth settings. By extending SPSR principles to IEWV, the authors provide a robust framework that balances incentive compatibility and information quantification, paving the way for more reliable and effective information systems.