Manipulation-Resistant Oracles via Continuous Peer Prediction

Junhao Song, Tanis Rolandi, Adam Novocky, Enrico Biffis, William Knottenbelt

Imperial College London · Hitachi Europe

MARBLE 2026 · Limassol, Cyprus

A carbon project operator can dry a site before measurement and be paid for soil organic carbon (SOC) that was never stored. In our mechanism, sensors report Gaussian beliefs and are paid with the continuous ranked probability score (CRPS) against their peers, which makes truthful reporting a strict equilibrium. A weighted least squares (WLS) read-out then splits the reports into the true value and the manipulation. The main result: manipulation can be identified and deterred from the reports alone if and only if the sensors respond to it by different amounts.

Results

Over-credit. Shift-naive aggregators credit up to 57% more carbon than is there. The WLS estimate stays near zero. (Fig. 5a)	Real spectra. As real spectra are wetted, the aggregators collapse. WLS stays within the models' own calibration bias. (Fig. 2a)	Diversity is necessary. As the sensor sensitivities converge, the error diverges, as the theorem predicts. (Fig. 2b)

Quick start

git clone https://github.com/Rqcker/crps-wls && cd crps-wls
pip install -r requirements.txt   # Python 3.10+
python -m src.plots               # every figure from the committed results, into figures/

No dataset or GPU is needed for the figures.

Reproducing the experiments

The experiments draw soil carbon values from the LUCAS 2018 topsoil survey, whose licence does not allow redistribution. Request the data and place the CSV as described in data/README.md, then run:

python -m src.experiments         # all 16 experiments, about 15 minutes on a laptop CPU
python -m src.plots

The committed results in src/data/ come from this version of the code. exp1–exp11 are in src/experiments.py; the other experiments are modules in src/.

Paper	Code	Output
Fig. 2(a)	src/real_manipulation.py (GPU)	fig13
Fig. 2(b)	exp3	fig4
Fig. 3(a), 3(b)	exp6, exp5	fig7, fig6
Fig. 4(a), 4(b)	exp4, exp_collusion	fig5, fig14
Fig. 5(a), 5(b)	exp4, exp2	fig12, fig3
Table 2	src/spectral_models.py (GPU)	ossl_data/measured_params_cluster.json
Table 3	exp4, exp8	src/data/exp4_data.csv, exp8_data.csv
Table 4	src/stake_worked_example.py	printed
Table 5	exp_regression_baseline	src/data/exp_regression_baseline_data.csv

The other figures are supplementary sweeps; the noise and calibration sweeps are also on the project page. The GPU stage that measures the sensor parameters is described in cluster/README.md.

Repository

src/          mechanism, experiments and figures
src/data/     committed experiment results
ossl_data/    measured sensor parameters
data/         place the LUCAS 2018 CSV here
cluster/      Slurm scripts for the GPU stage

Citation

@inproceedings{song2026manipulation,
  author        = {Song, Junhao and Rolandi, Tanis and Novocky, Adam and
                   Biffis, Enrico and Knottenbelt, William},
  title         = {Manipulation-Resistant Oracles via Continuous Peer
                   Prediction},
  booktitle     = {Mathematical Research for Blockchain Economy (MARBLE 2026)},
  publisher     = {Springer},
  year          = {2026},
  eprint        = {2610.35888},
  archivePrefix = {arXiv},
  primaryClass  = {stat.AP}
}

Licence

MIT. See LICENSE.