Harnessing the transparent blockchain user behavior data, we construct the Political Betting Leaning Score (PBLS) to measure political leanings based on betting within Web3 prediction markets. Focusing on Polymarket and starting from the 2024 U.S. Presidential Election, we synthesize behaviors over 15,000 addresses across 4,500 events and 8,500 markets, capturing the intensity and direction of their political leanings by the PBLS. We validate the PBLS through internal consistency checks and external comparisons. We uncover relationships between our PBLS and betting behaviors through over 800 features capturing various behavioral aspects. A case study of the 2022 U.S. Senate election further demonstrates the ability of our measurement while decoding the dynamic interaction between political and profitable motives. Our findings contribute to understanding decision-making in decentralized markets, enhancing the analysis of behaviors within Web3 prediction environments. The insights of this study reveal the potential of blockchain in enabling innovative, multidisciplinary studies and could inform the development of more effective online prediction markets, improve the accuracy of forecast, and help the design and optimization of platform mechanisms. The data and code for the paper are accessible at the following link: https://github.com/anonymous.