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The use of prediction markets (PMs) for forecasting is emerging in many fields because of its excellent forecasting accuracy. However, PM accuracy depends on its market design, including the choice of market mechanism. Standard financial market mechanisms are not well suited for small, usually illiquid PMs. To avoid liquidity problems, automated market makers (AMMs) always offer buy and sell prices. However, there is limited research that measures the relative performance of AMMs. This paper examines the properties of four documented and applied AMMs and compares their performance in a large-scale simulation study. The results show that logarithmic scoring rules and the dynamic pari-mutuel market attain the highest forecasting accuracy, good robustness against parameter misspecification, the ability to incorporate new information into prices, and the lowest losses for market operators. However, they are less robust in case of noisy trading, which makes them less appropriate in environments with high uncertainty about true prices for shares.