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We estimate the parameters of a reputational game of political competition using data from five two-party parliamentary systems. We find that latent party preferences (and party reputations) persist with high probability across election periods, with one exception: parties with extreme preferences who find themselves out of power switch to moderation with higher probability than the equivalent estimated likelihood for parties in government (extreme or moderate) or for moderate parties in opposition. We find evidence for the presence of significant country-specific differences. We subject the model to a battery of goodness-of-fit tests and contrast model predictions with survey and vote margin data not used for estimation. Finally, according to the estimated model parameters, Australia is less than half as likely to experience extreme policies and Australian governments can expect to win more consecutive elections in the long run as compared to their counterparts in Greece, Malta, New Zealand, and the United Kingdom.