Parliamentary or Presidential Government?

I compare parliamentary and presidential government in a model with an executive and a decisive parliamentarian, whose ability to submit bills of high quality, or learn their quality, respectively, is private information. After observing the actions of each politician, the voter chooses whether to retain each politician or replace them with a randomly drawn alternative. Under presidential government, the voter is allowed to choose distinct replacement strategies for each politician, whereas under parliamentary government, the voter is committed to using the same replacement strategy for both politicians. Whilst the richer set of strategies available to the voter under presidential government makes it a superior choice for the voter in an environment of complete information, in the case of private information and re-election motives the parliamentarian in a presidential system establishes a reputation for competence at the expense of the executive, by vetoing executive bills. In turn, this leads the executive to distort her choice of policy initiatives in order to conform to the prior belief of the voter, even when she has private information that contradicts the prior. Under parliamentary government, by contrast, the parliamentarian is effectively absent, unwilling to obstruct the executive’s program for fear of inducing their joint removal, but this provides the executive with stronger incentives to follow her private information. I compare the ability of the voter to learn about the quality of politicians under each system and her ability to remove politicians that she would wish to remove if she were perfectly informed about their types. I also consider the possibility of institutionalized cooperation between the executive and legislative branches under each system.