Why some democracies are headed by a monarch?

The paper inquires why in some countries traditionally ruled by absolute monarchs the monarchy survived in the form of constitutional monarchy but not in others. It considers constitutional monarchy as a negotiated settlement between the king and a liberal opposition to share office rents, while the alternative to the negotiation is a violent conflict that ends with either deposition of the monarchy or absolute rule by the monarch. A model of conflict between the king and the liberal opposition is explored where conflict for office rents is a costly contest with probabilistic outcomes and results in a reduction of available rents. The payoffs from conflict and rent sharing, modelled as a Nash bargain between the two sides, are compared. The model predicts that constitutional monarchy is more likely to emerge when office rents are large, the proportion of rents destroyed in fighting is large, the king enjoys a large fighting advantage, the cost of the collective action costs of the liberal is high, the liberal has a stronger preference for rents instead of anti–royalist ideology, but the effect of time preference is more nuanced.