The law of large districts: How district magnitude affects the quality of political representation

• Direct measure of congruence between representatives and voter preferences
• Analyze relationship between congruence and district magnitude
• Lower congruence of individual legislators in larger electoral districts
• However, higher congruence of majority of legislators in larger districts
• Evidence for existence of a law of large numbers in political representation

It is well established that individual parliamentary representatives are less likely to decide according to the preferences of their constituency when the number of representatives per district, i.e. district magnitude, increases. However, we propose that for majority decisions of district representatives the opposite holds due to the existence of a law of large numbers in political representation. The academic literature has so far focused on the behavior of individual politicians but disregarded systematic aggregation effects. We provide a theoretical discussion and offer empirical evidence for the validity of a law of large numbers in political representation: As district magnitude increases, the quality of political representation by the majority of representatives increases, too.