The Law of k/n: The Effect of Chamber Size on Government Spending in Bicameral Legislatures

Recent work in political economics has examined the positive relationship between legislative size and spending, which Weingast et al. (1981) formalized as the law of 1/n. However, empirical tests of this theory have produced a pattern of divergent findings. The positive relationship between seats and spending appears to hold consistently for unicameral legislatures and for upper chambers in bicameral legislatures but not for lower chambers. We bridge this gap between theory and empirics by extending Weingast et al.’s model to account for bicameralism in the context of a Baron––Ferejohn bargaining game. Our comparative statics predict, and empirical data from U.S. state legislatures corroborate, that the size of the upper chamber (n) is a positive predictor of expenditure, whereas the ratio of lower-to-upper chamber seats (k) exhibits a negative effect. We refer to these relationships as the law of k/n, as the two variables influence spending in opposite directions.