The ‘odd–even effect’: The link between the number of parties and district magnitude

In electoral systems with districts that vary in magnitude, the number of seats to be filled in each district will be even or odd. We argue that such a variation has crucial political consequences, called the ‘odd–even effect’. In low-magnitude districts, elections are more competitive when the district magnitude is odd than even; the incentives for coordination are thus stronger in the former scenario than in the latter. Employing quasi-experimental data from 780 districts in Spain's lower house elections, we show that the number of parties is smaller in low-magnitude districts with an odd number of seats than in low-magnitude districts with an even number of seats. The elite- and voter-level mechanisms driving the odd–even effect are examined using data on mobilisation efforts and wasted votes at the district level.