Assessing the Mechanical and Psychological Effects of District Magnitude

By Romain Lachat (Universitat Pompeu Fabra)

What is the story?

Under proportional representation (PR), the number of representatives elected may be very different from districts to districts. Portugal, for example, has very small districts where only 2 representatives are elected, and others that are much larger, such as Lisbon where 48 representatives are elected (for the 2005 national election). In a recent article, we used this specific institutional context to test how district magnitude affects electoral results.

The mechanical and psychological effects of district magnitude

The smaller district magnitude is, the more difficult it is for small parties to be elected, because of two inter-related effects. First, the ratio between the votes a party received and the seats it obtains cannot be fully proportional if the number of seats to be filled is low. For example, it is rather obvious that many small parties will not obtain any seats if they are only two seats to be filled in the district (and this is true regardless of the electoral formula used to assign those 2 seats). This is the mechanical effect of district magnitude.

Second, parties and voters, being aware of this mechanical effect, adapt their behaviour consequently. Parties may for example decide not to compete in districts in which they have very few chances of having a seat, or to invest fewer resources in the campaign there. In the same vein, voters may defect from their preferred party if its electoral chances are low, and opt for a party that has better prospects. This is the psychological effect of district magnitude.


In our article, we focused on the 2005 national election in Portugal. As mentioned above, district magnitude varied drastically across the country, which provides a great opportunity to test its effect. We relied on official results and on survey data from the Comparative Study of Electoral Systems. We compared the actual electoral results with simulations of what would have been these results if all districts were as large as the largest one (District magnitude = 48).

We showed that small parties would fare substantially better if the districts were larger. The share of seats of small parties would increase between 4 and almost 20%-points (depending on how large the original district was). We also showed that this change would be mainly due to the mechanical effect of district magnitude. Figure 1 illustrates this argument in showing how the number of seats going to small parties (left-hand panel) and the effective number of parliamentary parties (right-hand panel) would vary if all electoral districts were as proportional as the largest district.

Figure 1 (click to enlarge)

Figure 1

On the opposite, we found that the psychological effect of district magnitude on the electoral outcome was inexistent. Our data revealed than only about 2% of Portuguese voters did not vote for their preferred party for strategic considerations in the 2005 national election. This number is too small for the psychological effect to have an independent impact on the electoral outcome.

For further details and analyses, see Lachat, Romain, André Blais, and Ignacio Lago. Forthcoming. Assessing the Mechanical and Psychological Effects of District Magnitude. Journal of Elections, Public Opinion and Parties.

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