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District magnitude and representation of the majority’s preferences: a comment and reinterpretation

A REPLY FROM to this article was published on 27 November 2012

The Original Article was published on 14 January 2011


Drawing on new data that combine recorded votes from the Swiss National Assembly with canton-level referendum results on identical legislative proposals, Portmann et al. (Public Choice 151:585–610, 2012) develop an innovative strategy to identify the effect of district magnitude on the relationship between representatives and their constituents. We replicate PSE’s central result and also estimate a related model that allows for the possibility of non-monotonicity in the relationship between district magnitude and representatives’ deviance from referendum median voters. Our results indicate that representatives elected in low-magnitude multi-member districts deviate from canton-level majorities less than either MPs from single-member districts or those from high-magnitude multi-member districts.

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  1. An exception, focused on the effects of ballot technologies on voters’ abilities to make choices among a crowded field, is Shocket et al. (1992).

  2. PSE label this variable Canton = CH. We relabeled this variable to make it more transparent for non-Swiss readers.

  3. Like PSE, we estimate logistic regressions with robust standard errors, clustering on canton in recognition of the likelihood that the behavior of MPs from the same district are not independent.

  4. Overall, the rate of MPs voting against cantonal majorities is 32 %.

  5. As a robustness check we estimated all models with fixed effects for each referendum issue, and the results are identical to the results in Table 2. We also ran a variant of the alternative specification with the largest-magnitude districts (DM > 20) as the omitted category, to confirm whether districts in the lower-DM categories were statistically discernible from those at the high end. The results of this estimation are available from the authors.

  6. Table 2 reports both pseudo-R2 and the area under the receiver operating characteristic (ROC) curve—the ratio of deviations from popular majorities correctly versus incorrectly predicted. In terms of overall model fit, our alterative specification offers a slightly larger, but still quite modest, improvement over the basic model in PSE. None of the other alternative specifications tested (e.g., including squared or cubed permutations of the Seats variable) provides even as much of a marginal improvement in overall fit as does the specification with our series of district magnitude dummies.


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The authors want to express their sincere gratitude to Portmann, Stadelmann, and Eichenberger for their immediate willingness to share data, and for their engagement in a productive exchange of ideas about their research.

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Correspondence to John M. Carey.

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Carey, J.M., Hix, S. District magnitude and representation of the majority’s preferences: a comment and reinterpretation. Public Choice 154, 139–148 (2013).

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