District magnitude and substantive representation

I define the substantive ‘representativeness’ of elections in terms of voters’ electoral welfare, the ‘congruence’ between voters’ ideal policy positions and the stated position of their closest party. I specify and analyze a computational agent-based model of the effect of district magnitudes on voter welfare, in settings with multidimensional voter preferences. This model is dynamic and evolutionary, with endogenous entry and exit of candidates from local races, conditional on ‘survival thresholds’ which are a function of district magnitude. I find that increasing district magnitudes tends to increase voter welfare in two distinct ways. First, and as commonly expected, it increases the number of competing candidates – thereby offering voters more options. Second, and equally important, increasing district magnitude combined with endogenous candidate entry and exit affects the typical configuration of candidate positions in ways that increase voter welfare. Candidates tend to exit from over-served regions of the issue space and enter into under-served regions. Not only are there more competing candidates in larger districts, therefore, but their issue positions are distributed in ways that better reflect the preferences of voters.