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A preferential attachment model of campaign contributions in state legislative elections

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Abstract

In state legislative elections some candidates attract contributions from many donors whereas other candidates have much smaller donor pools. Why? What are the origins of these disparities? This paper conceptualizes contributions as a type of attachment between the donor and the state legislative candidate. To model the formation of these attachments, this paper proposes a variant of the Barabasi-Albert preferential attachment model. The theoretical model is tested with data on over one million contributions to state legislative candidates in 2008. The paper also derives implications for macro-level inequities across candidates which are tested by comparing the observed inequities to simulations of the preferential attachment model. The results provide strong support for the hypotheses and show that the preferential attachment model provides a parsimonious representation of contributions to state legislative candidates.

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Notes

  1. As discussed below, the pattern of large inequities in found in nearly every state, although some of the inequity is due to between-state differences (e.g., candidates in California have more money than candidates in Wyoming).

  2. Histograms for the other chambers are shown in the supporting information available online at http://v.web.umkc.edu/vonnahmeg/papers/puchSI_prefAtt.pdf. One notable exception to this pattern was Connecticut, where a system of publicly financed campaign spending was used statewide in 2008.

  3. For example, EMILY’s List is an organization that supports female candidates and particularly assists with raising early money (EMILY is an acronym for “early money is like yeast”—it raises the dough).

  4. A counter-argument is that contributions might be reinforcing to a point, but once a candidate has a sufficient number of donors, then subsequent donors might direct their resources towards other candidates. This raises the possibility that prior contributions might be unrelated or possibly negatively related to later contributions.

  5. The denominator includes all candidates to the chamber rather than a particular district, as most contributions come from beyond the district’s borders. This is not unanticipated as previous research finds that contributions to Congressional candidates are a form of monetary surrogacy in which a person who supports a candidate but lives outside her district contributes to the campaign as the voter cannot cast a ballot for the candidate (Gimpel et al. 2008). We found a similar pattern in the states by geocoding 250 randomly chosen donors from each chamber in 2008. We found that a clear majority of contributions came from out-of-district sources (74.1 % for lower chambers and 66.8 % for upper chambers—which have larger districts).

  6. The online supporting information includes an extensive discussion of the relationship between contribution amounts and the number of donors.

  7. One feature of the model is that it shows how a system that is initially very egalitarian with identical donors and candidates can produce highly inegalitarian outcomes.

  8. Additional details of the Polya-Eggenberger distribution are included in the online supporting information.

  9. Michigan and Minnesota held elections for their lower chambers in 2008, but not their upper chambers.

  10. In the event that the same donor gave to the same candidate more than once, only the date of the first contribution is recorded. We also excluded self-contributions from the analysis.

  11. If the party ran no candidate in 2002, this value was set at 10 %, which makes a very conservative allowance for a core group of party supporters even if the party ran no candidate in the previous election.

  12. For example, the conditional logit model has been used to analyze the choice between different modes of transportation (e.g., car, bus, train, etc.) where the choice might depend on characteristics of the mode of transportation, such as cost (Long 1997).

  13. At its logical extreme, the model leads to the expectation that the prior donor shares are fully determinative of future donors’ choice probabilities, such that the correlation would be 1 and all of the other factors would be entirely inconsequential. While the correlations are high they are not equal to one. The supporting information provides confidence bounds on the relationship between the predicted probabilities and prior donor shares.

  14. Connecticut was a notable exception to this rule. Connecticut had a substantially lower Gini than the other chambers (0.181 in the House and 0.205 in the Senate), suggesting that the system of public financing that was in place in 2008 substantially reduced inequities in the number of contributions to candidates.

  15. Kullback-Leibler divergence is a measure of the difference between two distributions. It represents the information lost by using one distribution to approximate the other, such that a smaller value represents a closer fit between the two distributions (Fox 2008).

  16. Details of these analyses are included in the supporting information.

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Acknowledgements

I am grateful for many helpful comments from Keith Hamm, Beth Miller, Hong Min Park, Emily Ritter, Robert Stein, Seiji Yamamoto, the editors and reviewers, and workshop participants at the University of Alabama. Supporting information is available online at: http://v.web.umkc.edu/vonnahmeg/papers/puchSI_prefAtt.pdf.

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  1. Department of Political Science, University of Missouri–Kansas City, Kansas City, MO, 64110-2499, USA

    Greg Vonnahme

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Correspondence to Greg Vonnahme.

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Vonnahme, G. A preferential attachment model of campaign contributions in state legislative elections. Public Choice 159, 235–249 (2014). https://doi.org/10.1007/s11127-012-0041-y

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