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Erschienen in: Public Choice 3-4/2020

16.10.2019

Campaign contributions and policy convergence: asymmetric agents and donations constraints

verfasst von: Eric Dunaway, Felix Munoz-Garcia

Erschienen in: Public Choice | Ausgabe 3-4/2020

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Abstract

We extend previous work on the role of politically motivated donors who contribute to candidates in an election with single dimension policy preferences. In a two-stage game wherein donors observe candidate policy positions and then allocate funding accordingly, we find that reducing the cost of donations incentivizes candidates to position closer to one another, reducing policy divergence. Furthermore, we find that as donations become more effective at influencing voter decisions, candidates respond less to voter preferences and more to those of donors. In addition, we analyze the presence of asymmetries in the model using numerical analysis techniques. We also extend our model by allowing for public funding from governments. By implementing stringent campaign contribution limits, candidate positions align with voter preferences at the cost of wider policy divergence. In contrast, unlimited campaign contributions lead to candidate positions moving away from voters to donors’ preferences, but increase policy convergence.

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Fußnoten
1
Campaign spending levels in US presidential elections increased by 45% ($687 million to $1 billion) from 2004 to 2008, and again by 40% ($1 billion to $1.409 billion) from 2008 to 2012. In the UK’s parliamentary elections, in contrast, donations declined 32% ($36.5 million to $24.9 million) from 2005 to 2010 and subsequently increased by 12% ($24.9 million to $28 million) from 2010 to 2015.
 
2
For an example of an election with three candidates, see Evrenk and Kha (2011).
 
3
Additional work by Barro (1973) examines how candidates’ motivations may not coincide with those of their electoral base.
 
4
Those results were extended in Calvert (1985), who demonstrated the assumptions under which policy convergence occurs. Empirical work by Morton (1993) tests the predictions and suggests that policy divergence occurs, but to a lesser extent than the theoretical prediction. Work by Zakharov and Sorokin (2014) suggests that the results also hold for a wide array of voting probability functions.
 
5
Candidates’ announcements of policy positions might not be credible to donors or voters. Work by Alesina (1988) and Aragonès et al. (2007), however, suggest that when candidates face repeated elections, voters (and, by extension, donors) recall when implemented and announced policy positions differ, and form their beliefs on a candidate’s true position accordingly. As a result, candidates announce the policy they intend to implement and the announcements can be considered credible. We assume that candidates cannot shirk on their announced positions, but our setting can be extended to models wherein candidates build their reputation.
 
6
Work by Hinich and Munger (1994) explores campaign contributions as a hindrance to a rival rather than a benefit to a preferred candidate.
 
7
Empirical work estimates the effects of campaign contribution limits. Jacobson (1978) and Coate (2004) focus on how contribution limits influenced the margins of victory between candidates (namely, an incumbent against a challenger). Our model, however, examines the effect of contribution limits on equilibrium positioning, rather than on the margin of victory.
 
8
In 2012, Mitt Romney faced a long primary challenge, which required him to spend 87% of the $153 million raised through June 2012, when he clinched the Republican nomination. In contrast, incumbent President Barack Obama spent 69% of the $303 million that he had raised over the same period. To generate additional funds, Romney courted donors who had either supported his rivals in the primary election or stayed out completely. Those donors were able to observe Romney’s policy positions long before ever offering him their aid.
 
9
We assume that donors are interested solely in policy outcomes, as in Ball (1999a) and Austen-Smith (1987).
 
10
Intuitively, both donors benefit from the contribution made to the supported candidate, and a situation similar to a public good arises, wherein donors free ride on each others’ contributions. In particular, every dollar donated to candidate i by donor l reduces donor k’s contribution by exactly one dollar.
 
11
Intuitively, contributions from one donor are detrimental to the other donor’s preferred election outcome, and the other donor has incentive to contribute further to his own candidate to protect his interests in the election.
 
12
Our model assumes a linear combination of the Downsian and Wittman utilities. While that assumption restricts the preferences of the candidates, the convexity of each candidate’s preferences is preserved. The authors wish to thank an anonymous referee for bringing that point to our attention.
 
13
Many studies consider functions such as \(v_{i}(x_{i})=-A(x_{i}-{\hat{x}}_{i})^{2}\), where \(A>0\), which is negative everywhere except at its max when \(x_{i}={\hat{x}}_{i}\), i.e., the implemented policy coincides with candidate i’s ideal, where \(v_{i}({\hat{x}}_{i})=0\).
 
14
In the first term on the right-hand side, an increase in \(x_{i}\) corresponds to candidate i moving closer to (away from) the median voter, thus making his policy position more (less) attractive to voters and increasing (decreasing) the probability that he wins the election. The second term depicts how candidate i’s policy position affects the contributions he receives from each donor. We know that \(\frac{\partial p_{i}}{\partial D_{i}}>0\) since an increase in donations to candidate i increases his chances of winning the election. The signs of \(\frac{dk_{i}^{*}}{dx_{i}}\) and \(\frac{dl_{i}^{*}}{dx_{i}}\) depend on candidate i’s policy position relative to the ideal policies of donors k and l, respectively.
 
15
Since candidate i was relatively close to donor k’s ideal policy position, and donors’ utility is concave by definition, candidate i’s shift in \(x_{i}\) causes only a small reduction in donor k’s expected utility, but yields to donor l a much larger gain in his expected utility.
 
16
Utilizing \(\alpha\) and \(\beta\), we can simulate several different population distributions. When \(\alpha =\beta >1\), we obtain a symmetric population of voters whose mean is 0.5 and are more concentrated towards the center of the distribution. Alternatively, when \(\alpha =\beta <1\), we obtain a symmetric population of voters whose mean is 0.5 but are more concentrated in the tails of the distribution. With \(\alpha>\beta >1\), we obtain a distribution that has a mean above 0.5 and has a negative skew. Lastly, with \(\beta>\alpha >1\), we obtain a distribution that has a mean below 0.5 and has a negative skew.
 
17
The setup is a significant departure from Ball’s (1999a) original model, which did not consider the effectiveness of donations as a linear combination, but rather as a parameter (Ball refers to it as \(\gamma\)). We choose (5) as it guarantees that the probability that candidate i wins the election falls strictly between 0 and 1.
 
18
The specification can lead to convexity issues. While we are unable to prove that the set of all Downsian and Wittman utilities are convex analytically, we examined several instances within those sets numerically. For the present analysis, all donation levels and the position of candidate j, \(x_{j}\), were fixed, and only the values of candidate i’s policy position, \(x_{i},\) and the linear combination between the Downsian and Wittman specifications, \(\gamma\), were varied. We then calculated the resulting payoffs for candidate i. Generally, we find that candidate i’s best response function exhibits discontinuities only when \(\gamma\) is extremely small, as described later in this section, or in the special case in which both candidates i and j have the same ideal policy position. In those cases, we can show numerically that our model predicts policy convergence. Otherwise, candidate i’s best response function is continuous and the set of Downsian and Wittman utilities is convex around candidate i’s best response.
 
19
To approximate continuity, the numerical analysis also was performed using 2,001 and 5,001 equally spaced points, confirming that the results are unaffected. We then reproduced our simulations by drawing 1,001 points randomly on the [0, 1] interval, showing that the results essentially were identical to those using equally spaced points.
 
20
For instance, if the parameters are \(\gamma =1\), \(\lambda =0.5\), \(w=0\), \(\alpha =\beta =2\), \({\hat{d}}_{k}=0.2\), \({\hat{d}}_{l}=0.8\), \({\hat{x}}_{i}=0.3\), \({\hat{x}}_{j}=0.7\), \({\bar{k}}={\bar{l}}=1\), \(\eta =0.5\) and \(c=0.03\), if we start with \(x_{j}=0.1\), candidate i’s largest payoff occurs at \(x_{i}=0.3\), where his payoff becomes \(-0.0053\).
 
21
In that situation, candidate i positions between his own ideal policy, \(\hat{x_{i}},\) and the location of the median voter, but prefers positioning closer to \(\hat{x_{i}}\).
 
22
In “Appendix 2”, we show how equilibrium candidate policy positions shift as the parameters c and \(\lambda\) vary. Consistent with the results in Corollary 4, as the marginal cost of donations declines, candidates position themselves closer to the median voter to deny donations to their opponent.
 
23
Intuitively, with symmetry, donor preferences also align with voter preferences.
 
24
The asymmetry measurement is derived from the difference between each position and that of the median voter, m, \(\left| x_{k}-m-(x_{l}-m)\right|\) which simplifies to our expression. Notably, when policy positions are equidistant from the median voter, the expression evaluates to zero.
 
25
When \(\gamma =0\), we return to policy convergence, as candidate policy preferences do not impact the Downsian equilibrium.
 
26
That is the only case of complete policy convergence in the Wittman specification we found.
 
27
The candidate receiving donations is more likely to win the election under such circumstances. The candidate who positions closer to the median voter (and receives no donations), however, still has a positive probability of winning. That scenario is reminiscent of the 1896 US presidential election won by William McKinley, an industrialist with strong backing by business interests. His opponent, William Jennings Bryan, adopted policy positions that were popular among the mass of voters, but was unable to raise money from potential donors. McKinley raised $3.5 million to Bryan’s $0.5 million, which led to McKinley winning the election.
 
28
For calculated values of \(k_{1}\) and \(k_{2}\), refer to the selected simulation results table in “Appendix 3”.
 
29
Which, as described in the numerical analysis section, produces more policy divergence than in the original Wittman (1983) model, but the candidates do not display the skewness towards donors’ ideal policies because \(\lambda >0\).
 
30
Other countries imposing limits on campaign contributions are Uruguay, Belgium, Finland, France, Greece, Ireland, Poland, Japan and South Korea; with most limiting individual donations below $8000. Countries limiting political parity spending include Canada, Austria, Belgium, Czech Republic, France, Greece, Hungary, Ireland, Israel, Italy, Poland, Japan, New Zealand, and South Korea.
 
31
Of note, intermediate values of \(\gamma\), the weight that every candidate places on policy implementation relative to the probability that they win the election, exist that yield policy convergence only for low values of \(\lambda\). For example, when \(\gamma =0.5\) with our assumed parameters, policy convergence occurs for \(\lambda <0.74\), but policies diverge slightly for values above that value.
 
32
At these parts of the best response function, candidate i obtains a higher probability of winning the election by distancing himself from his opponent and enabling donors to contribute to his own campaign (as donors will contribute approximately zero when candidates position next to one another).
 
33
Term \(N(D_{i}^{\eta }-D_{j}^{\eta })\) is our normally distributed contribution to the probability that candidate i wins the election based on their received donations.
 
34
As described in Propositions 3B and 4B in Wittman’s (1983) paper. The net effect of an increase in \(\lambda\) is ambiguous, as it strongly depends on the symmetry of ideal policy positions, but in general, as \(\lambda\) increases, candidates have stronger incentives to deny donations to their opponent by moving closer to one another; as described in Corollary 4.
 
35
We also find that for every cost \(c<{\bar{c}}\), no Nash equilibrium exists. Intuitively, as donations become extremely cheap, candidate behavior becomes erratic. Candidates receive large donations for even small deviations from their current positions, and constantly vie for the most donations from their respective donors. This causes no equilibrium to emerge. As a note, for large donations, the concavity property of our normal distribution also breaks down, which could be driving this result.
 
36
In our numerical analysis,\(\gamma =1\), \(\lambda =0.5\), \(w=0\), \(\alpha =\beta =2\), \({\hat{d}}_{k}=0.2\), \({\hat{d}}_{l}=0.8\), \({\hat{x}}_{i}=0.3\), \({\hat{x}}\), \(\eta =0.5\), we obtain that for the value of \(c_{w}=0.053\), the Wittman model and the Wittman specification of our model yield the same equilibrium policy positions for both candidates.
 
37
This includes extreme cases where candidates’ ideal policies are at the endpoints of the policy line, \({\hat{x}}_{i}=0\) and \({\hat{x}}_{j}=1\).
 
38
Once again, this also holds for extreme ideal policies, \({\hat{x}}_{k}=0\) and \({\hat{x}}_{l}=1\).
 
39
From disclosure website opensecrets.org, data obtained suggests that no major super PAC supports multiple candidates in the same election. This holds true for several elections, dating back to before 2008.
 
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Metadaten
Titel
Campaign contributions and policy convergence: asymmetric agents and donations constraints
verfasst von
Eric Dunaway
Felix Munoz-Garcia
Publikationsdatum
16.10.2019
Verlag
Springer US
Erschienen in
Public Choice / Ausgabe 3-4/2020
Print ISSN: 0048-5829
Elektronische ISSN: 1573-7101
DOI
https://doi.org/10.1007/s11127-019-00732-1

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