Campaign Contributions as Valence

Campaign Contributions as Valence Tim Lambie-Hanson Suffolk University June 11, 2011 Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 1 / 16

Motivation Under what conditions could campaign contributions from individual donors induce divergent equilibria in the political competition game? Without contributions MVT may not hold when: the policy space is multi-dimensional voting is probabilistic preferences aren t single-peaked Additionally, campaign contributions induce divergent equilibria if candidates care (at least in part) about maximizing total donations (Shieh and Pan, 2009; Glazer and Gradstein, 2005) or if contributions come from interest groups (Grossman and Helpman, 1996). Could office- or policy-motivated candidates search of funds from voters result in divergent equilibria in a deterministic framework? Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 2 / 16

Overview of the Model One-dimensional policy space assumed to be [0, 1]. Two candidates, L and R, propose policies x l and x r knowing that the policies they propose will induce both voting and donating behavior. Two types of voters: partisan voters and impressionable voters Candidates use any contributions they garner from partisan voters to lobby impressionable voters Can particular parameterizations (candidate objectives, voter and wealth distributions, etc.) lead to divergent equilibria in a deterministic framework? Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 3 / 16

Partisan and Impressionable Voters All voters have single-peaked, symmetric preferences over policy. Let W ( i x j ) be the indirect utility Voter i gets from Candidate J s policy where W ( ) is continuous and strictly-decreasing Partisan voters consider only policy when deciding for whom to vote. Further, only partisan voters contribute. Candidates use those contributions to lobby impressionable voters. Impressionable Voter i votes for Candidate L (R) if W ( i x l ) + sv L > (<)W ( i x r ) + sv R (1) vj is valence that Candidate J creates from contributions and s weights the impressionability of the impressionable voters Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 4 / 16

Why do voters contribute to campaigns? Similar to the paradox of voting Expressive vs. Instrumental motivation (Shieh and Pan, 2009) Consumption motivations (Campante, 2010) Empirical evidence that extreme voters donate more and more extreme candidates garner more in contributions Francia et al. (2005) Ensley (2009) I assume partisan donation behavior determined by rule: Donate more the more they like the candidate s policy Donate more the more they dislike the opponent s policy Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 5 / 16

Donations Define d(i, x j, x k ) W ( i x j ) W ( i x k ) Let πi J(d(i, x j, x k )) be the proportion of her wealth (or maximum donation) Partisan i donates to Candidate J. Assume: π J i = 0 if d(i, x j, x k ) ɛ. π J i ( ) is (weakly) monotonically increasing Partisans wealth is distributed across the policy space by cdf G( ) with corresponding pdf g( ). Total donations garnered by candidate J (and hence candidate J s valence) are then v J = 1 0 πj i (d(i, x j, x j ))g(i)di. Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 6 / 16

A brief example Let W ( i x j ) = (i x j ) 2, and suppose { πi J 1 if d(i, xj, x = j ) > T, 0 otherwise. (2) In such a parameterization Partisan i donates to candidate L if or, alternatively, if where b = T 2(x r x l ) (i x l ) 2 ( (i x r ) 2 ) > T, (3) i < x l + x r 2 denotes a buffer region. b, (4) Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 7 / 16

A brief example Suppose x l = 0.4 and x r = 0.5, with both the wealth and voter density given by the triangular density below. R wins the election since R garners more donations and has a more popular policy. Density 2.0 1.5 x l x r 2 1.0 b b 0.5 L's donations x l x r R's donations Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 8 / 16

Office-motivated candidates Proposition If a pure-strategy Nash Equilibrium (PSNE) to the political competition game exists when candidates are office-motivated, then in equilibrium both candidates propose the ideal policy of the median voter. Intuition: If one candidate proposes a policy different from the (ideal policy of the) median voter, the opponent can win by playing slightly closer to the median voter. By doing so, the opponent can ensure that d(i, x j, x j ) ɛ and thus πi J = 0 for all voters. Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 9 / 16

Policy-motivated candidates Assume that Candidate J has symmetric, single-peaked preferences over the policy space with ideal policy ĵ. ˆl is to the left of the median voter ˆr is to the right of the median voter Introduces an additional centrifugal force. We know that a candidate can always win if her opponent picks a policy different from the median policy. If policy-motivated, the candidate may not want to. Possible to construct divergent equilibria, but only under stylized assumptions. W ( i x j ) = i x j and wealth favors one candidate. W ( ) is strictly convex and wealth density is of a very particular form. Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 10 / 16

Divergent PSNE with linear utility When utility is linear, all partisans with i / (x l, x r ) have the same utility difference from policy. Since I assume that π J i = 0 if d(i, x j, x k ) ɛ, it is possible to construct a scenario where by changing policy infinitesimally, a candidate will activate the partisans to donate. (Introduces discontinuity in the voteshare.) Suppose ˆl = 0.25 and ˆr = 0.55 and the wealth distribution is such that all wealth is to the left of ˆl. Further suppose that partisan voters consist of 5 7 of the electorate and use a donation rule such as: { πi J 1 if d(i, xj, x = j ) > T, (5) 0 otherwise. If T = 0.1 in this case, a unique PSNE exists where x l = 0.25 and x r = 0.35 as long as impressionable voters are sufficiently impressionable. Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 11 / 16

Divergent PSNE with strictly convex utility 0.8 0.7 0.6 0.45 0.4 0.35 Utility difference 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Voter ideal points (a) r = 0.75 as x l varies from 0 to 0.5. Donations (Valence) 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 l (b) Suppose ˆl = 0.25 and ˆr = 0.75 Figure: How a convergent PSNE can be constructed when partisans have strictly convex utility. Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 12 / 16

Strictly concave utility Proposition If voter utility from policy is strictly concave, then no divergent PSNE exists. 0.35 0.30 0.25 0.20 0.15 0.10 0.05 x l x r 0.00 0 Figure: By moving slightly towards her opponent, a candidate is viewed more favorably by all voters. Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 13 / 16

Under typical setups a unique, convergent PSNE exists Proposition (Under typical frameworks) a unique equilibrium in which both candidates propose the ideal policy of the median voter exists. Density 2.0 1.5 x l xr 2 Density 2.0 1.5 x l xr 1.0 1.0 2 0.5 z x l xr z g y 0.5 z i x l xr m z g y (a) Symmetric single-peaked wealth. (b) Symmetric wealth and concave utility. Figure: Both assume the elctorate s median voter located at 0.5. Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 14 / 16

Implications Results can be seen somewhat as an impossibility result. Divergent PSNE exist, but assumptions are rather stylized. How do campaign contributions actually influence candidates? Probabilistic voting, popularity valence, and multi-dimensional policy space lead to Schofield s activist valence results In light of Citizens United v. FEC, interest groups are able to more freely participate in the political process (split of money spent is about 50-50 now). Perhaps combining a model of individual contributions with interest groups. (Simplest mechanism may be atoms in the wealth distribution). Why do voters actually contribute? Instrumental v. expressive considerations; Group-rule utilitarians; Consumption motives In the end, probably an empirical question... Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 15 / 16

References Campante, F. R. (2010). Redistribution in a model of voting a campaign contributions. Journal of Public Economics, forthcoming. Ensley, M. (2009). Individual campaign contributions and candidate ideology. Public Choice, 138:221 238. Francia, P. L., Green, J. C., Herrnson, P. S., Powell, L. W., and Wilcox, C. (2005). Limousine liberals and corporate conservatives: The financial constituencies of the democratic and republican parties. Social Science Quarterly, 86(4):761 778. Glazer, A. and Gradstein, M. (2005). Elections with contribution-maximizing candidates. Public Choice, 122(3/4):467 482. Grossman, G. and Helpman, E. (1996). Electoral competition and special interest politics. The Review of Economic Studies, 63(2):265 286. Shieh, S. and Pan, W.-H. (2009). Individual campaign contributions in a downsian model: expressive and instrumental motives. Public Choice, forthcoming. Tim Lambie-Hanson (Suffolk University) Campaign Contributions as Valence June 11, 2011 16 / 16