THE MODEL

We consider a one-period model of electoral competition with four players: two candidates (1 and 2), one representative voter, and an interest group (i). To focus on the informative component of outside spending, our set-up does not incorporate ideological considerations. Candidate j∈{1, 2} is office-motivated and commits either to a safe (p _j =0) or a risky (p _j =1) policy. While the safe policy provides a sure payoff of 0 to the voter, the impact of the risky policy depends on an underlying state of the world θ ^v ∈{H, L}. When the risky policy is implemented, the voter obtains 1+Δ, Δ>0 if the state of the world is high (θ ^v =H), and 1−Δ if θ ^v =L (notice that Δ can be above 1). For example, the risky policy corresponds to securing subsidies for particular industries or to revitalize an abandoned industrial site. The economic benefits of such policy are uncertain: they are large in state θ ^v =H and relatively low in state θ ^v =L. The parameter Δ>0 captures, in a reduced form, the policy risk associated with p=1. Players do not know the state of the world θ ^v .Footnote ⁴ However, it is common knowledge that the state θ ^v is drawn from a uniform distribution: Pr(θ ^v =H)=1/2.

The effect of the risky policy on the interest group i also depends on an underlying state θ ⁱ ∈{h, l}, which is the group’s private information. i’s payoff from the risky policy equals 1 when θ ⁱ =h and −1 otherwise. It is common knowledge that θ ⁱ is also drawn from a uniform distribution (i.e., Pr(θ ⁱ =h)=1/2) that is correlated with θ ^v . The degree of congruence between the voter and group i is captured by (and increasing in) the correlation parameter ρ∈(0, 1) (see Potters and VanWinden Reference Potters and vanWinden1992). We assume that the joint distribution of (θ ^v , θ ⁱ ) takes the following form.Footnote ⁵

The interest group can use outside spending to publicly endorse a policy platform. We denote by a _i ∈{0, 1, Ø} the group’s advertising strategy, where a _i =1 (a _i =0) corresponds to the interest group endorsing the risky (safe) policy, and a _i =Ø corresponds to no advertising. Advertising (a _i ≠Ø) is associated with a cost of raising funds c>0 that depends on the regulatory environment. Under a ban on union and corporate funding of outside spending, we impose c>1 (which guarantees that i never advertises). Absent a ban, we assume c∈(0, 1).

The voter’s payoff from candidate j depends on his platform choice p _j , the state θ ^v , and a valence shock ε ^j , j∈{1, 2}, which captures any additional payoff the voter might receive from candidate j’s personal attributes or his expected actions on other policy dimensions. We assume that ε ^j is drawn independently from a continuous cumulative distribution function (CDF) with support $$[0,\,\overline{{\epsilon}} ]$$ , that the difference ε:=ε ¹−ε ² is distributed according to the CDF $$F_{{\epsilon}} \,\sim\,\left[ {{\minus}\overline{{\epsilon}} ,\,\overline{{\epsilon}} } \right]$$ , with an associated probability density function f _ε (⋅) which is symmetric around 0. To simplify the derivation of the results and rule out uninteresting cases, we also assume that the value of the preference shocks is not too large or too small: $$\overline{{\epsilon}} \in(1{\minus}\rho \Delta ,1)$$ .Footnote ⁶ The voter’s utility function when she elects j assumes the following form: $$u^{v} (j)\,{\equals}\,p_{j} (1{\plus}\Delta {\minus}2\Delta {\Bbb I}_{{\{ \theta ^{v} \,{\equals}\,L\} }} ){\plus}{\epsilon}^{j} {\rm ,}$$ where $${\Bbb I}_{{\{ \theta ^{v} \,{\equals}\,L\} }} {\equals}1$$ if θ ^v =L.

A candidate gets 0 when he is not in office. When elected, he gets 1 and his payoff is reduced by an amount k∈(0, 1) when he implements the risky policy. This cost corresponds to the political capital required to implement a policy initiative (Hall and Deardorff Reference Hall and Deardorff2006). Candidate j’s payoff if elected is then: u ^j (p _j )=1−kp _j .

The interest group’s payoff when candidate j is elected depends on his policy choice p _j as well as the state θ ⁱ . If it engages in outside spending (a _i ≠Ø), the group also pays the cost c. Its utility function is then $$u^{i} (a;\theta ^{i} ){\equals}p_{j} (1{\minus}2{\Bbb I}_{{\{ \theta ^{i} \,{\equals}\,l\} }} ){\minus}c{\Bbb I}$$ _{a≠Ø}.

To summarize, the timing of the game is as follows. (1) Nature draws (θ ^v , θ ⁱ )∈{H, L}×{h, l} and the valence shocks ε ¹, ε ². (2) The interest group observes θ ⁱ. (3) Candidates choose a platform: p _j ∈{0, 1} j∈{1, 2}. (4) The voter and the interest group observe (p ₁, p ₂). The interest group chooses a policy endorsement a _i ∈{0, 1, Ø}. (5) The voter observes i’s endorsement and the valence shocks, and elects a candidate. (6) The elected candidate implements his platform, and payoffs are realized.

Notice that the interest group intervenes after candidates’ platform choices. This assumption (whose role is discussed in detail when we evaluate the current regulatory framework) captures the idea that the interest group cannot coordinate with candidates by directly influencing their platform choice.

The equilibrium concept is perfect Bayesian equilibrium, with two additional requirements. First, the assessment must satisfy the intuitive criterion (Cho and Kreps Reference Cho and Kreps1987).Footnote ⁷ Second, when multiple equilibria arise, we select the one associated with the highest expected payoff for the voter (henceforth, voter welfare).Footnote ⁸ In what follows, the term “equilibrium” refers to this class of equilibria.

EQUILIBRIUM WITH AND WITHOUT A BAN

We first determine candidates’ equilibrium behavior under a ban on the funding of outside spending by corporations and unions. Let a _i (θ ⁱ , p ₁, p ₂) denote the interest group’s advocacy strategy as a function of the state θ ⁱ and candidates’ policy platforms. Under a ban (c>1) the interest group never advertises (a _i is constant at Ø). As a result, i’s behavior does not convey any additional information to the voter, who thus relies on her prior. Since the voter then prefers the risky policy, a candidate proposing the safe policy faces certain defeat when his opponent chooses p=1. Both candidates thus converge to the risky policy.Footnote ⁹

We now study the equilibrium absent a ban. Let $$\underline{\pi } $$ be the probability that a candidate is elected when he campaigns on the safe policy, his opponent commits to the risky policy, and the voter learns that θ ⁱ =l. Simple computation yields $$\underline{\pi } \,{\equals}\,F_{{\epsilon}} (\rho \Delta {\minus}1)$$ .Footnote ¹⁰

Outside spending only occurs when candidates choose different platforms (otherwise i cannot influence electoral outcomes): ∀p∈{0, 1}, a _i (h, p, p)=a _i (l, p, p)=Ø. Lemma 1 in the Appendix shows that when the cost of advertising satisfies $$c\,\lt\,\underline{\pi } $$ and there is a meaningful policy choice (p ₁≠p ₂), the interest group engages in outside spending and its endorsement (a _i ≠Ø) fully reveals θ ⁱ to the voter.

Intuitively, due to their commonality of interests, the interest group can always credibly transmit information to the voter. As a result, outside spending improves the voter’s electoral decision. Whenever θ ⁱ =l, outside spending reduces the chances of electing the “wrong” candidate (whose commitment to the risky policy is either suboptimal or insufficient to compensate a large gap in valence).Footnote ¹¹

Having established that outside spending is beneficial taking candidates’ behavior as given, we study how outside spending affects candidates’ behavior, assuming $$c\,\lt\,\underline{\pi } $$ in what follows.

Recall that under a ban on outside spending, a candidate wins the election with positive probability only if he commits to the risky policy. When the voter receives policy information through outside spending, this is no longer the case. Indeed, outside spending has an asymmetric effect on the electoral rewards associated with each platform choice. When θ ⁱ =h, the interest group’s behavior does not affect the already high winning probability of a candidate committing to p=1. In contrast, when θ ⁱ =l, outside spending strictly improves (from 0 to the strictly positive probability $$\underline{\pi } $$ ) the electoral chances of a candidate who chooses the safe policy against an opponent committing to the risky policy. This directly implies that a candidate only obtains a moderate electoral reward for proposing the risky policy even if his opponent proposes the safe policy. When the cost of implementing p=1 satisfies $$k\,\gt\,\overline{k} (\rho \Delta )$$ , this electoral reward is too low relative to the cost. The unique equilibrium then features both candidates offering p=0.

Ironically, due to the lack of additional policy information, under a ban, the risky policy is the only electorally viable bet from the perspective of candidates when facing an opponent committing to p=1. In contrast, when the voter receives information about the risky policy via outside spending, she can condition her electoral response to the group’s endorsement. This, in turn, spills over into the candidates’ incentives: proposing the safe policy while facing a 50/50 chance of being endorsed by the group becomes a viable electoral strategy.

Further, upon learning θ ⁱ =l, the voter’s evaluation of the risky policy becomes more negative the higher the policy risk (Δ) or congruence with the interest group (ρ). As a result, the electoral benefit of committing to the risky policy for a candidate is decreasing in ρΔ, and so is the threshold $$\overline{k} (\rho \Delta )$$ for any candidate to propose p=1.Footnote ¹²

Despite the above result, one might suspect that whenever candidates have some electoral incentives to propose the risky policy absent a ban (i.e., $$k\leq \overline{k} (\rho \Delta )$$ ), outside spending increases voter welfare by decreasing the probability that p=1 is implemented when it is less beneficial. This intuition, however, is not complete since the interest group intervenes only if candidates propose different platforms. Hence, $$k\leq \overline{k} (\rho \Delta )$$ is only necessary, but not sufficient, for outside spending to benefit the voter.

Two conditions need to be satisfied for outside spending to improve voter welfare. First, candidates must propose different platforms with positive probability, so the interest group has an incentive to engage in outside spending. In this set-up, platform divergence requires candidates to play a mixed strategy and can only happen if the policy cost is sufficiently large ( $$k\in(k^{{\asterisk}} ,\overline{k} (\rho \Delta ))$$ ). Second, the informational gain from learning θ ⁱ must be high enough to compensate for the risk that no candidate proposes p=1 (ρΔ>D*).

These results do not automatically invalidate the Supreme Court’s arguments in favor of removing restrictions on the source of funding of outside spending. However, they provide restrictions on observables under which these arguments are likely to be correct. In particular, in the Appendix (see Corollary 1) we show that in order to be beneficial, outside spending needs to be “rare,” in the sense that it has to happen with probability strictly lower than 1/2.Footnote ¹³ Finally, even if Citizens United has increased voter welfare, the campaign finance framework may still be inefficient from a social welfare perspective, as the next section now shows.

EVALUATING THE CURRENT REGULATION

In this section, we allow for coordination between the interest group and candidates. In particular, we assume that in stage 2 of the game (see The Model section) the interest group can send a cheap talk message m _i (j)∈{h,l} to candidate j∈{1,2}, and focus on the most informative equilibrium strategy. To allow for the possibility of outside spending in equilibrium, we continue to assume that $$c\,\lt\,\underline{\pi } $$ .

Coordination increases the interest group’s ability to obtain its preferred policy. The group can use messages to “warn” candidates that the policy reduces its payoff (θ ⁱ =l), and credibly signal that should a candidate commit to the risky policy, the group will endorse his opponent. Such strategy, however, can be supported in equilibrium only when the policy cost k is large enough (see Lemma 2 in the Appendix). Intuitively, when k is too small relative to the electoral return of choosing the safe policy ( $$\underline{\pi } )$$ , proposing the risky policy is always a dominant strategy for both candidates.Footnote ¹⁴ Proposition 4 examines the welfare consequences of allowing for coordination between candidates and the interest group.

Proposition 4 implies that the current campaign finance legislation is inefficient. If the informational gain from learning θ ⁱ is low (ρΔ≤1), then reducing the cost of outside spending harms the electorate. Conversely, if the group’s private information is highly valuable to the electorate (ρΔ>1), voters would be better off if coordination was permitted.

This last result highlights the importance of the timing assumptions. When i can engage in outside spending before candidates choose their platform, direct communication is no longer beneficial for voters. This, however, does not invalidate the reasoning in this section. Allowing for coordination is still Pareto improving because it induces the same candidate behavior without on path costly outside spending. Further, our set-up, where advertising expenditures occurs after platform choices, focuses specifically on the type of outside spending affected by Citizens United. A group’s advertising prior to candidates’ platform decision is more closely related to policy advocacy, which was already protected by the First Amendment prior to the 2010 Supreme Court’s decision.

This observation also implies that Proposition 4 holds even when we incorporate the group’s payoff in our welfare criteria. Indeed, whenever coordination improves the voter welfare, it also improves the joint welfare since the group obtains its preferred policy at no cost. Further, under our payoff assumption, the group is indifferent (ex ante) between the risky policy and the safe policy. Consequently, lifting a ban has no effect on the group’s payoff whenever it hurts the voter by eliminating all candidates’ incentive to offer the risky policy.