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Erschienen in:

25.05.2017

# Mystifying but not misleading: when does political ambiguity not confuse voters?

verfasst von: Maarten C. W. Janssen, Mariya Teteryatnikova

Erschienen in: Public Choice | Ausgabe 3-4/2017

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## Abstract

The purpose of political campaigns in democracies is to provide voters with information that allows them to make “correct” choices, that is, vote for the party/candidate whose proposed policy or “position” is closest to their ideal position. In a world where political talk is often ambiguous and imprecise, it then becomes important to understand whether correct choices can still be made. In this paper we identify two elements of political culture that are key to answering this question: (i) whether or not political statements satisfy a so-called “grain of truth” assumption, and (ii) whether or not politicians make statements that are comparative, that is contain information about politicians’ own positions relative to that of their adversaries. The “grain of truth” assumption means that statements, even if vague, do not completely misrepresent the true positions of the parties. We find that only when political campaigning is comparative and has a grain of truth, will voters always make choices as if they were fully informed. Therefore, the imprecision of political statements should not be a problem as long as comparative campaigning is in place.
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Fußnoten
1
The fact that politicians’ talks can be and often are ambiguous is well known and documented in the literature (Downs 1957; Kelley 1961; Page 1976; Campbell 1983; Edelman 1985; Laslier 2006).

2
Thus, the main body of our paper studies the mirror image of traditional spatial models of elections, going back to Hotelling (1929), Black (1948) and Downs (1957). While in that literature political parties choose their positions and the electorate is immediately informed about them, in the central case of our model positions cannot be chosen, but what is disclosed about them is a result of strategic competition between the parties.

3
This assumption, that utility is derived directly from voting, is standard in the literature on “expressive” voting (see, e.g., Brennan and Hamlin 1998; Schuessler 2000; Glaeser et al. 2005; Clark and Lee 2016).

4
See, Crawford and Sobel (1982) and the subsequent literature on cheap talk games. The main focus of the cheap talk literature is on studying how informative some equilibria can be, whereas our focus is on the informativeness of all equilibria. Also, we focus on one-dimensional information asymmetries, whereas Battaglini (2002) and Chakraborty and Harbaugh (2010, 2014) consider multi-dimensional settings.

5
See for example, Alesina and Cukierman (1990), Glazer (1990), Chappell (1994), Aragones and Neeman (2000), Jensen (2009), Frenkel (2014) and Kartik et al. (2015).

6
Other related papers on the determinants of positive and negative campaign spending include Harrington and Hess (1996), Chakrabarti (2007) and Brueckner and Lee (2015).

7
Despite their difference in modeling assumptions and focus, Polborn and Yi (2006) and our paper deliver results that are similar in flavor. Positive/non-comparative campaigning in both papers results in less informed electoral choices, while negative campaigning in Polborn and Yi (2006) and comparative campaigning in our model facilitate “correct” voting decisions.

8
See, e.g., Viscusi (1978), Grossman and Hart (1980), Grossman (1981), Jovanovic (1982), Milgrom (1981), Daughety and Reinganum (1995) and Board (2003).

9
The sum of parties’ vote shares is always equal to one.

10
The assumption of symmetry around 0.5 is not crucial for the results. The changes one would need to introduce under arbitrary distribution with full support on [0, 1] are nominal and have to do with the fact that the median voter is located not at 0.5 but at $$\lambda _{med}$$, where $$\int _0^{\lambda _{med}} g(\lambda )d\lambda =\int _{\lambda _{med}}^1 g(\lambda )d\lambda$$.

11
A prominent early model with costly voting is Ledyard (1984).

12
The probability measure function is called non-atomic if it has no atoms, i.e., measurable sets which have positive probability measure and contain no set of smaller but positive measure.

13
Note that owing to the fact that the probability density function f from which the parties’ positions are drawn is non-atomic, the ex-ante probability of any specific position is zero. In this case, Bayes’ rule should be applied as follows. Suppose that position z of party i belongs to the set of types $$S=\{y,z\}$$ that, given the equilibrium strategy, could make statement $$S_i$$. Then the probability of the event $$x_i=z$$ should be updated as
\begin{aligned} \mu _{i}^{*}(z|S_{1},S_{2})=\lim _{\varepsilon \rightarrow 0}\frac{ F(z+\varepsilon )-F(z)}{F(z+\varepsilon )-F(z)+F(y+\varepsilon )-F(y)}. \end{aligned}
Using l’Hôpital’s rule,
\begin{aligned} \mu _{i}^{*}(z|S_{1},S_{2})=\lim _{\varepsilon \rightarrow 0}\frac{ f(z+\varepsilon )}{f(z+\varepsilon )+f(y+\varepsilon )}=\frac{f(z)}{f(z)+f(y) }. \end{aligned}

14
Note that in case of voluntary voting, the indifferent voter may actually prefer to abstain, depending on the realization of her voting cost. Nevertheless, the position of the indifferent voter marks the important threshold between voters who never vote for a given party and those who—conditional on voting—always vote for this party.

15
In the Supplementary Appendix we also provide a specific example of voter preferences and costs in elections with voluntary voting that lead to this condition.

16
Indeed, under full disclosure $$\widehat{\lambda }>0.5$$ (and so $$\pi _{L}>\pi _{R}$$ ) if and only if $$x_{L}+x_{R}>1$$, which is the case either when both $$x_{L}\ge 0.5$$ and $$x_{R}>0.5$$, or when $$x_{L}\le 0.5<x_{R}$$ and positions $$x_{L}$$, $$x_{R}$$ are not exactly symmetric around 0.5 but such that $$x_{L}$$ is closer to 0.5 than $$x_{R}$$. In both cases, the position of the left party is closer to 0.5 than the position of the right party.

17
Such a definition of the government policy is common in papers on elections with proportional representation. See, for example, Herrera et al. (2014, 2015), Lizzeri and Persico (2001) and Kartal (2015).

18
See the seminal paper by Crawford and Sobel (1982) for reference on cheap talk games.

19
Admittedly, these are special out-of-equilibrium beliefs that support the described equilibrium. However, as we explain in more detail later (Sect. 5), such beliefs cannot be ruled out by standard equilibrium refinements such as the Intuitive Criterion (Cho and Kreps 1987) and the Divinity Criterion, or D1 (Cho and Sobel 1990). Recall that both criteria restrict the receiver’s beliefs to those types of senders for which deviating towards a given off-the-equilibrium message could improve their equilibrium payoff. On top of that, the D1 criterion considers that, among all potential deviators, the full weight is assigned to those types of senders who have the greatest incentive to deviate.

20
With majority rule elections, such as presidential elections, where the candidate gaining the largest vote share wins (payoff is one), and the other candidate looses (payoff is zero), the same proposition and proof apply.

21
In the case of presidential elections (majority rule principle) only the resultant policy, that is, the winning candidate is always determined “correctly”, while the actual voters’ choices might be different from those under full disclosure for many actual pooling types. For example, there exists an equilibrium where all types $$(x_1,x_2)$$ such that $$x_2<x_1<0.5$$ or $$0.5 < x_1< x_2$$ (candidate 1 is located closer to 0.5 than candidate 2) pool, and where all types $$(x_1,x_2)$$ such that $$0.5<x_2<x_1$$ or $$x_1<x_2<0.5$$ (candidate 2 is located closer to 0.5 than candidate 1) pool. Such an equilibrium is not ex-post efficient according to our definition because given the pooling statements, the location of the indifferent voter is different from that for any actual pooling type, so that voters’ choices are distorted with positive probability. However, the nature of pooling in this equilibrium (and in fact, in any nondisclosure equilibrium) is such that the candidate that is perceived as located closer to 0.5 is, in fact, located closer to 0.5. Therefore, the candidate that wins the election is the same as under full disclosure.

22
Note that this logic is similar to the traditional unraveling argument in the literature on quality disclosure (e.g., Milgrom 1981). However, our setting is very different: it features horizontal rather than vertical differentiation, a constant sum of players’ payoffs and a two-dimensional type space.

23
Note that symmetric or equal positions of the two parties are non-generic owing to the assumption that both positions are drawn independently from a non-atomic probability distribution. In Sect. 6.1 we consider an alternative model specification with strategic positions and show that our conclusions remain conceptually similar: full disclosure turns out to be the unique equilibrium outcome under comparative, but not non-comparative, campaigning.

24
The proof of equilibrium is provided in the “Appendix”.

25
The same strategies constitute an equilibrium in presidential elections (majority rule), with zero-one payoffs. Hence, also in this case, many nondisclosure equilibria are ex-post inefficient and result in the implemented policy being different from the one under full disclosure.

26
The same proposition holds true in case of presidential elections (majority rule), where the payoffs are zero-one.

27
The same equilibria exist in case of presidential elections.

28
If positions are chosen strategically, nothing much changes. We state this at the end of the section.

29
Some examples of equilibria include the situation where both parties of each type choose non-comparative statements and then fully disclose own position, or where both parties make comparative statements, or where one party makes non-comparative and the other comparative statement and then both or only the second party disclose the positions precisely.

30
Under presidential elections only the resultant policy, that is, the winning candidate, is always determined “correctly”, while the actual voters’ choices might be different from those under full disclosure. The equilibrium example in footnote 21 (Sect. 4) applies here, too.

31
Recall that $$x_1=x_2$$ along the upward-sloping diagonal, and $$x_1=1-x_2$$ along the downward-sloping diagonal.

32
$$S_i\bigcap S_j\ne \emptyset$$ owing to the grain of truth condition.

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Titel
Mystifying but not misleading: when does political ambiguity not confuse voters?
verfasst von
Maarten C. W. Janssen
Mariya Teteryatnikova
Publikationsdatum
25.05.2017
Verlag
Springer US
Erschienen in
Public Choice / Ausgabe 3-4/2017
Print ISSN: 0048-5829
Elektronische ISSN: 1573-7101
DOI
https://doi.org/10.1007/s11127-017-0459-3

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