Strategic dissent in the Hotelling–Downs model with sequential entry and private information

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Abstract

We analyze the Hotelling–Downs model of winner-take-all elections with sequential entry where n2 ‘office-seeking’ candidates with privately known qualities choose entry decisions and commit to policy platforms on entering. Voters receive informative public signals about the quality of each contestant once all platforms are announced. We characterize two-party equilibria when the order of entry is exogenously given. In these equilibria, entry can occur in any ‘round’ with positive probability: high-quality candidates signal their type through showing ideological dissent with the voters while low-quality ones randomize between (mis)-signaling quality through dissent and staying out. Interestingly, while informative public signals can keep low-quality candidates out of competition up to a certain degree, electoral competition improves the voter׳s information about candidate types beyond what the signals can reveal. However this endogenous mechanism of strategic information transmission leads to political polarization.

Introduction

Models of electoral competition typically analyze the type of policies that arise in equilibrium and pay less attention to other dimensions that may influence voters. Yet media coverage of elections suggests that policy is only one dimension of what voters take into account and non-policy issues are often predominant in deciding electoral outcomes. This non-policy dimension, recurrently described as firmness of purpose (or character) or quality of governance, is something that in principle voters agree as desirable and which can persuade them to vote for a candidate even when they disagree with his policies. This is what Stokes (1963) terms as valence. But when this non-policy dimension is private information to the candidates, not pandering to the wishes of electorally pivotal voters can itself be regarded as a signal of strength. A large body of literature has developed that looks at what is called the marginality hypothesis which suggests that weaker candidates are more likely to contest with electorally popular platforms.3 But beliefs that pandering is symptomatic of low quality may of course lead to strategic choices by politicians to deliberately distance themselves from popular ideologies—we call this strategic dissent.

There is evidence of ideologically unpopular politicians (or parties) winning elections because voters believed they would be more efficient or trustworthy in what they do, making up for any loss in ideological alignment. Margaret Thatcher may have been the most conservative and certainly the most radical Prime Minister that Britain had (in the words of her biographer Charles Moore)4 but she won elections and an IPSOS Mori Poll in 2011 finds that she is considered the most capable Prime Minster in the last few decades.5 To take another example, it is believed that the staunch left-wing politician Paul Wellstone was seen by the Minnesota voters as having integrity. Although his opponent Rudy Boschwitz׳s ideological position was popular, Wellstone, starting as a clear underdog, surprised all with a remarkable victory in the 1990 US Senate elections. In 1999 the Dutch party VLD (Open Vlaamse Liberalen en Democraten) won on a right-wing platform (contrary to when they deliberately chose a policy aligned with the majority and lost in 1995).6 A recent example of a politician who seems to deliberately flaunt a certain amount of sectarian and economic extremism is India׳s current Prime Minister Narendra Modi, who led his party (the BJP) to power in the recent parliamentary elections. Several press releases and opinion polls suggest that voters saw him as an efficient and decisive leader which compensated for his extreme image. Indeed as the New York Times reports, Modi, ‘has emerged with a bold, right-wing narrative in a country with a staunchly socialist past’ even while the centrist Congress is struggling with an image of policy paralysis.7

These examples seem to indicate that ideological extremism can be used to signal quality and our paper analyzes conditions under which strategic extremism occurs in a Hotelling–Downs (HD) model (Hotelling, 1929, Downs, 1957) with one-dimensional policy space, free entry and incomplete information about candidate quality. The choice of a Downsian framework (or purely office-seeking candidates) is to allow us to filter out the impact that party ideology may play in the choice of platforms. As candidates do not care for policy in the classical HD world, any deviation from the median voter׳s ideology must come from strategic reasons. The model we study has n2 potential entrants (or candidates) and a decisive voter group (which we may think of as the median voter).8 Free entry puts pressure on parties to move towards popular ideologies in order to thwart future entry. Thus, while it is a stark way to model endogenous entry, obtaining extremism in such a framework if anything understates the forces for policy divergence. Unlike most of the literature on valence which studies competition between two given parties, we endogenize the size of political participation under the free-entry assumption. A complication that arises is that HD models with free entry run into problems concerning equilibrium existence. While competition between two parties yields a unique Nash equilibrium outcome where both parties locate at the ideal policy of the median voter (often called the Median Voter Theorem that has remained central to the formal literature on elections), when there are n>2 potential candidates a Nash equilibrium in pure strategies fails to exist (see Osborne, 1995). Further with sequential entry, which is the focus of this paper, equilibrium characterization becomes a more intriguing problem. While for n=3,4 there exists a unique sub-game perfect equilibrium where only candidates 1 and n contest with the median policy (while all other candidates stay OUT), this result remains an open conjecture for n5.9 Given this, we ask if incomplete information can ease the existence problem and allow one to analyze equilibrium behavior with free entry.

Following the HD framework, we assume that entrants can credibly commit to any policy and policies are perfectly observable.10 However each candidate has a non-policy quality (or valence) parameter, which is not known to the voter or other candidates. Voters receive partially informative11 public signals about the quality of the final contestants after they have made their ideological commitments. One can think of this as occurring because of media investigation or simply from the party campaigns that reveal some information about the candidate through her speeches, handling of questions, etc. Given the signal and the announced policies of the candidates, the voter makes a choice in a winner-take-all election. As in the environment where the Osborne conjecture is analyzed, we assume that while the cost of entering the contest is zero (free entry), candidates incur a cost only if they do not tie for the first place.12

It has been pointed out that we could consider the incomplete information framework with costly messages, as in Honryo (2013), where each potential entrant announces his or her type and a large reputational cost is associated with a signal that is of low probability given the announcement. This possible framework is not considered here because modelling the reputation cost explicitly would have involved considering repeated elections explicitly and such a framework would, of course, obviate the need for dissent.

With an exogenously fixed order of entry, we prove generic existence of equilibria that exhibit the phenomenon of strategic dissent and is consistent with Duverger׳s Law of two-party systems (see Duverger, 1964). We show that for each n2 there are conditions (on costs and signal precision) under which exactly two candidates choose to enter the contest while all other candidates stay out. Entry can take place in any period and unless the last candidate (called n ) faces a history where there is no past entrant (the only case where policy becomes arbitrary), each contesting party commits to policy platforms that are away from the median voter׳s ideal point, thereby leading to political polarization (with probability 1 for the case n3).13 While a high quality entrant contests with a dissenting platform with probability 1, a low quality party randomizes between contesting with an equally dissenting platform and staying out. As a consequence, ideological dissent becomes a signal of quality although the equilibrium is only partially revealing. As expected, the more weight the voters attach to the quality parameter the bigger is the deviation of the winner׳s policy from the median voter׳s ideal point. We show that to obtain this result one requires relatively high but bounded costs and intermediate degree of exogenous signal precision. We also show that for each finite n, the median voter (prior to receiving exogenous signals) strictly prefers the first entry to take place as early as possible in the entry game; but once the first entry takes place he is indifferent about the timing of the second entrant. Moreover, he always strictly prefers the second entrant to the first. This implies that in equilibrium the earlier the first entry more likely it is to be of high quality but the second entrant is always more likely to be high quality than its first-entrant counterpart. We then show that as n grows unboundedly, this strict temporal and history-dependent preference of the voter disappears so that in the limit neither timing nor position of the entrants matter. A consequence of this limit observation is that the probability of a voter-pandering contestant decreases as the number of potential competitors increases even though a two-party contest is maintained. This is counterintuitive as one expects stronger centripetal forces with more competition. Our analysis also proves that this limit equilibrium is indeed an equilibrium for the case when n=. It is important to observe in the background of these results that they continue to hold with generic distributions of voters׳ ideal points as long as these distributions are sufficiently thin over extreme policies.

The limit equilibrium (when n=) where the voter is indifferent between the two contesting parties has some interesting comparative static properties. Starting from a certain level of informativeness of exogenous signals, an increase in informativeness has two effects: extremism falls, which improves voter welfare but it comes at a cost as the low type׳s probability of entry increases reducing voter welfare. Given this tradeoff one may ask the following: can better public information sources hurt voters? We show that fortunately not, that is, the voter׳s ex-ante welfare must increase with more informative signals. Finally, we show that even if the prior probability of high quality candidates in the population becomes very small so that incomplete information is almost absent in the environment, the two party equilibrium with platform extremism continues to exist. This result stands out as an interesting contrast with Osborne׳s conjecture though the two models are not conceptually comparable.

Given the extensive literature on HD models with 2 candidates, we look at other possible equilibria when n=2 with a fixed order of entry. We show that dissent is not necessary to signal strength as a mere entry (even with a voter-pandering policy) can serve this purpose as well. In particular, there are indeed equilibria where the high type entrant contests under a popular platform while a low type randomizes between that and staying out. Yet, under a plausible assumption on signals such an equilibrium with full pandering becomes fragile. The assumption we make is that the more extreme a candidate׳s position, the more likely it is for him to generate public signals. This is plausible as there is strong evidence that the press investigates extreme candidates more routinely (see for example McCluskey and Kim, 2012). Such an assumption makes higher quality candidates deliberately choose dissent, thereby increasing the probability of getting favorable signals, leaving low-quality rivals no other option but to randomize between staying out and mimicking high quality actions of unpopular platforms. Further, with free entry (n>2), an equilibrium where two parties stand at the median voter׳s ideal point will be fragile and particularly so when we move to general distributions of voter׳s ideologies.

Our results contrast with Groseclose (2001), who finds conditions under which marginal candidates (that is those with low quality) take more extreme positions unlike in our case where this is never true. Groseclose obtains this in a model where quality is perfectly observable but the voter preferences are not perfectly known. Given this, the weaker (in valence) candidate׳s only hope is not to be near the stronger candidate on the policy line since if the pivotal voter (whose exact position is unknown) sees two candidates close to each other, she will vote for the one with higher valence. The idea that platform choice can affect voters׳ beliefs about an unobserved but important trait of a party has been analyzed in Kartik and McAfee (2007), which is possibly the most related paper to this one. Similar to our work, they show how parties indulge in strategic dissent (thus choosing policies away from the median). While they study two-candidate games (and we look at endogenous entry and obtain two party contests as equilibrium outcomes) Kartik and McAfee assume the (exogenous) existence of non-strategic candidates with character (the committed types as in Kreps et al., 1982) who act according to their beliefs about what would be the ‘right’ policy (modeled as a random process that assigns probabilities to different policy platforms), rather than catering to popular demands. Voters like character and since strategic office-seeking candidates typically announce popular policies, extremism attracts favorable attention. Given this, strategic candidates cannot afford to be too populist anymore, although on average they are closer to the median voter than an expected committed type. In the main text of their paper, such principled candidates with character are essentially non-strategic and have no explicit desire to signal anything to anyone. In contrast, we endogenize participation of different candidate types and their policy choices. We should mention that in a supplementary appendix, (http://www.columbia.edu/~nk2339/Papers/integrity_webappendix.pdf), Kartik and McAfee show how one can construct an equilibrium in which candidates are indifferent among available positions, so that the randomised choice of positions by the committed type can, in fact, be an equilibrium strategy. Moreover, the notion of character we use is more about productive efficiency in the political arena (like good governance rather than appropriateness of the policy in question since in our model, voters are fully informed about policy appropriateness) that is signaled by choice of unpopular policies.14 There are also some other papers which show that some form of extremism in actions signals quality. Starting with Rogoff (1990) who looks at higher than optimal deficit spending, a large body of literature has sprung up where politicians take more extreme positions than socially optimal to signal quality. Applications include inefficient transfers to special interest groups (Coate and Morris, 1995) and excessive litigation in the courtroom (Bandyopadhyay and McCannon, 2013).15 However, in all these models policy makers care for policy as well as winning and thus signaling is credible in such models because it is directly costly for them to choose an ideology more extreme than their own favorite policy about which voters are fully informed. Our model is also related to models of endogenous entry that have looked at policy choices under alternate assumptions on commitment and in some cases barriers to entry.16 In general these models of policy extremism have not modeled the entry decision and models of political entry have typically not been concerned with the asymmetric information about candidate quality and how that affects policy choice during the political entry stage.17

The rest of the paper is structured as follows. In Section 2 we describe the model. Our main results are in Section 3. Section 4 analyzes the model with two candidates. We conclude in Section 5 where we also summarize our main results. All proofs are in an appendix.

Section snippets

Model

A politically decisive constituency with ideal policy mR and Euclidean preference over the policy line R selects a candidate via winner-take-all elections. There are n2 candidates called i=1,2,,n who arrive in an exogenous order to decide whether to stay OUT or contest the elections by committing to a platform in R. We denote by xi the platform commitment of candidate i if he chooses to contest. The distance zi=|xim| is the extent of dissent of platform xi with respect to the ideal policy

Informative equilibria with n=

We begin with the following remark that characterizes equilibrium behavior under full information.

Remark 1 Full information

In the full information version of our model there is a unique subgame-perfect equilibrium where all high quality candidates contest by committing to the platform m while all low quality candidates stay OUT.19

Two-candidate contests

Section 3 established conditions under which elections select exactly two contesting parties (out of infinitely many candidates) and transmit information about the qualities of each contestant over and above what exogenous signals can provide. We now consider what happens when the number of candidates is 2. Following Duverger׳s Law, this is not only the most analyzed case in the literature but the median voter remains decisive for all distribution of voters ideal points and all sets of

Conclusion

We analyzed a Downsian model of sequential entry and incomplete information about candidate quality when entry timings are exogenously given. We conclude by first summarizing all our results and then discussing some generalizations of the framework in which these results remain robust.

The central message of our analysis is as follows: ideological dissent can be an equilibrium feature with good quality candidates using dissent to signal their type while low-quality candidates randomize between

Acknowledgments

We thank Sandro Brusco, Antonio Cabrales, Navin Kartik, Colin Rowat and seminar participants at the University of Birmingham and the Indian Institute of Management - Calcutta for insightful comments and Katharine Inglis for research assistance. Chatterjee wishes to thank the Richard B. Fisher Endowment of the Institute for Advanced Study, Princeton, NJ for making his membership of the Institute possible for 2014-15.

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