Ambiguity in election games

We construct a model in which the ambiguity of candidates allows them to increase the number of voters to whom they appeal. We focus our analysis on two points that are central to obtain ambiguity in equilibrium: restrictions on the beliefs that candidates can induce in voters, and intensity of voters' preferences. The first is necessary for a pure strategy equilibrium to exist, while the second is necessary for ambiguity in equilibrium when there exists a Condorcet winner in the set of pure alternatives (e.g. the spatial model of electoral competition), and when candidates' only objective is to win the election. In this last case, an ambiguous candidate may offer voters with different preferences the hope that their most preferred alternative will be implemented. We also show that if there are sufficiently many candidates or parties, ambiguity will not be possible in equilibrium, but a larger set of possible policies increases the chance that at least one candidate will choose to be ambiguous in equilibrium. We would like to thank Alberto Alesina, Antonio Cabrales, Steve Coate, Olivier Compte, Tim Feddersen, Itzhak Gilboa, Joe Harrington, Michel Le Breton, Alessandro Lizzeri, George Mailath, Steve Matthews, Steve Morris, Ignacio Ortuno, Tom Palfrey, Larry Samuelson, Murat Sertel, Fernando Vega, Eyal Winter and an anonymous referee for helpful comments. The first author acknowledges financial support from DGICYT-PB 95-0983. This work was done while the first author was visiting the Center in Political Economy at Washington University, and visiting the Center for Basic Research in the Social Sciences at Harvard University. Their hospitality is gratefully acknowledged. The support of the second author's research by the National Science Foundation is also gratefully acknowledged.     

Voter turnout in a multidimensional policy space

Many factors influence the likelihood of citizens turning out to vote. In this paper we focus our attention on issue voting, that is, on the likelihood that different policies offered by politicians affect the probability of voting. If voters consider both the benefits and the costs of voting, rational voters will only vote when politicians offer differentiated policies. In a multidimensional policy space this implies that citizens only vote when they perceive enough difference on the issues they care about the most. We investigate the role of voter abstention due to indifference in a unidimensional and a multidimensional policy setting using data from the US National Election Studies for 1972–2000 and find support for our predictions: voters perceiving a small difference between the platforms of the Democratic and Republican parties are less likely to vote; and voters who perceive the two parties as more different on a larger number of issues are significantly more likely to vote.     

How two-party competition treats minorities

The paper studies Downsian electoral competition in the framework of redistributive politics among groups of unequal size. As soon as no group forms a majority on its own, parties treat all voters in the same way at an equilibrium of the Plurality game. This paper has benefited a lot from the referees' careful reading. I also thank for their comments Steve Brams and other seminar participants in Caen and Paris. All remaining errors are mine.     

Targeted campaign competition,loyal voters,and supermajorities

We consider campaign competition in which candidates compete for votes among a continuum of voters by engaging in persuasive efforts that are targetable. Each individual voter is persuaded by campaign effort and votes for the candidate who targets more persuasive effort to this voter. Each candidate chooses a level of total campaign effort and allocates his effort among the set of voters. We completely characterize equilibrium for the majoritarian objective game and compare that to the vote-share maximizing game. If the candidates are symmetric ex ante, both types of electoral competition dissipate the rents from office in expectation. However, the equilibria arising under the two electoral objectives qualitatively differ. In majoritarian elections, candidates randomize over their level of total campaign effort, which provides support for the puzzling phenomenon of the emergence of supermajorities in majoritarian systems. Vote-share maximization leads to an equilibrium in which both candidates make deterministic budget choices and reach a precise fifty–fifty split of vote shares. We also study how asymmetry between the candidates affects the equilibrium. If some share of the voters is loyal to one of the candidates, then both candidates expend the same expected efforts in equilibrium, but the advantaged candidate wins with higher probability for majoritarian voting or a higher share of voters for vote-share maximization.     

Two-Sided Platforms: Product Variety and Pricing Structures

This paper provides a new modeling framework to analyze two-sided platforms connecting producers and consumers. In contrast to the existing literature, indirect network effects are determined endogenously, through consumers' taste for variety and producer competition. Three new aspects of platform pricing structures are derived.   First, the optimal platform pricing structure shifts towards extracting more rents from producers relative to consumers when consumers have stronger demand for variety, since producers become less substitutable. With platform competition, consumer preferences for variety, producer market power, and producer economies of scale in multihoming also make platforms' price-cutting strategies on the consumer side less effective. This second effect on equilibrium pricing structures goes in the opposite direction relative to the first one.   Third, variable fees charged to producers can serve to trade off producer innovation incentives against the need to reduce a platform holdup problem.     

Strategic participation and the median voter result

In a seminal paper on electoral equilibrium under majority rule, Ledyard (1984) demonstrates that strategic participation by voters results in an electoral equilibrium at the proposal that maximizes the utility of a randomly selected voter. Palfrey and Rosenthal (1985) limit the usefulness of this result by showing that strategic participation rates are miniscule in large electorates, and that the incentive to participate vanishes completely as the electorate grows without bound. The most reasonable modification of Ledyard’s approach that circumvents these criticisms is to allow for a negative cost of voting. We show that when voters can have even an arbitrarily small negative cost of voting, there is an electorate sufficiently large so that any proposal is defeated or tied by the median proposal. This observation raises questions about the existence of electoral equilibrium under strategic participation, and is relevant to the efficiency of elections.     

Competing Platforms

Why do competing platforms or networks exist? This paper focuses on instances where the value of a platform depends on the adoption decisions of a small number of firms, and analyzes the strategic competition among platforms to get this oligopolistic side on‐board. I study a bilateral contracting game among platforms and firms that allows for general externalities across both contracting and noncontracting partners, and examine when a market will sustain a single or multiple platforms. When firms can join only one platform, I provide conditions under which market‐tipping and/or market‐splitting equilibria may exist. In particular, even without coordination failure, congestion effects, or firm multihoming, multiple platforms can co‐exist in equilibrium despite being inefficient from the perspective of the contracting parties. Expanding the contracting space to include contingent contracts may exacerbate this inefficiency.     

Endogenous party structure

This paper proposes a model of two-party representative democracy on a single-dimensional political space, in which voters choose their parties in order to influence the parties’ choices of representative. After two candidates are selected as the median of each party’s support group, Nature determines the candidates’ relative likability (valence). Based on the candidates’ political positions and relative likability, voters vote for the preferable candidate without being tied to their party’s choice. We show that (1) there exists a nontrivial equilibrium under natural conditions, and (2) the equilibrium party border and the ex ante probabilities of the two-party candidates winning are sensitive to the distribution of voters. In particular, we show that if a party has a more concentrated subgroup, then the party tends to alienate its centrally located voters, and the party’s probability of winning the final election is reduced. Even if voter distribution is symmetric, an extremist party (from either side) can emerge as voters become more politically divided.     

On the relationship between economic development and political democracy

A politico-economic model is defined, in which consumers, at date 0, decide how much to invest in a firm (and how much of its stock to purchase), whose production possibilities are determined by the outcome of an election, to be held at date 1. At date 1, consumers vote on the level of pollution the firm shall be allowed to emit. There are incomplete markets; the states of the world are the two possible electoral outcomes at date 1, each associated with the victory of a particular party. In turn, the parties represent poor and rich voters; voters’ interests at date 1 are determined by the investments they have made at date 0. Because parties are uncertain about a parameter of voter preferences, the electoral (Nash) equilibrium at date 1 is not median-voter: there are two possible policies (pollution levels), occurring with probabilities that can be calculated. A full equilibrium of the model is an economic equilibrium with incomplete markets at date 0 and a political equilibrium at date 1, each of which induces the other. In a fictional ‘benevolent dictatorship,’ elections are called off, and the dictator announces a pollution policy which is the expected outcome of the would-be elections. By substituting the expected value of a lottery for a lottery, the utilities of citizens, who are risk-averse, increase. There are, however, costs to dictatorship, in the form of the absence of civil liberties. For any economic environment, it is possible to compute the equilibria under democracy and benevolent dictatorship, and to evaluate what coalition of the population prefers one to the other. In this way, the benevolent dictatorship is a benchmark against which to measure the costs of democracy. We examine to what extent the support for democracy, contrasted with benevolent dictatorship, grows among the population as economic development occurs. Development is simulated in five different ways, and it is not unambiguously the case that it induces a growing social preference for democracy. I have benefitted from discussions with A. Alesina and M. Quinzii, from the comments of S. Barbera at the International Economic Association conference on democracy and development (1992), from the comments of Michael Winston at the NBER political economy conference (1992), and from comments by participants at these conferences and at several university seminars.     

Exclusivity and Control

We model competition between content distributors (platforms) for content providers, and show that whether or not content is exclusive or “multihomes” depends crucially on whether or not content providers maintain control over their own pricing to consumers: if content providers sell their content outright and relinquish control, they will tend to be exclusive; on the other hand, if content providers maintain control and only “affiliate” with platforms, then multihoming is sustainable in equilibrium. We show that the outcome under affiliation depends on the tradeoff between platform rent extraction (which increases in exclusivity) and content rent extraction (which increases in multihoming), and demonstrate that the propensity for exclusivity can be increasing, decreasing, or even nonmonotonic in content quality. Finally, if a content provider internalizes the effect of its own price on platform demand, we prove that a platform that already has exclusive access to content may prefer to relinquish control over content pricing to the content provider in order to reduce price competition at the platform level.     

Dynamics in the fragmentation of political party systems

Fragmentation is an important dimension of political party systems. It concerns the proliferation of minor parties and the willingness of voters to vote for them. Past research relates party fragmentation to the voting system in a country; by Duverger's hypothesis, fragmentation should be highest in counties with proportional representation. The entropy measure is used to quantify fragmentation. The upper limit of fragmentation is analyzed in 24 countries, and the patterns of change in fragmentation are identified with mathematical difference equations, testing the idea that voters and parties evolve toward an equilibrium in fragmentation. The highest level of fragmentation is found comparable with a psychological limit on human information processing. In 17 of 22 countries, fragmentation moves toward an equilibrium, regardless of the type of voting system, and countries with higher equilibrium levels usually evolve more slowly. The results affirm the stability of democratic governments but raise questions about voters' strategies and suggest that some voters may try to control fragmentation when they vote.     

Career Concerns and Product Market Competition

This paper studies the effect of increased competition in the product market on managerial incentives. I propose a simple model of career concerns where firms are willing to pay for managerial talent to reduce production costs, but also to subtract talented executives from competitors. This second effect is privately valuable to firms, but is socially wasteful. As a result, equilibrium pay for talent can be inefficiently high and career concerns too strong. Explicit incentive contracts do not solve the problem, but equilibrium pay is reduced if managerial skills have firm‐specific components, or if firms are heterogeneous. In this second case, managers are efficiently assigned to firms, but equilibrium pay reflects the profitability of talent outside the efficient allocation. The effect of increased competition is ambiguous in general, and depends on the profit sensitivity to cost reductions. This ambiguity is illustrated in two examples of commonly used models of imperfect competition.     

Equilibria in the spatial stochastic model of voting with party activists

Stochastic models of elections typically indicate that all parties, in equilibrium, will adopt positions at the electoral center. Empirical analyses discussed in this paper suggest that convergence of this kind is rarely observed. Here we examine a stochastic electoral model where parties differ in their valences – the electorally perceived, non-policy “quality” of the party leader. It is assumed that valence may either be exogenous, in the sense of being an intrinsic characteristic of the leader, or may be due to the contributions of party activists, who donate time and money and thus enhance electoral support for the party. Theorem 1 shows that vote maximization depends on balancing these two opposed effects. Theorem 2 provides the necessary and sufficient conditions for convergence to the electoral mean when activist valence is zero. The paper then examines empirical electoral models for the Netherlands circa 1980 and Britain in 1979, 1992 and 1997 and shows that party divergence from the electoral mean cannot be accounted for by exogenous valence alone. The balance condition suggests that the success of the Labour party in the election of 1997 can be attributed to a combination of high exogenous valence and pro-Europe activist support.     

Platform market competition with endogenous side decisions

This paper develops a framework to analyze platform competition in two‐sided markets in which agents endogenously decide on which side of a platform to join. We characterize the equilibrium pricing structure and perform a comparative statics analysis on how the distribution of agents’ preferences affects the platforms’ profits. We also show that the market equilibrium under profit‐maximizing platforms leads to the first best social surplus, which illustrates the importance of the price mechanism to induce more balanced participation across the two sides. This framework can be applied to analyze market competition for “rental” or “sharing” platforms. In addition, we extend our analysis to consider an initial investment stage, which makes participants the owner of some durable goods to rent out.     

Vertical externalities and control of politicians

A major role of (repeated) elections is to create incentives for politicians to act in the interests of voters. This paper considers the disciplining role of elections in countries with either one or two levels of government. Simple retrospective voting strategies which are based on cut-off levels with respect to expenditure and tax rates are considered. It is shown that the power of voters is weakened if a second independent level of government is added. However, voters can partially reinforce their power by making politicians not only liable for their own policy, but also for the policy carried out at each other level of government. Received: June 30, 2000 / Accepted: April 4, 2001     

Political selection of public servants and parliamentary oversight

In this paper, we propose a framework to integrate the identity of legislators in a politico-economic analysis of parliamentary oversight. Legislators decide about the effort they invest in oversight activities depending on their individual control costs and the level of electoral competition. We focus on public servants elected to parliament who face a conflict of interests but also have lower control costs due to their experience and information advantage. If held accountable, oversight becomes a relatively attractive activity for them to win votes. For German Laender, we find that the fraction of public servants in parliament is positively related to the number of submitted parliamentary interpellations. This result holds when instrumenting the fraction of public servants in parliament with its institutional determinants. Moreover, a mixed-member electoral system as well as a tighter race between the two biggest parties is related to more, a larger number of parties in parliament to less minor interpellations.     

On robust asymmetric equilibria in asymmetric R&;D-driven growth economies

In R&D-driven growth models with asymmetric fundamentals, the steady-state equilibrium R&D investments are industry-specific, and they are such that R&D returns are equalized across industries. Return equalization, however, makes investors indifferent as to where to target research and, hence, the problem of allocation of R&D investments across industries is indeterminate. Agents’ indifference creates an ambiguous investment scenario. We assume that agents hold “ambiguous” beliefs on the per-industry profitability of their R&D investments. Investors’ aversion towards ambiguity eliminates the indeterminacy of the investment problem. In particular, the asymmetric return-equalizing equilibrium is robust against a however small degree of investors’ ambiguity aversion.     

Alpha-robust mean-variance reinsurance-investment strategy

Inspired by the α-maxmin expected utility, we propose a new class of mean-variance criterion, called α-maxmin mean-variance criterion, and apply it to the reinsurance-investment problem. Our model allows the insurer to have different levels of ambiguity aversion (rather than only consider the extremely ambiguity-averse attitude as in the literature). The insurer can purchase proportional reinsurance and also invest the surplus in a financial market consisting of a risk-free asset and a risky asset, whose dynamics is correlated with the insurance surplus. Closed-form equilibrium reinsurance-investment strategy is derived by solving the extended Hamilton–Jacobi–Bellman equation. Our results show that the equilibrium reinsurance strategy is always more conservative if the insurer is more ambiguity-averse. When the dependence between insurance and financial risks are weak, the equilibrium investment strategy is also more conservative if the insurer is more ambiguity-averse. However, in order to diversify the portfolio, a more ambiguity-averse insurer may adopt a more aggressive investment strategy if the insurance market is very ambiguous. For an ambiguity-neutral insurer, the investment strategy is identical to the non-robust investment strategy.     

From plurality rule to proportional representation

I consider the decision of a parliament that might change the electoral system from the plurality rule to proportional representation for forthcoming elections. Parties are office-motivated. They care about winning and about the share of seats obtained. I examine two different scenarios of how parties in government share the spoils of office: equally or proportionally to their share of seats. If the government is formed by a single party and parties expect that each party will obtain the same share of votes in the next election, the electoral rule will never be changed. Therefore, for a change to occur, the government should be formed by a coalition. I find that a change is more likely to occur when there is a larger number of parties and also when the spoils of office are shared equally among the members in the governing coalition. These results are extended to analyze the decision to change from a less proportional rule to a more proportional one.     

To dissent or not to dissent? Informative dissent and parliamentary governance

Legislative dissent has detrimental effects for both party and legislator, i.e., legislators depend on their party label for re-election, which value in turn depends in part on the party’s reputation of cohesiveness. Commonly dissent has been attributed to “extreme” preferences. I provide an informational rationale for dissent. Costly dissent allows the legislator to credibly signal information about his constituency’s preferences to the Cabinet. As a result the Cabinet can better calibrate its policies with the electorate’s preferences. Dissent is shown to depend on policy preferences as well a the legislators’ electoral strength, electoral volatility, and the cost of dissent. Finally, the results suggests that parties may sometimes benefit from tolerating some level of dissent. I am grateful to Christopher Kam, Randall Calvert, John Duggan, Mark Fey, Eduardo Leoni, Sona Golder, and the anonymous referees for their helpful comments and suggestions. I also wish to thank the Political Institutions and Public Choice Program at Michigan State University for its support. All remaining errors are mine.