Incumbency Advantage in Non-Democracies

Transcription

1 Incumbency Advantage in Non-Democracies Georgy Egorov Northwestern University Konstantin Sonin New Economic School December 2011 Abstract Many nondemocratic countries held regular or semi-regular elections even for top officials, often plagued with fraud. We build a simple one-period model, where the regime ultimately faces a threat of revolution, and acts strategically to limit its scope. The dictator decides on whether or not to repress (e.g., eliminate any potential for protests), whether or not to have elections, and if he decides to have elections, he determines the extent of the vote fraud. Elections, even fraudulent, convey information about the real number of supporters of the regime. If the regime is sufficiently confident, making this information public makes citizens less likely to protest. In equilibrium, the strongest dictators have elections, which will necessarily be partially fraudulent. The weakest dictators repress, and the intermediate range of dictators neither has elections nor represses. Higher costs of protests for citizens make both elections and repressions more attractive options, and higher cost of repression makes repressions less likely and elections more likely. In contrast, lower cost of repression reduces the need for elections as a signal the dictator s strength: absence of repressions already does this. The possibility of fraud makes it possible for unpopular dictators to signal that they still have some support, and it may also make repressions more likely. Keywords: non-democratic politics, dictatorships, political economy, elections, fraud, political eliminations, revolutions. JEL Classification: H00. An earlier draft of this paper was titled Incumbency Advantage in Non-Democratic Elections. We thank Daron Acemoglu, Alberto Alesina, Alvaro Sandroni, Mehdi Shadmehr, participants of Harvard-MIT Positive Political Theory seminar, MOVE Workshop on Selection of Politicians in Barcelona and MPSA conference for helpful comments and suggestions.

2 1 Introduction In 1987, 1993, and 1999, the Egypt s president Hosni Mubarak held elections, in which no other candidates where allowed to run. In 2005, Mubarak agreed to allow other candidates to be on the ballot; however, elections were marred with uneven playing field, extensive fraud, and jailing of opponents of the dictator. In early 2011, Mubarak faced mass protests, was abandoned by his key supporters, and ended up under home arrest on corruption charges. In Europe, Belarus president Alexander Lukashenko held authoritarian elections, which were not recognized by the international community as free and fair, in 2001 and In 2010, he allowed multiple opposition candidates to be on the ballot, yet had most of them jailed on the election night. Following events in Tunisia and Egypt, Nursultan Nazarbaev, Kazakhstan s ruler since 1991, suddenly announced that he will stand for re-election (his term from the previous elections in 2005 would expire in 2012; before that, the term was prolonged in 1995 and 1999). On April 3, 2011, with no opposition candidates on the ballot, Nazarbaev, was reported the winner with 95.5 percent of the vote. The above examples point out to an important political phenomenon. Scholars of democratic regimes recognized long ago the impact of political competition on both the policy pursued by elected individuals (Downs, 1957, Baron, 1994, Myerson, 1993, Persson and Tabellini, 2000) and characteristic traits of individuals that are elected (Besley, 2005, Acemoglu et al, 2010). However, political competition is extremely important, and in no way less fierce, in non-democratic regimes as well (Spearman, 1939, Tullock, 1987, Grossman and Noh, 1990, B.Bueno de Mesquita et al, 2003, Geddes, 2006, 2010, Svolik, 2008, 2009, Egorov and Sonin, 2010). We focus on major political decisions that separate the autocratic decision-making from the democratic one, and study consequences of political institutions that allow the incumbent leaders in non-democracies to act in the way that is not available to their democratic counterparts. Specifically, we investigate consequences of the non-democratic incumbency advantage, i.e. the ability of dictators to influence election outcomes by organizing vote fraud, cancelling elections, or even directly eliminating political opponents. In an electoral model (Ashworth and E.Bueno de Mesquita, 2008), incumbents have, on average, greater ability than challengers for two reasons: first, candidates with higher abilities win elections with higher probability (electoral selection, e.g., Ashworth, 2005), and, second, the presence of a high-ability incumbent deter challengers from seeking office (strategic challenger 1

3 entry, e.g., Gordon, Huber, and Landa 2007). We show that though both mechanisms, the selection and strategic entry, work in non-democracies as well (see, e.g., Geddes, 2010, for a discussion of entry deterrence as an explanation for fraudulent elections; Magaloni, 2006, on PRI rule in Mexico), the situation is drastically different when the incumbent can cancel elections or imprison, exile, or kill his would-be challengers. 1 We develop our model backward from the point where it ends for most dictators: the dictator faces protests, and his goal is to make these protests as limited and contained as possible. We build a simple model of protests with two main features: an individual is more likely to protest if her dislike for the dictator is relatively high, and also if she believes that the likelihood of success, measured by the share of people protesting, is sufficiently high. (Formally, this part of our model is based on Persson and Tabellini, 2009, approach, which is in turn employs the global games approach; see Boix and Svolik, 2007.) While the dictator cannot manipulate attitude towards him, we show that he can use elections to manipulate citizens beliefs about the success of protests. In fact, this happens in a very straightforward manner: elections deliver a credible signal about the shares of people supporting and opposing the dictator, and even when marred by fraud, they allow citizens to get a more precise signal about others attitude towards the dictator than the prior everyone has. Needless to say, having elections is a strategic choice for the dictator, and he will do so to maximize the probability of staying in power. In our model, the dictator decides both on whether or not to have elections and chooses the extent of fraud. Citizens update their prior beliefs about the dictator using his decisions as signals on his vulnerability, and decide wherther or not to revolt. Quite naturally, the dictator will opt to have elections when he is strong enough with the aim to discourage protests and uprising. A more subtle effect is that sometimes the dictator will be compelled to have elections even when he is sufficiently weak, because not having elections will send a signal that he is truely afraid to reveal his true popularity. This effect is stronger if the dictator is expected to have elections by default, and weaker if not having elections is nothing extraordinary, e.g., in countries with irregular elections and lack of a democratic history. The dictator who is afraid of losing elections may use fraud to get the 50% of votes that he needs. In many cases, dictators want to get many more votes, and for a reason: barely getting 1 Empirical evidence on incumbency advantage in democratic regimes is solid (e.g., Ansolabehere, Snyder, and Stewart, 2000, Ansolabehere and Snyder, 2002). Implications of our model shall allow to test its predictions for non-democratic regimes. 2

4 50% will tell citizens, who believe that elections are fraudulent, that the dictator actually has very little support. Our model indeed predicts that the dictator will use fraud to signal that they are supported by very many people even if he is absolutely sure to win elections. But at the same time, fraud makes elections more costly. Thus, if losing was out of question, fraud may make elections less likely. Our final prediction deals with the possibility of elimination of dictator s likely opponent. It turns out, counterintuitively, that the possibility of elimination decreases the need for election, as survival of the contender is already a signal that he is weak and the dictator is strong. Both selection and entry deterrence mechanisms (Ashworth and Bueno de Mesquita, 2008) are at work, but work somewhat differently from the democratic setting. A higher cost of elimination makes elections more likely as those opponents who are alive are, on average, stronger. In these circumstance, not having elections signals dictator s weakness. This makes elections and eliminations natural substitutes. However, a lower cost of canceling elections makes political eliminations less likely as now, with citizens aware that the dictator can cancel elections more or less at will, the absence of elections is attributed to high cost rather than fear to be exposed as unpopular. Hence, on the margin, killing opponents does not make sense. Here, elections and eliminations are complements. There is a substantial literature that strives to explain elections held by autocrats (see, e.g., Miller, 2010, for a recent survey). 2 There are two main explanations: first, information-gathering on national and local issues (Martinez-Bravo, 2010; second, projecting a message of strength of the regime. In an important case study of Mexican party dictatorship, Magaloni (2006) analyses both motives. Blaydes (2006, 2008) focuses on Egypt to demonstrate how local elections are used as a monitoring device to identify optimal, from the dictator s standpoint, allocation of offices and distribution of patronage. Lust-Okar (2006) finds similar patterns in Jordan; Brandt and Turner (2007) analyse local elections in China. (See also, Koehler, 2008.) Similarly, information might be gathered at the national level. In Londregan and Vindigni (2006), election outcome is a signal that helps to arrange a stable agreement with the dictators opponents. In Gandhi and Przeworski (2006), Magaloni (2008), Boix and Svolik (2008), and Miller (2010) power-sharing arrangements are based on signals provided by the elections outcomes. The second major reason for dictators to have elections is to demonstrate the strength of 2 There is a recent trend to dub elections held by dictators authoritarian elections. This is an unfortunate terminology as it obscures the defining feature of these events; that is, 3

5 their position. Miller (2010) quotes Przeworski (2009) on elections that are used by regimes to demonstrate that it can force everyone to appear in a particular place on a particular days and perform the act of throwing a piece of paper into a designated box. (See Gaddes, 2006; both Blaydes, 2006, and Magaloni, 2006, find evidence of this motive in their respective countries of study.) Howard and Roessler (2006) provide a classification of regimes based on their decisions to have elections and to allow opposition to participate. Our analysis suggests that this may be a feature of the perceived danger by the dictator, not just an exogenously given institutional feature. Any political leader has to exert efforts to stay in power as his subjects evaluate his performance in office (Barro, 1973, Ferejohn, 1986, Rogoff, 1990). Any autocrat, unlike a democratically elected leader, faces the choice whether or not to use violence against their opponents. The degree to which autocratic leaders can kill or imprison their opponents vary. At the height of their power, Joseph Stalin or Mao Zedong were able to eliminate their would-be opponents at will. In other circumstances, even a strong dictator might fail to get rid of an opponent, or have to take into account political constrains that preclude an outright elimination of a challegner. Many of the 20 th century leaders - including Stalin and Mao - have spent, before coming to power, time in prison or exile: their predecessors were unable to stop their accession to power by these means (on Stalin, see Gregory, 2004, Montefiore, 2003; on Mao, see Change and Halliday, 2005). In Egorov and Sonin (2005) and Debs (2010) the winner of a power contest has to decide the fate of the loser. This generates a vicious cycle that breeds violence: the more you kill, the more dangerous is leaving office, the larger are incentives to kill once more. In our model, the possibility of elimination splits the set of opponents as follows. The weakest will be allowed to participate in elections. The stronger will not participate in elections, but will have a chance to stay and organize protests. The strongest will be eliminated. However, the more are eliminated, the less sense it makes for the dictator to have elections. Intuitively, the dictator has elections to show that the opponent is not very strong (that is low). But if elimination is possible, that the mere fact that the opponent lives provides substantial evidence that the threat is low. The rest of the paper is organized as follows. Section 2 introduces a formal model. This model is analyzed in Section 3. We first study the citizens decisions to protest, then dictator s incentives to use elections and repressions, and then we introduce the possibility of electoral 4

6 fraud. Section 4 concludes. 2 Model Consider a one-period model of a country populated by a continuum of citizens and an incumbent dictator. The dictator maximizes his chance of staying in power. If he succeeds, he gets a payoff. In the end of the period, there is a possibility of a popular uprising, and we follow Persson and Tabellini (2009) in assuming that the probability of dictator leaving the office,, equalsto the share of population protesting,. 3 We assume that each individual in the society makes the decision to protest independently and simultaneously, taking the following payoff matrix in mind: Dictator leaves Dictator stays Citizen protests (1) Citizen stays home 0 The payoff matrix deserves some discussion. If a citizen decides to protest, he gets a disutility of (where 0), which may involve the probability of being shot, wounded, fired from the job, etc; we expect to be higher in more cruel regimes. Parameter captures individual s dissatisfaction with, or hatred towards, the dictator; it may be positive or negative (or equal to zero). Persson and Tabellini (2009) introduced this parameter to capture the warm glow that an individual may experience from (successfully) defending the idea he/she firmly believes in, such as defending democracy or overthrowing a much-hated dictator. this paper, we assume that this warm glow from the right action may be experienced even if the uprising ultimately fails, albeit to a less extent ( in the top-right cell). In This is in line with the recent (and growing literature) about ethical actions and warm glow in voting (cf. Feddersen, Cherepanov, and Sandroni, 2010). We also think that the assumption that a sufficiently dissatisfied citizen may protest even if he does not expect the protest to bring him immediate benefits is justified empirically (say, the recent revolution in Tunisia started with a young merchant setting himself on fire). 4 Finally, we allow for the possibility that a citizen benefits from seeing the dictator leave the office even if he did not protest himself ( 3 To model the probability of success of an uprising in a more realistic fashion, we would need to have a much more complicated model, which would involve the dynamics of protests, participation of police force and the army, etc. Since our focus is on dictator manipulating his chance of survival, the simplest monotonic function of the number of protesters seems a reasonable assumption for our purposes. 4 Kricheli et al (2010) build a two-period model of protests, where protests in the first period serve a signaling role. There, this signaling motive ensures that a citizen who dislikes the dictator enough will protest so as to make the public discontent with the dictator public information. In this light, the assumption we make may be viewed as a shortcut for this model. 5

7 in the bottom-left cell), although may be assumed to be 0 without affecting our results. This may be summarized as follows: a person hating the dictator strongly enough (i.e., if is high enough) gets the highest utility if the dictator leaves and he was a part of that and the lowest utility if the dictator stays and he did not protest; the other two cases are intermediate. With this interpretation, the coefficients at (1 at the top-left and 0 at the bottom-right) are mere normalizations. Clearly, these preferences are reversed for a person who strongly supports the dictator (i.e., if is negative and large in absolute value). We maintain the following assumptions throughout the paper. Assumption 1 0, 0, 0, + 1. For the model, the assumption that 0 is important: it will imply that there will always be an agent who will protest (notice that then for high enough, protesting is a dominant strategy). The last assumption, + 1, captures the increasing-differences intuition: If a citizen wants the dictator to leave ( 0), his marginal utility of protesting (as compared to not protesting) is higher if the dictator leaves than if the dictator stays. Indeed, this is equivalent to which simplifies to + 1. ( ), (2) Each of the continuum citizens has preference randomly drawn from a distribution ( ), where itself is a random variable unknown to the citizens. Variable therefore parametrizes the distribution of. To be specific, we assume that is taken from a normal distribution N 2 and = + where are jointly independent, independent from, and distributed as N 0 2. Our interpretation of is therefore the average attitude towards the dictator (and we will refer to in this way throughout the paper). We want to emphasize, however, that our results would hold for a more general set of distributions: essentially, there are three important assumptions: (a) conditional on, preferences of citizens are independent: { } are independent variables; (b) distribution ( ) has full support for each, and continuously differentiable densities, (c) for each citizen, and are (strictly) affiliated. 5 To save on 5 Two one-dimensional random variables and with continuous joint density function ( ) are affliated if for any 1 2, 1 2,wehave ( 1 1 ) ( 2 2 ) ( 1 2 ) ( 2 1 ). They are strictly affiliated if for all 1 2, 1 2, the inequality is strict. See Milgrom and Weber (1982) for a discussion of affiliated randome variables. Under our assumptions, and are affiliated for any citizens. 6

8 notation and for clarity, we will refer to distribution functions without appealing to a specific functional form, except for the following simple assumption that would ensure the existence and uniqueness of equilibria. The assumption says that an individual s is not a good predictor of the average and thus of other citizens attitudes toward the dictator, because there is a sufficient variance in citizens tastes. Assumption 2 The variance of error term, 2,issufficiently large. More precisely, assume ³ 2, that 2 2 so that ( ) 2 (1 ) 2 (1 ). Throughout the paper, we assume that each citizen initially knows only, whereas the dictator knows the value of, and thus of the entire distribution of. Our motivation for this assumption is that the dictator has access to many sources of information: opinion polls, reports of secret agents, etc. Of course, in many cases there are limits to information that the dictator may collect; there agency problems, his subordinates may be yes-men etc. Yet we believe that the assumption that the dictator knows more than an individual citizen is in many cases realistic, and to simplify the exposition, we take this assumption to the extreme, i.e., that the dictator knows precisely. Prior to the uprising, the dictator may decide to hold elections or to cancel elections. By elections, we mean one of the two scenarios (the choice between these is not strategic, but rather a parameter of the model). The first one is actual elections, in which the dictator himself partipates. Counting the results may involve fraud (a choice parameter for the dictator), but if even after the fraud is administered the dictator still gets less than 50% of the vote, he is out. Most importantly, the population not only learns the technical outcome (whether the dictator won or lost), but also the vote tally, of course, corrected by fraud. The second possibility is a referendum. In a referendum, the citizens also vote for or against the dictator, but there are no consequences if the dictator gets less than 50%. In other words, referendum, like elections, reveals some information about the support for the dictator without him running the risk of actually losing. We view the case of a referendum as a benchmark case, and refer to the case where the dictator loses if he gets less than half of votes as true elections. For various reasons, the dictator may not always have an option to have elections. possible that there were elections recently, and it is too costly or too awkward to have another one, or perhaps organizing elections is costly. At the same time, it is possible that it is costly to cancel elections, e.g., if a formal constitution prescribes the dictator to have elections. To 7 It is

9 keep things simple, we assume that with some probability (0 1) the dictator may decide to have elections (or, if there are elections scheduled, he may decide to cancel them), but with probability 1 there are no elections. This parameter,, will be high if elections are expected, and it will be low when it is very rare for the country or the regime to have elections. 6 Let us denote the share of people who support the dictator and want him, to stay by : = ( ) =Pr( 0 ) = (0). (3) It is natural to assume that at elections, individuals with 0 cast vote (to replace the dictator), and individuals with 0 cast vote (to let the dictator stay). This is a reasonable assumption for two reasons. First, each voter is infinitesimal, and thus his vote does not matter. More importantly, it is possible to show that this is precisely what the voter would do if he controlled a small, but non-zero, share of votes (as happens in reality). Notice that conditioning on pivotality, often assumed in similar models, makes little sense here: it is not only the elections immediate outcome that matters, but also the exact tally of votes, as it influences the citizens decisions to protest or not. To save on notation, we denote the share of citizens who voted by = ( ). Instead of, however, the dictator may report a fraudulent figure ˆ. We assume that to report ˆ when the actual vote share is, the dictator has to pay a cost = (ˆ ). Here, is a non-negative, twice continuously differentiable function defined on (0 1) (0 1), and we assume the following natural assumptions are satisfied: (ˆ ) =0whenever ˆ, 2 (ˆ ) 0 for ˆ (1),and ˆ 2 2 ˆ (ˆ ) 0 in this same region ˆ (this means that getting result ˆ is cheaper when is higher than lower). We also assume that limˆ 1 (ˆ ) = for any and lim 0 (ˆ ) = for any ˆ (i.e., it is infinitely costly to claim full support when this is not the case, and it is infinitely costly to claim any support when the dictator has none). Getting to ˆ 1 2 is necessary to win the elections, but this is not the case for a referendum. We maintain that people do not observe fraud directly, but they have rational expectations about the dictator s choice of. Before elections, the dictator not only decides on whether to have elections and, if to have them, on the amount of fraud. Instead of doing any of these, we can assume that at some 6 This parameter will also serve an important technical purpose: If =1, then absense of elections is always a negative signal about the dictator s popularity, and the dictator would be compelled to have elections. While there are many reasons for why this last effect would not be present in reality, including imprecise information possessed by the dictator, or the possibility that having elections was not even on the dictator s list of options, we believe that having an exogenous possibility of no elections is a reasonable shortcut. We could add a cost of having elections (or the cost of canceling elections); the results and the insights would not change much. 8

10 cost 0, the dictator can eliminate any possible threat. By this, we mean one of the two interpretations. On the one hand, may be the cost of repressions, say, the cost of state of emergency or having excessive military presence in the cities. On the other hand, we can think that there is an opposition leader or leaders who would have challenged the dictator during elections, or whom protesters would support (as this leader performs no strategic function in the model, we omit him). In that case, at cost, the dictator can eliminate the current opposition and thus ensure that there is no alternative that citizens could focus on, and therefore there are no protests. This ability is yet another manifestation of incumbency advantage, and we will study how the cost of elimination affects other choices by the dictator. To summarize, the timing of the game is as follows. 1. Collective attitude and citizens individual preferences are realized. The dictator learns theexactvalueof. 2. The dictator learns cost and decides whether to eliminate the threat at this cost. If he does so, then the game ends, the dictator gets. Otherwise, the game proceeds to the next period. 3. The dictator, with probability, decides whether to hold elections or not. In the case of elections, the game proceeds to the next stage, otherwise to stage The dictator decides the figure ˆ that he wants to report, and pays cost (ˆ ) where is the share of his true supporters. In the case of true elections (not referendum) and ˆ 1 2, the dictator is removed from office and the game ends. 5. If the dictator is not removed as a result of elections, each citizen decides whether to protest, and the probability of dictator leaving equals the share of citizens who decided to protest. We use the following equilibrium concept of Perfect Bayesian equilibria, so the dictator, when choosing whether to have elections and the extent of fraud, and citizens, act fully rationally. Note that we do not explicitly model voting strategies, to simplify the exposition. As noted earlier, the sincere voting strategies assumed earlier are best responses in the equilibria of the game, and would still be if voters were not infinitesimal. We start our analysis with the case where is very high (say, ), so elimination is prohibitively costly. 9

11 3 Analysis Our analysis proceeds as follows. First, we study the decision of citizens to revolt. We show that, under the Assumption 2, there is always a unique equilibrium which takes the form of a threshold: citizens with low do not protest, and citizens with high protest. This is true both in the case where citizens know the value of, and when they only know its distribution. Second, we assume away the possibility of fraud and of elimination and study the dictator s decision to have elections. We show that there is a unique threshold equilibrium as well: the dictator will have elections if is below some threshold, and will not if is above it. We then add the possibility of political eliminations and study, how the possibility to decide the timing on elections impacts the decision to eliminate or repress, and how the cost of eliminations impacts the decision to have elections. Finally, we introduce the possibility of fraud and show that our results largely hold. Moreover, under some circumstances the possibility of having fraudulent elections not only leads to more frequent elections, but also makes repressionss and eliminations more likely. 3.1 Decisions to Protest Since we solve the game by backward induction, our first goal is to find the number of people who protest (and thus the probability of overthrow of the dictator). First, we assume that is common knowledge. Second, we consider the more general case where the exact value of is not known. Our first observation is that if agent protests, then agent also will, if.tosee this, notice that citizens have symmetric information, and thus the probability that the revolt succeeds is the same for both. Now, the expected payoff of protesting and staying home for citizen are thus, respectively, Π = Π ( )= +(1 ) (4) Π = Π ( )= (5) Since 1 0and 0, we see that Π ( ) Π ( ) = ((1 ) + ) is an increasing function of for any [0 1]. This means that if there are both citizens who protest and who do not, there is always a threshold, such that citizens with protest, and citizens with do not. The assumption that has full support ensures that there is 10

12 always a threshold. For a given probability of success, this threshold is given by = (1 ) +. (6) Let us first find this threshold under the assumption that is known. If all citizens with protest, and is known, then the share of protesters is 1 ( ), and thus, by assumption, the probability of success is =1 ( ). (7) If we define = ( ) to be the threshold for protests, and = ( ) to be the chance of success, then is to be determined from = and ( ) is to be determined from µ =1 ( )=1 We have the following result. (1 ) 1 ( ) +, (8) (1 ) +. (9) Proposition 1 Suppose that is known to all citizens. Then there is a (essentially) unique threshold = ( ) such that a citizen protests whenever and stays home otherwise; the probability of a successful revolt is then. The threshold is decreasing in and and increasing in and. The probability of success is increasing in and, and is decreasing in and. All proofs which are not in the text are in the Appendix. This result relies on Assumption 2 which guarantees that the density of is sufficiently low, which ensures uniqueness. Without it, there is a potential for multiple thresholds, due the following strategic complementarity: more citizens protesting makes the success of a revolt more likely, and this encourages even more people to protest. Under the assumption on, thiseffect is not sufficiently strong. In this paper, our focus is on the situations where thresholds and equilibria are unique (the qualifier essentially refers to that the citizen with = may either protest or not). We want to stress, however, that even in the case of non-uniqueness, virtually all our comparative statics results would apply to the least and the greatest of equilibria. 11

13 The comparative statics is very intuitive. As becomes higher, the probability of success increases, which lowers the threshold for protests. Remarkably, a higher givesprotestssupport from two sources: first, for a given threshold, the number of people surpassing this threshold becomes higher (due to affiliation assumption, which ensures that for a higher first order stochastically dominates for a lower ); second, the threshold itself becomes lower, so even citizens who are more tolerant to the dictator are now willing to protest. The effects of changes of parameters is straightforward as well: the threshold is lower, and thus the probability of success is higher, if protests are less costly ( is low), or if a citizen who dislikes the dictator does not get enough pleasure from seeing him go, unless he participates in the protests himself ( is low). At the same time, a low, i.e., less desire to participate in unsuccessful protests, raises the threshold and thus decreases the probability of success, leaving the dictator with a higher chance of staying in power. Suppose now that the citizens do not have complete information about, but they believe that has a distribution = (apart from knowing the prior,, they may observe some events, like canceling elections or (non-)elimination of opponents by the dictator; to save on notation, we summarize this information as ). The only thing that we require now about is that and are still affiliated (this will be true in equilibrium). Unlike the previous case, each citizen will use his signal to update on. From his perspective, the likelihood of success of protests, if the threshold is, equals =1 ( ) ( ). (10) The difference between (7) and (10) is not only that in the latter, is conditioned on. Thekey difference is that now individual will use his signal to update on : the higher is, the more likely it is that is high, and the higher are the chances that other citizens have high signals. If the threshold is sufficiently high, this effect may lower it. As we will see below, if the dictator knows that threshold citizens are overly enthusiastic about the chance of success (this happens if the threshold is sufficiently high), the dictator may benefit from credibly disclosing, and elections will be the means to achieve it. For citizens who believe that has a distribution, the threshold is given by the equation. = ³ (1 ) 1 ( = ) ( ). (11) + 12

14 From the threshold citizen s viewpoint, the probability of success =1 ( = ) ( ). (12) Notice, however, that the dictator, knowing, may have a more precise information about the probability of success: not only he knows the threshold ( ), but also the share of citizens who are above the threshold, and from his perspective, the probability of success is simply =1 ( ). (13) We have the following proposition. Proposition 2 Suppose that citizens have information that. Under the same conditions as in Proposition 1 there exists a unique threshold such that a citizen protests whenever and stays home otherwise. From the viewpoint of the threshold citizen with =, the probability of success is given by. From the viewpoint of the dictator, who knows, the probability of successisgivenby. The comparative statics are the same as in Proposition 1 (holding information fixed): higher distribution of (in the sense of stochastic dominance) and higher decrease the threshold and thus increase the likelihood of success of protests, whereas higher and higher increase the threshold and makes success less likely. It is worth noting the same condition of low density of is sufficient to guarantee uniqueness. Here, a decrease of the threshold not only makes citizens more enthusiastic about the probability of success. In addition, it has the opposite effect: it makes the threshold citizen more sceptical about the overall negative attitude towards the dictator,. This decreases the positive spillover effect described earlier, and makes uniqueness of equilibrium more likely. The intuition for the comparative statics is basically the same is for Proposition 1. Whether or not there will be more protesters if citizens know or when they do not depends on and. For any information (i.e., for any ) there will be citizens who are overly optimistic about, given their signals, and thus more willing to protest, and there are those who are overly pessimistic and thus less willing to protest. For the collective decision of citizens it is important whether the threshold citizen,, is overly optimistic or overly pessimistic. Let us fix, and thus,andletusvary. There is a threshold such that for,thethreshold citizen is overoptimistic (has,where is the probability of success if is the true 13

15 value and is the threshold protester), and for, the threshold citizen is too pessimistic ( ). Moreover, in these two cases, and, respectively. The dictator would therefore benefit fromrevealing in the former case, and would prefer to withhold in the latter case. Naturally, if =, then equalities = and = = are satisfied; in this case, the threshold citizen is exactly the citizen who is indifferent between protesting and staying home if is known. This discussion is summarized in the following proposition. Proposition 3 For any conditional distribution there is such that for, and,andfor, and. This threshold satisfies ( ) (0 1), i.e., there is a positive mass of on both sides of. Our next step is to analyze the dictator s incentive to have elections. 3.2 Elections Our first benchmark case is where there is no fraud or, equivalently, if fraud is prohibitively costly. We start with the simple analysis of individuals voting behavior. If a citizen is not infinitesimal, but controls a small, but finite share of votes, then a strategy to vote against the dictator if 0 and for the dictator if 0 is an equilibrium one. First, this vote may influence whether the dictator wins or loses the elections. Even in the case of a referendum, following this strategy is still optimal for an individual if other citizens follow it. Indeed, in this case, citizens know that results of the election is a monotonic function of dictator s support. By voting against the dictator, a citizen would increase other citizens belief about if his vote were not infinitesimal, and this is profitabletodoif 0 (even is marginally higher than 0, so that the citizen is not going to participate in protests himself). Similarly, a citizen with 0 should vote for the dictator. Consequently, the share of votes for the dictator will be = ( ) =Pr( 0 ) = (0). Since ( ) is a strictly decreasing function, by observing, the citizens will infer precisely. Given the information that citizens have, there is a threshold citizen who is going to protest, and from his viewpoint, the chance of success is. From the dictator s viewpoint, the chance of successful protest is. By having elections, and thereby revealing, the dictator will make this chance equal to. Consequently, it would be profitable to have elections if and only if two conditions hold: (a) and (b) 1 2, if elections are real and not a referendum. 14

16 Both conditions would mean that is below some threshold 0. But having elections if 0 and not having them if 0 need not be an equilibrium. Indeed, if the dictator was known to follow such pattern, the citizens would know that absence of elections means 0,and this would make them more optimistic about the success of protests. Indeed, let us denote the new information by 0 = { 0 },then 0 first order stochastically dominates,and therefore 0, in other words, more citizens will participate in protests: 0.Atthe same time, remains the same, and this compels the dictator to have elections more frequently unless the binding condition was (b), not (a). Nevertheless, there exists a threshold equilibrium, which is characterized in the next proposition. Proposition 4 Suppose fraud is impossible. Then: (a) in the case of referendum, there is a unique threshold, such that the dictator has elections if and only if. This threshold is increasing in. (b) in the case of elections, there is a unique threshold, such that the dictator has elections if and only if. This threshold is nondecreasing in. Moreover, =min( ),where solves equation (0) = 1 2.Inparticular,. (c) if is above some threshold, then =. This result says that both in the case of referendum and in the case of elections there is a threshold equilibrium. If is sufficiently low, the dictator wants to make this clear by having elections whenever he has such choice. If, however, is sufficiently high, the dictator would rather not have elections; this desire is stronger if citizens would think that the dictator could not have elections, rather than avoided out of the fear of losing. The threshold is unique both in the case of referendum and true elections. In the case of referendum, the threshold is found from the condition =, (14) where corresponds to distribution of given by,where (1 ) ( ) 1 ( ) = ( ) if ( ) ( ) 1 ( ) if. (15) In the case of elections, is the minimum of and. In particular, if is close to 1, then the dictator would almost always want to have a referendum, being afraid that if he does not, 15

17 the citizens will become (correctly) optimistic about their chances to overthrow him, which will hurt his chances even more. In this case, elections are different from referendum: the binding constraint for the dictator will be the perspective of losing elections, and in equilibrium such dictator will allow all elections that he can win. In both cases, uniqueness relies on the Assumption 2 because of the following positive spillover: if the dictator allows elections (or referenda) more often, then not doing so portrays him as even weaker and thus makes him worse off; consequently, he becomes more compelled to have elections. The assumption on density ensures that we have a unique threshold equilibrium in both cases. The comparative statics result is natural. While the chance that the dictator could have elections, but did not, does not have a direct effect on his payoff in case he wants to have elections, there is an indirect effect. Indeed, if is high, the citizens know that absense of elections is likely a signal that the dictator is unpopular. This changes information in such way that increases, decreases and, for a fixed, increases, so not having elections becomes more dangerous for the dictator. As a result, the thresholds, and,increase. The difference between these two cases is that there is a limit in the case of true elections: if the dictator is to lose elections, in the absense of fraud, then he would rather face protests, as then his chance of staying in power is non-zero. Hence, if,then =, and the dictator participates in all elections that he can win. One may wonder about the impact of the cost of protesting,, as well as of parameters and, on the choice to have elections. Here, the effect is more subtle. Indeed, a higher raises both the threshold for the case where citizens know and the threshold if citizens only know its distribution (this follows from Proposition 1 and Proposition 2, respectively). Nevertheless, when the equilibrium is unique, then the following result holds. Proposition 5 Under the assumptions of Proposition 4, a higher cost of protests makes elections more likely (it raises inthecaseofreferendumandraises in the case of true elections). Parameter, which increases the utility of staying at home for citizens who despise the dictator, has a similar effect, while parameter, which increases the utility of even unsuccessful protests, has the opposite effect. Despite its subtleness, the result follows naturally from the following intuition. Truly, a higher discourages protesting both after elections and when their were no elections. However, there is an additional effect: this less participation also makes citizens more pessimistic about 16

18 the success of an uprising, which further decreases participation. The first effect is similar in size in both cases, but the second effect is more pronounced if when citizens are better informed about. Intuitively, when citizens know, the borderline citizen, who is indifferent between protesting and not protesting, interpretes his increased scepticism (higher )asasignthat fewer people will protest, not as a sign that is actually high. In contrast, when citizens only know a distribution of, theeffect is mitigated by that this citizen also updates on : thefact that it is higher makes him more optimistic. Consequently, a higher cost of protests is more likely to deter citizens who know the true value of, and this makes the dictator choose elections for a larger set of values of. The intuitions for changes in and are very similar. Let us denote the expected payoff of the dictator, if citizens behavior follows the above pattern, by ( ), where is known to the dictator. We have (1 ) if elections are held ( ) = 1 if no elections, but elections would be true. (16) 1 if no elections, but elections would be referendum Here, by and we denoted the information about absence of elections in case of true elections and referendum, respectively. Since,wehave. In other words, in the case of true elections, not having them is less dangerous for the dictator than in the case of referendum. Intuitively, the chance of losing gives the dictator an excuse to cancel elections without signaling that he is extremely weak. We have the following result. Proposition 6 The dictator s equilibrium utility, ( ), is a strictly decreasing function of. If is high, then is decreasing in, andif is low, then is increasing in. The last comparative statics is natural. If is low, the dictator wants to have elections, and any restriction on the possibility to have them will be binding. If is high, the dictator does not want to have elections. But if is higher, then the threshold below which dictators do not have elections, (or in the case of referendum) will be higher. Hence, conditional on not having elections, the dictator would look weaker, which would increase the share of citizens participating in protest, and thereby decreasing his expected chance to stay in power. 3.3 Eliminations Suppose, as before, that fraud is not feasible. However, add that possibility that at cost, the dictator can eliminate the threat (either through repression or through elimination of opposition 17

19 leaders). Our question is when the dictator will use the possibility, and how this will affect his choice between elections and no elections (and citizens decision about protests) if he opts not to eliminate. Naturally, to make a decision about elimination, the dictator compares his expected utility ( ) in case of no elimination (this utility is known to him) with his payoff from elimination. This suggests that, unless is prohibitively high, the dictator would eliminate if is above some threshold and will not eliminate if is below some threshold. However, this threshold needs to be adjusted, as when the decision to eliminate is strategic, absence of elimination is public information which, like elections, will impact citizens beliefs about and thus the likelihood of success of protests, even though this will not change the attitude towards the dictator. 7 We formulate the following result. Proposition 7 If, there are no eliminations. Otherwise, there is a unique threshold such that for the dictator elimates the threat at cost, andbelow he does not. There are thresholds and such that such that elections are held if for true elections and for referendum. In both cases, there is a region of where elections are held and a region where there are no elections, but no elimination either. All thresholds,, and are increasing as a function of. This result suggests that as elimination becomes more affordable ( decreases), elections are held more rarely. Intuitively, no elimination implies that is not high enough to frighten the dictator. Consequently, Bayesian updating citizens must conclude that is sufficiently low, and thus if elections are not held, fewer of them will protest. This, in turn, makes having elections less necessary for the dictator, as absense of elections does not signal that is extremely high, as in that case the dictator would eliminate the threat. Hence, even though the dictator never faces a direct choice between elimination and having elections (there is always a region where neither elimination nor elections are used) the possibility of eliminations makes elections less likely. This effect is becomes stronger as decreases, while if approaches from below, eliminations become increasingly costly, tends to infinity, and thus the thresholds for elections, and 7 It is possible, of course, that absence of elimination improves citizens attitudes towards the dictator. This would only make the effect in the Proposition stronger. Alternatively, one can think that the attitude towards the dictator remains the same without elimination and gets worse with elimination. While this would be inconsequential in the current model (elimination ensures the survival of the dictator for sure), allowing for a chance that the opponent survives elimination and becomes more popular ( increases) is a direction to explore in the future. 18

20 increase and tend to their values for the case where eliminations are impossible. We can summarize this as follows. The dictator has elections to show that the opponent is not very strong (that is low). But if elimination is possible, that the mere fact that the opponent lives provides substantial evidence that the threat is low. The previous proposition described the impact of the possibility to eliminate. We may wonder how the possibility to have elections, and citizens costs of protests, impacts the dictator s decision to eliminate. This result is straightforward. Proposition 8 Eliminations are more likely (threshold is lower) if the dictator is less constrained about having elections ( is high), if protests are less costly ( is low), or if is low or is high. Intuitively, low cost of protests decreases the dictator s utility both when elections are held and not. Hence, it becomes more beneficial to eliminate; the intuition for and is similar. Higher means(seeabove)thatthedictatorismorecompelledtohaveelectionswherehewould not want this, and hence conditional on canceling elections, more people are going to protest. Since at the threshold the dictator is indifferent between elimination and simply canceling elections, we must conclude that higher implies that the dictator will use elimination more often. Notice that lowering the cost of protests may thus have an unambiguous effect on elections. Indeed, on the one hand, this makes elections less likely, due to the effect described above (imperfectly informed citizens do not react to lower cost of protests as strongly). At the same time, indirectly, this makes elimination more likely, which also decreases the need for elections. Consequently, the earlier comparative statics still holds: if is low, elections will used be less often (and elimination will be used more often). 3.4 Costly Fraud Suppose that in addition to the decisions to eliminate the threat and to have or cancel elections, the dictator may choose to introduce fraud in the elections. Recall that his utility in the case is revealed is given by = (1 ). This formula assumes that citizens with participate in protests, and their share is given by. Suppose, however, that the citizens were persuaded that the true value of is ˆ (which we 19