EXTANT WORK

The empirical puzzles described above are not limited to recent elections in Russia or even a small number of cases. Fraud is rarely pivotal in determining the winners of elections (Lehoucq Reference Lehoucq2003), and it is even more common in elections that are not close (Simpser Reference Simpser2013). While a large margin of victory reflects the potentially rampant fraud, it is still puzzling why ruling regimes commit an incremental amount of fraud to raise the total from, as in the recent Russian election, 62 to 63 percent.Footnote ⁴

Surely the fraud required to get that last percentage point is not about winning. This insight is not new; for example, a seminal article on the types of electoral manipulation in contemporary regimes notes that the greatest offenders hold elections “without running the risks of democratic uncertainty” (Schedler Reference Schedler2002). Still, with the exception of some recent and contemporaneous work (for example, Simpser Reference Simpser2013; Gehlbach and Simpser Reference Gehlbach and Simpser2013) discussed in more detail below, most of the small (but growing) game-theoretic literature on fraud assumes that it is primarily used to win elections. Tellingly, in one exception to this rule fraud is used to manipulate beliefs in order to win future elections (Simpser Reference Simpser2005). Magaloni (Reference Magaloni2009) and Fearon (Reference Fearon2011) present models in which election monitoring can help incumbents by rendering the election results credible—similar in spirit to the arguments made here—though again in the context of competitive elections.

In addition to an excessive focus on fraud as a tool to pass a victory threshold, existing work tends to ignore the question of how fraud can be effective if the defrauded are strategic actors who form beliefs about the amount of fraud committed and behave accordingly.Footnote ⁵ Existing models with a standard treatment of these beliefs tend to rely on binary fraud decisions or type spaces: in one, fraud either does not happen in equilibrium or is so rampant that elections are completely uninformative (Fearon Reference Fearon2011); the other assumes that only some types of incumbents have an incentive to commit fraud (Simpser 2005). An appealing aspect of the approach used here is that the incumbent always has an incentive to commit fraud and will always do so, though the amount chosen can be arbitrarily small.

Closer to the approach here, Simpser (Reference Simpser2013) argues that blatant manipulation of non-competitive elections is used as a costly signal of repressive capacity.Footnote ⁶ Kuhn (Reference Kuhn2012) also treats fraud as a hidden action to distort information, though using a model with costly signaling-like dynamics, in the context of a competitive election, and without modeling the choice to invite monitoring.Footnote ⁷ Another informational argument is made in Rozenas (Reference Rozenas2011) and Gehlbach and Simpser (Reference Gehlbach and Simpser2013), in which the main effect of fraud is to “jam” the electoral signal (that is, render it less informative) in a manner favorable to the incumbent. While this jamming effect can make fraud useful in some contexts (and could have different implications for inviting monitoring), most fraud has the more direct effect of increasing the votes for the incumbent, which is how I model it here.

While these arguments and mine both center around information, they differ on how fraud manipulates information. Most notably, for fraud to serve as an effective costly signal of strength, it must be observed, and jamming models can work whether fraud is directly observed or not. These approaches fruitfully contrast with theories of fraud that ignore blatant manipulation, but a large amount of fraud is purposefully clandestine.

The models in this article treat fraud as a partially hidden action. The formal structure is most similar to theories of incentives for workers (Prendergast Reference Prendergast1999) and, more specifically, “career concerns” models (Holmstrom Reference Holmstrom1999). This type of model has been applied in political science settings such as political business cycles (Lohmann Reference Lohmann1998), politician effort (Ashworth Reference Ashworth2005) and terrorist violence (Bueno De Mesquita Reference Bueno De Mesquita2010).

In a previous article I modeled fraud with career concerns dynamics in a game that focuses more on the decision to hold an election and strategic interactions among potential protesters (Little Reference Little2012).Footnote ⁸ The baseline model here generates more straightforward and clear versions of some secondary results from that article. This makes the logic of why fraud and monitoring both occur in equilibrium more transparent, and allows for tractable extensions that generate a rich set of empirical predictions and demonstrate that the logic of the model is robust to loosening some of the more problematic assumptions.

Treating fraud in this manner generates new (and sometimes surprising) results about the causes and effects of international election monitoring. By the 1990s, inviting international election monitors was the “best-established, most visible, and often best-funded type of democracy-related assistance” (Carothers Reference Carothers1997). More recently, international monitoring of elections has become nearly universal, particularly (though not exclusively) outside of consolidated democracies (Kelley Reference Kelley2008; Hyde Reference Hyde2011, Reference Hyde2012).

In addition to international monitoring, many forms of domestic monitoring are becoming prevalent. Over half of the countries in the world have meaningful independent electoral commissions (ACE Electoral Knowledge Network 2012). Further, Russia is not the only country to use webcams in polling stations: Azerbaijan did so in nearly 10 percent of polling stations for its 2008 presidential election, and Ukraine followed suit for parliamentary elections in 2012 (Herron Reference Herron2010; Sjoberg Reference Sjoberg2012). In an even more extreme form of monitoring, the ballot counting for contested seats in Singapore's Parliament is done in the presence of a representative of the opposition (Au Reference Au2011).

If these domestic and international institutions make fraud more difficult, why do incumbent regimes so commonly choose them? Perhaps more puzzling, why cheat in front of voluntarily invited monitors? These questions are not new (see the works cited above), but here I show how both fraud and monitoring can arise in a simple formal model.

Past work on election monitoring focuses on pressure from international actors, both as a benefit of inviting monitoring and as a source of punishment for regimes that are caught cheating (Carothers Reference Carothers1997; Bjornlund Reference Bjornlund2004; Kelley Reference Kelley2009; Donno Reference Donno2010; Hyde Reference Hyde2011). The question of why regimes invite monitoring and still cheat is addressed in Kelley (Reference Kelley2008) and Hyde (Reference Hyde2011, Reference Hyde2012). In general, these explanations assert that regimes gain more legitimacy by inviting monitors and cheating than by not inviting monitors at all, either because refusing monitors is a “self-declaration of cheating”Footnote ⁹ (Kelley Reference Kelley2008) or because regimes have a chance of not being “caught” by the monitors (Hyde Reference Hyde2011).

The argument here provides a domestic and purely instrumental explanation for why monitoring and cheating often go together. This contrasts with the approach of Hyde (Reference Hyde2012), who claims election monitoring is a puzzle because, absent international benefits, it “contradicts … states rational self-interest.” The central result here suggests that, particularly in the case of non-competitive elections, this is not the case.

An appealing feature of my model is that it does not require assumptions about how the international community interprets the decision to invite monitors, or why (and when) they are willing to punish regimes for fraud. Further, the explanation here is directly linked to a theory of why those who invite monitoring and cheat—which often occurs in non-competitive elections—have an incentive to cheat in the first place. The domestic-centered approach is not intended to argue that the more internationally focused explanations of fraud and monitoring are theoretically or empirically wrong. Rather, the goal is to demonstrate a new way to approach fraud and monitoring that is consistent with some key empirical facts.

THE GENERAL ARGUMENT: FRAUD AS SIGNAL DISTORTING

Before presenting the details, this section describes the general strategic setting that the model is intended to represent. I argue that the results of non-competitive elections matter because they generate public information that affects how the incumbent interacts with other elites and citizens. For a wide variety of reasons, convincing election results generate higher payoffs to the incumbent from these interactions; the desire to been seen as strong or popular is what is “at stake” in non-competitive elections. This need to appear strong gives the incumbent an incentive to manipulate the results using fraud, potentially well beyond what is necessary to win the election.

To capture this intuition in a simple fashion, the incumbent plays a game with an audience, which after the election chooses a level of support to give the incumbent. The audience is treated as a unitary actor for convenience, but can also be interpreted as a typical or representative agent from some larger group such as citizens, powerful businessmen, bureaucrats and other members of the regime, or the military. Choosing high support can mean actively supporting the regime in the literal sense (for example, attending pro-regime rallies for citizens, vocally backing the incumbent for elites, or faithfully paying taxes for citizens or elites). Giving support can also be tacit. For example, high support could mean refraining from anti-regime activity such as protesting or attempting to remove the incumbent regime from office by running against them in future elections (or using irregular means). While these notions of support are qualitatively different, what drives the logic of the model is that the incumbent wants the audience to provide high levels of support, and the audience wants to provide high levels of support when the incumbent is strong or popular.Footnote ¹⁰

The election result generates a public signal of this incumbent strength. Further, the model assumes this is the only role the election plays. This is why I call the model one of a non-competitive election: the election result in itself does not directly affect whether the incumbent remains in office, as would be true in a competitive election.

Fraud is a partially hidden distortion of this information. Technically this could represent any hidden action that inflates the election result, such as manipulation of fiscal policy or other aspects of the economy. However, for conceptual clarity and consistency with the emphasis on election monitoring, I focus on the types of manipulation that monitors intend to detect: for example, multiple voting, ballot stuffing or miscounting of votes.

This abstract setting can reflect many political interactions. For example, the audience can be a powerful elite—such as an opposition leader or a high-ranking member of the incumbent coalition—and supporting the incumbent can correspond to accepting lower rents from office or not attempting to remove the incumbent by force. In the Russian case, a natural audience to consider is the powerful businessmen collectively referred to as “oligarchs.” In 2000, Putin and the oligarchs agreed to a pact in which the oligarchs would pay taxes and refrain from supporting opposition candidates (Guriev and Rachinsky Reference Guriev and Rachinsky2005).Footnote ¹¹ Convincing the oligarchs that he has popular support is crucial for Putin to maintain a favorable bargain. More generally, the main assumption for the logic of the model to apply is that the elites are more apt to accept lower rents and not revolt when the incumbent is strong or popular. This article does not seek to identify which particular political actors and interactions are most affected by fraud, which surely varies considerably across cases, but to illustrate a logic of fraud in a transparent and general manner.

The signal-distorting approach, where fraud is a (partially) hidden action used to manipulate public information, is not the only way to model fraud with a focus on information. Notably, the baseline is not a costly signaling model (as in Simpser Reference Simpser2013) where fraud is a observed action used to affect beliefs about the incumbent's private information. I also do not consider the possibility that fraud can be used to render the election less informative (that is, to “jam” the electoral signal, as in Rozenas Reference Rozenas2011; Gehlbach and Simpser Reference Gehlbach and Simpser2013), which can also be done with observed manipulation. So, the model here is more appropriate for modeling fraudulent actions such as ballot stuffing or making up results, which do not fit well in a costly signaling model in which the “signal” generated by fraud must be observed to be effective.Footnote ¹² The signal-distorting approach is less appropriate for highly visible strategies such as denying the opposition the ability to campaign effectively, which are more effective at signaling that the incumbent is willing and able to do so.Footnote ¹³

THE BASELINE MODEL

In the baseline model, there are two actors: an incumbent (I; pronoun “she”) and an audience (A; pronoun “he”). The sequence of moves is:

The game begins with Nature selecting the incumbent popularity or strength, denoted ω. This is drawn from common knowledge prior density f(ω). The parameter is intended to capture genuine popularity among citizens as well as forms of strength that may be reflected in the election result, such as control over a repressive apparatus.

Neither actor has private information about the incumbent popularity. This greatly simplifies the baseline model, and one of the extensions demonstrates that the core results are robust to giving either the incumbent or the audience private information. The only restriction on the prior belief is that $$$ f(\omega )\, \gt \,0 $$$ for all $$$ \omega \in {\Bbb R} $$$ . So, the equilibrium analysis of the baseline model holds for generally popular or unpopular incumbents, and for when the actors have arbitrarily precise or imprecise information about the incumbent's popularity before the election.

Next, the incumbent chooses a monitoring level m, which the audience observes. Monitoring is treated as a continuous choice, where $$$ \underline{m} $$$ is the lowest feasible level of monitoring and $$$ \overline{m} $$$ is the highest possible level. High values of m correspond to inviting more or higher-quality domestic and international observers. Choosing $$$ \underline{m} $$$ could correspond to inviting no international monitors and choosing election administrators close to the regime. In the baseline model, inviting monitoring imposes no direct costs on the incumbent. This applies more plausibly to international monitors who pose little or no financial cost to the regime, and less to expensive types of monitoring such as installing webcams in polling stations, a point addressed in one of the extensions.

The incumbent also selects an amount of fraud to commit x ≥ 0, which is not directly observed by the audience. Since the true level of pro-regime fraud in an election is a function of the actions of many individuals, this is best interpreted as the level of fraud chosen by the top national leadership, holding all other types of fraud constant.Footnote ¹⁴

Following the incumbent decisions, the audience observes an election result e that is a function of both the true incumbent popularity and the amount of fraud committed: $$$ e\, = \,\omega \, + \,x $$$ . That is, the election result will be high when the incumbent is genuinely popular (high ω) or when she commits a high level of fraud (high x). Since $$$ f(\omega )\, \gt \,0 $$$ for all $$$ \omega \in {\Bbb R} $$$ , the election result can be any real number as well. This proves convenient, as all election results are on the equilibrium path regardless of the incumbent's strategy.

The election result need not correspond to a vote share, but can represent a combination of many observable outcomes from the election: turnout, the number of spoiled ballots or the vote share in particularly important geographic units such as cities with nascent protest movements.Footnote ¹⁵

This is admittedly a very reduced-form way to model an election. Typical concerns—such as setting platforms and voters’ decision to turn out and who to vote for—are purposefully omitted. All that matters is that the election generates a signal of the incumbent's popularity, and that this signal can be distorted by fraud.

The audience also observers a monitoring report r = γx, where γ = 1 with probability $$$ q(x,m):{{{\Bbb R}}_ + }\times \,[\underline{m}, \overline{m} ]\, \rightarrow \,(0,1) $$$ , and γ = 0 otherwise. The q function represents the probability that the monitoring report detects the true level of fraud. This is because if γ = 1 and the incumbent commits fraud, the audience observes a monitoring report greater than zero and directly infers that exactly x = r fraud has been committed. If γ = 0, the audience will observe r=0 regardless of how much fraud is committed. I often call this a “null” monitoring report. Loosely speaking, this corresponds to a case in which election monitors and other sources do not report any notable malfeasance.

Let q be continuous and differentiable in both arguments, and strictly increasing in level of monitoring $$$ \left( {\frac{{\partial q}}{{\partial m}}\, \gt \,0} \right) $$$ . This is why m is referred to as the monitoring level: a higher m means there is a higher probability that the true amount of fraud is directly revealed. The probability of detection is either constant or increasing in the amount of fraud $$$ \left( {\frac{{\partial q}}{{\partial x}}\,\geq \,0} \right) $$$ .

As is inevitable in models, numerous aspects of how monitoring and the detection of fraud are formalized are unrealistic or could be done in other defensible ways. To highlight a few issues, most contemporary elections are monitored by multiple observation missions—which could be modeled as strategic actors with influence over how stringent the monitoring is—that release detailed and nuanced reports about various aspects of the electoral process. I reduce this process to a unidimensional “report” that either reveals the exact level of fraud or reports that there is no fraud to generate simple and transparent results. As will become clearer when analyzing the model, what matters in the end is that the benefit of committing more fraud than expected decreases in the monitoring level. While there are many potential information structures with which to model election fraud and monitoring that may have different implications, this property could emerge from a wide range of more realistic (but more cumbersome) formulations, some of which are explored in the extensions.

Finally, the audience chooses a support level $$$ s \in {\Bbb R} $$$ . As elaborated below, when making this choice, he takes into account what he observes up to this point—the monitoring level, election result and monitoring report—as well as a conjecture about how much fraud was committed. Crucially, this conjecture will have to be correct in equilibrium.

PAYOFFS

Fraud is costly, and the incumbent wants the audience to provide a high level of support. To formalize this, let the incumbent utility be $$$ {{u}_I}(x;s)\, = \,b(s)\,{\rm{ - }}\,c(x) $$$ , where b and c are increasing, continuous and twice-differentiable.Footnote ¹⁶ Further, assume that the benefit function b is strictly increasing and concave (b′ > 0 and b′′<0), and that the cost function c is increasing and convex (c′ ≥ 0 and c′′ > 0) with c′(0) = 0 and $$$ {\lim }_{x \rightarrow \infty } c&#x0027;(x)\, = \,\infty $$$ . Loosely speaking, the assumptions about the cost function imply that the cost of falsifying the first ballot is free, but falsifying an additional ballot eventually becomes prohibitively costly.Footnote ¹⁷

To capture the intuition that the audience wants to choose high support levels when the incumbent is popular, let his utility function be a quadratic loss function centered around $$$ \omega :{{u}_A}\, = \,{\rm{ - }}{{(s\,{\rm{ - }}\,\omega )}^2} $$$ .Footnote ¹⁸ A convenient implication of this utility function is that the audience's best response is to provide the level of support equal to his average belief about the incumbent strength $$$ {\Bbb E}[\omega &#x007C; \cdot ] $$$ . This belief may be conditioned on the election result, monitoring report and the proposed incumbent strategy.

EQUILIBRIUM

I solve for Perfect Bayesian Equilibria with pure strategies (hereafter, equilibria).Footnote ¹⁹ Given the sequence of moves, write the strategy of the incumbent as the level of monitoring m and the amount of fraud she would commit for each potential monitoring level x(m). A strategy for the audience is a function s(m,e,r) mapping the monitoring level, election result and monitoring report to his level of support.

The analysis below first finds the equilibrium level of fraud and support—call these x*(m) and s*(m,e,r)—for a fixed monitoring level m, and then determines the optimal monitoring level (m*) given how the game plays out following this decision.Footnote ²⁰

When r > 0, the audience decision is easy. Since r can only be strictly positive when the report detects the exact amount of fraud (that is, γ = 1), the audience is at a singleton information set and can directly infer the true incumbent popularity by subtracting the monitoring report from the election result: $$$ \omega \, = \,e\,{\rm{ - }}\,r $$$ . So, the audience best response whenever r > 0 is to give a support level of e – r regardless of the monitoring level and his conjecture about the level of fraud.

If r = 0, the audience does not directly observe the level of fraud, and cannot directly infer the incumbent's popularity. In particular, the audience is in the same information set for any r = 0 and ω ₁,ω ₂ and x ₁,x ₂ such that $$$ {{\omega }_1}\, + \,{{x}_1}\, = \,{{\omega }_2}\, + \,{{x}_2} $$$ . So the audience best response depends on his conjecture about the level of fraud committed; call this $$$ \hat{x}(m) $$$ . In words, the audience best response when r = 0 is to subtract the conjectured amount of fraud—which will eventually be pinned down in equilibrium—from the election result. We can write the audience's best response function as:

$$ \hat{s}(m,e,r;\hat{x}(m))\, = \,\left\{ \matrix{ {e\,{\rm{ - }}\,\hat{x}(m)} &amp;#x0026; {r\, = \,0} \cr {e\,{\rm{ - }}\,r} &amp;#x0026; {r\, \gt \,0}. \end{}} \right $$

Introducing notation for the audience's expectation of how much fraud will be committed is mostly to clarify the equilibrium derivation, and loosely corresponds to what we would refer to in plain English as expectations of how much fraud will be committed leading up to an election. Still, this mapping is not perfect: in equilibrium, the audience's expectations will be derived purely by strategic reasoning about the incumbent's incentives, and not by factors such as how much fraud the incumbent has committed in past elections.

Now consider the incumbent payoff for choosing an amount of fraud x given this audience best response function. With probability q(x,m) the true amount of fraud is revealed by the monitoring report, and with probability 1 – q(x,m) the monitoring report will be null. If the true level of fraud is revealed, the audience directly learns the incumbent popularity and hence the equilibrium level of support is always $$$ e\,{\rm{ - }}\,r\, = \,\omega \, + \,x\,{\rm{ - }}\,x\, = \,\omega $$$ . When the monitoring report does not reveal the amount of fraud, the level of support as a function of the true popularity, conjectured equilibrium level of fraud and actual level of fraud is $$$ e\,{\rm{ - }}\,\hat{x}(m)\, = \,\omega \, + \,x\,{\rm{ - }}\,\hat{x}(m) $$$ .

Crucially, when the monitoring report is null, the incumbent can get a higher level of support than she would if the audience knew her true popularity by committing more fraud than expected ( $$$ x\, \gt \,\hat{x}(m) $$$ ). Conversely, the incumbent will appear weaker than she is and garner a lower level of support when committing less fraud than expected ( $$$ x\, \lt \,\hat{x}(m) $$$ ). That is, for a fixed audience strategy, he could be fooled by fraud by an unexpected (that is, off the equilibrium path) level of fraud. However, the standard equilibrium condition that the incumbent and audience play mutual best responses will imply that the audience forms a correct conjecture about the level of fraud.

Since the incumbent is uncertain about her popularity when making the fraud decision, the benefit portion of her expected utility is obtained by integrating over the payoffs derived above with respect to ω. When the monitoring report is correct and the audience always chooses support level ω, the relevant benefit is $$$ {\Bbb E}[b(\omega )]\, = \int \!b(\omega )f(\omega )d\omega $$$ .Footnote ²¹ When the monitoring report is null, this term becomes $$$ {\Bbb E}[b(\omega \, + \,x\,{\rm{ - }}\,\hat{x}(m))] $$$ , or the expected benefit of committing amount of fraud x when the audience expects $$$ \hat{x}(m) $$$ .

So, the incumbent payoff for choosing fraud level x when the audience expects $$$ \hat{x}(m) $$$ can be written as:

$${{u}_I}(x,m;\hat{x}(m))\, = \,q(x,m){\Bbb E}[b(\omega )]\, + \,(1\,{\rm{ - }}\,q(x,m)){\Bbb E}[b(\omega \, + \,x\,{\rm{ - }}\,\hat{x}(m))]\,{\rm{ - }}\,c(x)$$

The key trade-off facing the incumbent is that by increasing the amount of fraud, she appears more popular when the fraud is not directly revealed (the second term), but pays more through the cost function c (the third term).Footnote ²²

As with any standard equilibrium concept, it must be the case that the incumbent fraud strategy and the audience support level are mutual best responses to each other. In this model, this requires that an equilibrium level of fraud for monitoring level m—again, denote this x*(m)—satisfies two conditions. First, the audience conjecture about the level of fraud must be correct: that is, $$$ \hat{x}(m)\, = \,{{x}^\ast} (m) $$$ . Second, given that the audience conjecture is that the incumbent will choose fraud level x*(m), it is optimal for the incumbent to choose this fraud level. Combining these conditions with the continuity of the primitive functions, for x*(m) to be an interior equilibrium it must solve:

$${ 0\, &amp;#x0026; =\,\frac{\partial }{{\partial x}}{{[q(x,m){\Bbb E}[b(\omega )]\, + \,(1\,{\rm{ - }}\,q(x,m)){\Bbb E}[b(x\, + \,\omega \,{\rm{ - }}\,\hat{x}(m))]\,{\rm{ - }}\,c(x)]}_{x\, = \,x{^\ast}(m),\hat{x}(m) = x{^\ast}(m)}} \, \cr &amp;#x0026;= \,(1\,{\rm{ - }}\,q(x{^\ast}(m),m)){\Bbb E}[{{b}&#x0027;} (\omega )]\,{\rm{ - }}\,{{c}&#x0027;} (x{^\ast}(m)) \cr},$$

where $$$ {\Bbb E}[{{b}&#x0027;} (\omega )]\, = \,\int \!{{b}&#x0027;} (\omega )f(\omega )d\omega $$$ is the expected benefit of committing marginally more fraud than expected when the monitoring report does not catch the unexpected fraud. Rearranging gives a more easily interpretable form of the equilibrium condition:

$$\mathop{\underbrace{{c^{\prime}({{x}^\ast} (m))}}}\limits_{{\rm{Marginal}}\,{\rm{Cost}}}\, = \,\mathop{\overbrace{{(1\,{\rm{ - }}\,q({{x}^\ast} (m),m))}}}^{{\rm{Pr(deviation}}\,{\rm{undetected)}}}\,\times\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\mathop{\underbrace{{{\Bbb E}[b^{\prime}(\omega )]}}}\limits_{{\rm{Marginal}}\,{\rm{Benefit}}\,{\rm{if}}\,{\rm{undetected}}}$$

Equation 2 states that the marginal benefit of committing more fraud than expected (the right-hand side) equals the marginal cost of committing more fraud (the left-hand side). The marginal benefit is strictly positive and non-increasing in x*(m) because the higher levels of fraud are more likely to be revealed, hence there is a lower chance of the unexpected fraud going undetected. Given the assumptions made about c, the marginal cost is increasing in x*(m). These two observations (and the assumption about the range of c) ensure that for each monitoring level there is a unique level of fraud x*(m) such that Equation 2 is met. Given the functional form assumptions for b and c, this solution will be a global maximizer, so:

Proof: The existence of an equilibrium x*(m) for each m is demonstrated above. (See the supplementary information for a proof of uniqueness). The second part follows from implicitly differentiating Equation 2. □

A key characteristic of this part of the equilibrium (that is, all but the monitoring choice) is that the incumbent's fraud does not actually fool the audience. This notion is well described in an open letter from Russian human rights activist Sergei Kovalev to Vladimir Putin in 2008: “You lie, your listeners know this and you know that they don't believe you … Everybody knows everything. The very lie no longer aspires to deceive anyone, from being a means of fooling people it has for some reason turned into an everyday way of life, a customary and obligatory rule for living” (Myagkov, Ordeshook and Shakin Reference Myagkov, Ordeshook and Shakin2009, 9).

However, the audience could be fooled by an off-the-path deviation—that is, if the incumbent were to choose x > x*(m) and the monitoring report is uninformative, the audience will give a support level higher than the incumbent strength. This may seem like a technical observation, but it drives both of the central results of the article. An incumbent committing less fraud than expected would appear to be less popular and garner less support from the audience. As illustrated by Figure 1, the incumbent would prefer an equilibrium with no fraud to avoid paying the cost, but this is unattainable; if the audience expects no fraud, the incumbent's optimal response is to commit a strictly positive amount of fraud, as this deviation may not be detected. In other words, the incumbent would prefer to be able to commit to not perpetrating fraud, but absent an ability to make such a commitment, it is always optimal to take fraudulent actions. This is the first main insight from the baseline model.

Fig. 1

Incumbent utility as afunction of the amount of fraud for various expected levels of fraud Note: when no fraud is expected (left panel), the incumbent utility is maximized at a higher level, and hence the incumbent would deviate to this level. When proposing an equilibrium with a higher level of fraud (dark curve in middle panel), the incumbent would deviate to a lower amount. When proposing the amount x* derived from Equation 2, the optimal level of fraud is exactly x* (right panel).

Inviting high levels of monitoring provides such a commitment device. Since more monitoring makes unexpected fraud more likely to be caught (and hence less effective), it leads to a lower equilibrium level of fraud and hence cost paid. Further, because the monitoring is observed and there is a unique fraud level for each m, the equilibrium level of support is unaffected by the monitoring level. Thus the second main insight from the baseline model is that the incumbent always invites the highest level of monitoring:

Proof: The equilibrium payoff associated with monitoring level m is $$$ {{u}_I}({{x}^\ast} (m);m)\, = \,{\Bbb E}[b(\omega )]\,{\rm{ - }}\,c({{x}^\ast} (m)) $$$ . The change in the incumbent equilibrium utility with respect to m is $$$ \frac{{\partial {{u}_I}}}{{\partial m}}\, = \,{\rm{ - }}\,{{c}&#x0027;} ({{x}^\ast} (m))\frac{{\partial {{x}^\ast} }}{{\partial m}} $$$ . Since c′ is positive and $$$ \frac{{\partial {{x}^\ast} }}{{\partial m}}\, \lt \,0 $$$ from implicitly differentiating Equation 2, $$$\frac{{\partial {{u}_I}}}{{\partial m}}\, \gt \,0$$$ and hence the incumbent chooses $$$ {{m}^\ast} \, = \,\overline{m} $$$ . The remainder of the equilibrium follows from Proposition 1. □

These results present a simple and stark explanation of why incumbent regimes invite domestic and international scrutiny that makes fraud more difficult: under broad assumptions, doing so always raises their equilibrium payoff. Despite the inherent international dimension of external monitors, the incumbent decisions are entirely driven by domestic politics, not international pressure or the desire to appear democratic. As long as the monitoring is not perfect, there is still fraud in equilibrium despite this invited scrutiny, which is consistent with the empirical fact that cheating occurs even when monitors are invited. However, if monitoring is extremely strong, as with the ballot counting in Singapore, the amount of fraud will become arbitrarily small.Footnote ²³

An alternative way to interpret this result is that monitoring is valuable because it lowers the expectation of how much fraud is committed. While Vladamir Churov's boast in the second epigraph about the transparency of Russian elections merits substantial skepticism, it may contain a grain of truth: increasing the transparency of elections can benefit autocrats. The robustness checks will explore some potential reasons why the desire for maximal monitoring is not universal.

One implication of this result is that when monitors are present in an election and detect cheating—even blatant amounts—this does not constitute a failure of the monitors to reduce fraud. Without knowing the counterfactual level of fraud, it is impossible to say whether there would have been more or less without the monitors. While this is ultimately an empirical question,Footnote ²⁴ my model presents a theoretical basis for why cheating in monitored elections should not surprise us and predicts that fraud would be even more rampant in the absence of monitors.

At first glance, the fact that the availability of monitoring is helpful to leaders holding non-competitive elections (generally autocrats) may seem problematic. Still, the fact that monitoring helps autocrats does not mean it is bad for the audience or for advocates of democratic reform. With the utility function here, the audience is equally well off with low or high monitoring. However, if fraud creates negative externalities that harm the audience—which is certainly true if the technologies of fraud used include violence or intimidation—then the audience is better off with a higher level of monitoring. I revisit this point in the discussion of strategic monitors below.

COMPARATIVE STATICS

While the incumbent always chooses the maximal level of monitoring, the model does generate comparative statics on the level of fraud.

1. (1) decreasing in the maximal level of monitoring

2. (2) decreasing in the popularity of the incumbent

3. (3) provided b′′′ > 0, increasing in the uncertainty about the incumbent's popularity.

Proof: Part 1 immediately follows from the first order condition evaluated at $$$ m\, = \,\overline{m} $$$ . For Part 2, consider two distributions of popularity such that F ₁ first-order stochastic dominates F ₂. Then b′′ < 0 implies –b′ is increasing, so $$$ {{{\Bbb E}}_1}[{\rm{ - }}b^{\prime}(\omega )] \gt {{{\Bbb E}}_2}[{\rm{ - }}b^{\prime}(\omega )] $$$ and hence $$$ {{{\Bbb E}}_1}[b^{\prime}(\omega )]\, \lt \,{{{\Bbb E}}_2}[b^{\prime}(\omega )] $$$ , where $$$ {{{\Bbb E}}_j} $$$ is the expectation operator with respect to distribution F_j. This implies that the equilibrium level of fraud with distribution F ₁ is lower than the equilibrium level of fraud with distribution F ₂.

For Part 3, consider two distributions of popularity such that the expectations are equal, but F ₁ second-order stochastic dominates F ₂ (that is, there is more uncertainty in F ₂). Since b′′ < 0 and b′′′ > 0, –b′ is increasing and concave, so $$$ {{{\Bbb E}}_1}[{\rm{ - }}{{b}&#x0027;} (\omega )]\, \gt \,{{{\Bbb E}}_2}[{\rm{ - }}{{b}&#x0027;} (\omega )] $$$ , which implies $$$ {{{\Bbb E}}_1}[{{b}&#x0027;} (\omega )]\, \lt \,{{{\Bbb E}}_2}[{{b}&#x0027;} (\omega )] $$$ . Hence the incumbent commits more fraud under F ₂ □

The intuition behind Parts 2 and 3 is as follows. More popular incumbents care less about marginally increasing the level of support, and hence commit less fraud. Being more uncertain about the incumbent's popularity means that she is more likely to be far less popular than average (giving a higher incentive for fraud) or far more popular than average (giving a lower incentive for fraud). If b′ is convex—that is, b′′′ > 0—the former effect will be bigger, leading to more fraud on average.

This third derivative is admittedly difficult to interpret—one intuition is that it means the degree to which the marginal returns of more support are diminishing is also decreasing in the level of support. More concretely, this third derivative condition holds for standard increasing and concave functions.Footnote ²⁵ Further, it cannot be the case that b′′′ < 0 for all s, so the result will hold if the incumbent strength generally lies on the part of b where b′′′ > 0.Footnote ²⁶

EXTENSIONS AND EMPIRICAL PREDICTIONS

In this section I describe various modifications and extensions to the baseline model. These serve two purposes. First, they demonstrate that the results are not sensitive to some of the more objectionable simplifying assumptions. Second, adding more parameters and complexity creates new comparative static results, which could be used to test the value of this modeling approach in future work. Formal statements and proofs are available in the supplemental information.