Literature

Our work is related to principal agent models starting from Spence [10]. More specifically our paper has modeling similarities with the so called incumbent-challenger models which are essentially agency models of political competition. There are a wide variety of incumbent challenger models in the literature (see Besley [11] for a good discussion of the literature), with the simplest involving pure selection strategies to weed out bad politicians. There are several well known models with electoral accountability when politicians make unobservable choices [12–16]. Rogoff and Sibert [14] and Rogoff [15] use this framework to study political budget cycles, while the other papers look at pure moral hazard problems. There are models with elements of both moral hazard and adverse selection, in which politicians differ in both ability (leading to adverse selection) as well as some kind of unobservability of action (leading to moral hazard) [17]. Coate and Morris [18] consider the issue of the form of transfers to special interest groups in an incumbent challenger framework. They address a pure efficiency question: namely, given that politicians may owe allegiance to special interest groups what is the most efficient way to make transfers to such groups and is this efficient form of transfer employed? In their framework, politicians do not essentially differ in ability but in their preference over the transfers they would like to make to special interest groups, in principle both politicians could have chosen the best outcome. Such models of electoral accountability have a fair amount of empirical support as well [19]. In the context of conflict, Carter [20] finds that electoral incentives can lead to conflict, in particular they find term limited dovish leaders are less likely to initiate conflicts, on average, compared to those who are electorally accountable while there is no such relationship for hawkish leaders, consistent with our model.

Several papers have used the political agency model to shed light on different forms of political failures arising from electoral concerns and asymmetric information. Majumdar and Mukand [21] consider a model of political agency where leaders ability is modeled as his ability to pick a socially desirable policy reform. The leader gets an interim signal as to whether or not his reform is likely to succeed. While it is socially desirable that a failing reform be scrapped, such an action will lead the voters to realize that the politician took a wrong decision and therefore to lower their estimate of his ability. Under certain conditions, this leads to the politician resorting to a gamble by sticking to a failing policy. Aidt and Dutta [22] examine political failure arising out of the interaction between observation lags, economic growth and a binding revenue constraint. The political failure in their paper does not arise from asymmetric information about politician ability (their politicians are homogenous) and their aim is to look at the mix of short term vs. long term public good that is provided because of these interactions. Unlike in our model, their policy myopia is constrained optimum. In our analysis of second best we find a result similar to that of Haan and Onderstal [23] that randomization over which politician to re-elect gives higher voter welfare than trying to separate types (and randomization always dominates welfare under a pooling equilibrium).

Our work is also related to rational choice explanations of terrorism and the high cycle of violence which is based on terrorism as a strategic choice [24, 25]. Leadership in conflict is analyzed in a complete information framework by Hess and Orphanides [26] (see the Discussion section for a discussion of their paper) and is related to the literature that looks at whether multilateralism can provide an efficient level of security and the structure it takes [27–29]. Schultz [30] analyses the behavior of hawks and doves over the period that the US-USSR conflict continued using a different definition of hawks and doves-he assumes that doves are people who inherently have optimistic priors over the opponents motives and the opposite for hawks. Some of the empirical evidence on the policy positions of hawks and doves in that period is interesting and worth analyzing to see how well it fits the predictions of our model. Broadly, from our model, we expect to see hawks continue to support hawkish positions while doves will fluctuate depending on their ability. This seems consistent with the data presented in Schultz. None of these papers are however concerned with the political failure arising out of asymmetric information.

There is a well established literature on conflict and the distribution of resources across groups [9, 31–34]. We contribute to the literature by analyzing what kind of outcomes arise when conflict resolution occurs via the political process.

The rest of the paper proceeds as follows. In the Materials and Methods section we set up the model, and characterize the first best, the second best and the Perfect Bayesian equilibrium (PBE) outcomes. The Results section compares the second best and the PBE with each other and with the first best. This section provides our main insights about how the the political process leads to a hawkish drift. The Discussion section considers some extensions and concludes.

The model

We develop a simple two period model that formalizes the basic insight discussed above. The framework used here was developed by Grossman [9] and the specifics of the model are based on Bandyopadhyay and Oak [35]. Let us denote by the total amount of land, which is the dimension of conflict between two groups: citizens denoted by C, and an insurgent group (or protesters) denoted by I. While we use the nomenclature of an intra-country conflict for convenience, the model can capture any dispute over a fixed resource, including border disputes between two countries. The division of land is determined by an incumbent politician, specifically, the incumbent chooses a division (y, Y − y) on behalf of group C where y is the amount of land retained by the group C, and consequently, (Y − y) is the land conceded to I. Hereafter, we will refer to the representative member of C as the voter, and the politician in office who decides the land division as the incumbent. We can think of the representative member of C as the median voter, an interpretation that holds under single peaked preferences.

The voters preferences over land division are represented by a utility function The incumbents preferences over land division may differ from those of the voter. We denote the incumbents preferences by α ⋅ u(y) where α ∈ (0, ∞) is a parameter that captures politicians ideology—a value of α < (>)1 means the incumbent is dovish (hawkish) relative to the voter. After observing the choice of y made by the incumbent, the voter decides whether or not to re-elect him.

Following the choice of y, some members of group I may undertake terrorist activities or violent insurgency. The cost imposed by this insurgency upon the voter is realized in the next period and it is increasing in y. The politician in office in the next period manages the cost of this conflict, which (given y) depends on his ability θ. Let c(y, θ) denote the expected cost of terrorism to the voter when the settlement is y and the ability of the next periods politician is θ. We assume that c₁, c₁₁ > 0 and c₂ < 0. In Appendix I.A in S1 File we present a simple model that provides a micro foundation for the cost of insurgency.

Benchmark (α, θ)-contingent contract

Suppose that the incumbent politician’s ideology as well as ability is known to the voter; we will denote an incumbents type as(α, θ). The first best outcome (FB for short) sets an ideal benchmark for the highest utility attained by the voter if he could offer a type-contingent contract, subject to the incumbent’s and voter’s participation constraints. In order to define and analyze the first best, it is useful to define a few terms. If an incumbent knew/anticipated that he is not going to be elected, his optimal strategy would be to choose y to maximize his expected utility given by where the expectation is taken over the replacement’s ability θ′, which yields y that depends on α only, and which we denote by Let the expected utility from replacing an incumbent (and therefore him choosing policy y₀(α)) be denoted by v₀(α) for the incumbent, and by V₀(α) for the voter. It can be verified that, The first best, can be formally defined as follows:

Definition 1 The first best contract for a type (α, θ) is a pair (d*, y*) whereby the agent implements policy y* ∈ Y and the voters re-election decision is d* ∈ {re-elect, replace} such that

• d* = re-elect, and (3) if
  1. a solution to the above problem exists, and
  2. u(y*) − c(y*, θ) ≥ V₀(α);
• otherwise, d* = replace, and y* = y₀(α).

When describing the first best for each possible type (α, θ), we will use the notation d*(α, θ) and y*(α, θ).

A complete characterization of the first-best is tedious as it depends on the different configuration of parameters α, θ and r. We will characterize the first best in specific cases of interest in the later sections. However, some cases are worth mentioning here.

If Problem (3) has an interior solution, then it is y(α, θ) = 1 + θ, yielding the voter indirect utility . The voter will re-elect (replace) the incumbent if , i.e. Thus, we have the following lemma.

Lemma 1 If α, θ and r are such that Problem (3) has an interior solution, then the first best policy is given by, (4) (5) Problem (3) is more likely to have an interior solution if i) r and θ are large and ii) if α is not too large or small relative to 1.

In the following sub-sections we analyze a more realistic setting where the voter cannot observe the incumbents ability. In such a setting, the voters re-election decision can be contingent only on the observed policy choice. The second best refers to the case where the voter can credibly commit to a re-election standard. The Perfect Bayesian Equilibrium (PBE) refers to the case where no such commitment is possible.

The second best, or equilibrium under commitment

Now suppose that the voters cannot observe the incumbents type but can commit to a re-election strategy based on his choice of y. In this section we will assume that the politicians ideology (α) is known to the voter. We will discuss the implications of relaxing this assumption in the next section. We will assume that voters use a cut-off strategy: one where they re-elect the incumbent if and only if y ≥ z. We restrict attention to cut-off strategies to aid comparison with the PBE in monotone beliefs which involves cut-off strategies. This restriction, which is standard in the literature [18], is the equivalent of having monotone beliefs and rules out PBE supported by unappealing off the path equilibrium beliefs. Throughout when we refer to second best and PBE, we restrict attention to cutoff strategies.

We now look at the incumbent’s strategy in response to a re-election standard z set by the voter. The incumbent will choose to fulfill the standard z and get re-elected, if there exists a y ≥ z, such that (6) Holding ideology fixed, the behavior of politicians of different ability levels can be described as follows:

• Incumbents with “low ability” will prefer to drop out of the race than meet the re-election standard, i.e. ∀θ ≤ θ₁
• Incumbents with “intermediate ability” will just meet the re-election standard, i.e., ∀θ ∈ (θ₁, θ₂] we have and z ≥ α(1 + θ)—the optimal policy of the incumbent of type (α, θ) if he is guaranteed re-election;
• Incumbents with “high ability” θ > θ₂ implement their optimal policy subject to guaranteed re-election, ie, they choose α(1 + θ).

We first compute θ₁. This is the lower limit of the ability of the politician who meets the standard. Evidently, at this limit, the politician is indifferent to re-election and being replaced, hence (7)

We now compute θ₂ which is the upper limit of the re-election standard. θ₂ is the value of θ at which the politicians ideal policy coincides with the standard z: (8)

Given the expressions for θ₁(z) and θ₂(z), the expected utility of the voter can be written as (9)

The above expression has three components which correspond to the three possible types of choices made by the politicians, depending on their abilities, given the re-election standard. Note that the cut-off strategy of the voter include, as special cases, setting z equal to 0 (always re-elect) or infinity (always replace). The second best re-election standard is .

If the voter chooses to always replace the incumbent, then the expected utility of the voter is given by If the voter were to always re-elect the incumbent, the expressions differ depending on whether the rents from office r are high enough for voluntary dropout never to occur. As our purpose is to look at a world where the rents from office cause a divergence between the voter and the politicians behavior, one particular case of interest is when the rents from office are high enough such that no one voluntarily drops out. In that case, the utility is given by the expected utility of voter In this formulation, the utility from re-electing everyone is again bigger than replacing everyone as V₀ < V_E.

Perfect bayesian equilibrium or equilibrium standard without commitment

The second best formulation above assumes that there is no additional constraint in terms of incentive compatibility of the voting standard. That is, the voters cannot renege from the re-election strategy after they observe the politicians choice of y. However, for the re-election standard to be incentive compatible, given the beliefs of the voter about the expected ability of the incumbent, his voting decision must be optimal. We will use the Perfect Bayesian Equilibrium (PBE) as the solution concept to analyze the outcome of a game in which the voter is unable to commit to a re-election standard. The PBE is formally defined as follows:

Definition 2 A PBE of the game is (1) a re-election standard set by the voters ŷ; (2) a choice of y(θ, ŷ), by the incumbent politician, given the re-election standard ŷ; (3) a set of beliefs b: [0, 1] → B(θ) i.e. a mapping from the y chosen into a probability distribution over types denoted by B(θ) and (4) a re-election decision upon observing the policy choice y, such that

1) the politician of type θ chooses y to maximize his expected payoff, which is if y < ŷ, and αu(y) − c(y, θ) + r if y ≥ ŷ;

2) the voters choose ŷ to maximize their expected utility given the politicians best response y(θ, ŷ);

3) voters beliefs about the incumbents type are formed using the Bayes Rule (whenever possible);

4) Voters re-elect a politician only if given their beliefs (as in 2) their expected utility from re-electing is greater than from replacement; and

5) Voters re-election strategy (as in 3) is consistent with the re-election standard (as in 1).

Additionally, we restrict attention to PBE in monotone beliefs, i.e., the use of cutoff strategies. In particular, the voters expected utility from retaining those politicians who just meet the standard must be bigger than the (constant) expected utility from replacement, i.e., V₀. This gives us the following incentive compatibility constraint i.e. (10) Thus, the equilibrium standard without commitment, ŷ, maximizes the expression for the expected utility function (as in the previous subsection): (11) but subject to the incentive compatibility constraint in Eq (10) as given above. This constraint requires that the standard must be sufficiently high such that some ability types find it costly to mimic it in order to seek re-election. The chosen re-election standard under PBE is given by ŷ.

Note that we cannot find closed form solutions for the above equations in the general range of parameters. We solve the maximization problem using Mathematica as well as R to see how y varies across the relevant range of α and r.

It is worth noting that the PBE may involve replacing everyone as it satisfies the incentive compatibility constraint, however it should be clear that re-electing everyone does not satisfy the additional constraint. This is because, if incumbents chose their optimal strategy when guaranteed re-election (i.e. y = α(1 + θ)), it perfectly reveals their type and for incumbent with the voters would be better off, ex-post, by reneging on their promise to re-elect the incumbent. Thus, in general, the second best and the equilibrium standard without commitment will not coincide. We illustrate this in more detail in the next section.

Homogeneous case

To fix ideas, lets first focus on the case where the ideology of the incumbent is same as that of the voter, i.e., α = 1. Plugging α = 1 in Eqs 7 and 8 we get and Substituting these in Eq 9, we get the expected utility of the voter as

Voters will choose optimal re-election standard to maximize the above function. Denote by the second-best re-election standard, i.e., the standard chosen by the voter if he can commit re-electing an incumbent who meets, or exceeds, the standard. It is not necessary for the second best standard to be a strictly positive finite number. It may well be the case that either of two polar strategies viz. always re-elect () or always replace () is the optimal choice. Under the always replace standard, the expected utility of the voter is given by , while under always re-elect, the expected utility of the voter is given by . In this formulation, the utility from re-electing everyone is bigger than replacing everyone as This gives rise to the following remark:

Remark 1 The second best policy is either to always re-elect the incumbent, or to use a cut-off strategy . The latter is the optimal choice only if .

It follows that the Welfare of the voter under second best is bounded below by 0.75 since the strategy of always re-elect is a feasible strategy for the voters, and it yields payoff 0.75.

As discussed in the previous section, the PBE, i.e. the equilibrium without commitment puts an additional constraint on the re-election standard in terms of the incentive compatibility constraint

i.e. when r is high enough, this holds with equality and everyone gets replaced yielding a welfare of As noted, always re-elect is not incentive compatible, and hence cannot be part of a PBE.

We now provide a numerical example of the first best, second best and the PBE for specific numerical values. In Appendix II in S1 File we provide a more detailed set of calculations for a more general set of parameters.

Example 1 Consider the case α = 1, r = 0.2. Under the second best re-election standard is , which yields θ₁ = 0.222 and θ₂ = 0.691. That is, incumbents with ability below 0.222 choose and therefore do not get re-elected, those with ability in the range [0.222, 0.691] choose to just meet the re-election standard , and those with ability θ > 0.691 choose y = 1 + θ. This outcome exhibits hawkish drift since the incumbents in the range [0.222, 0.691) implement policy greater than their choice under the first best.

Also note that the selection under the second best is significantly worse relative to the first best since, under the second best, those with ability greater than 0.222 get re-elected, whereas under re-election threshold under the first best is 0.443. It can also be verified that satisfies the incentive compatibility constraint given by Eq 10 and hence the second best outcome is also the PBE.

However, the second best outcome need not always be attained under the equilibrium standard (i.e. the PBE), as seen in the following examples.

Example 2 Consider the case α = 1, r = 0.3. In this case, the second best re-election standard is , leading to θ₁ = 0.157 and θ₂ = 0.76. However, the second best does not satisfy the incentive compatibility constraint. The PBE re-election standard is which yields θ₁ = 0.161 and θ₂ = 0.77. In this case, both the second best and the PBE exhibit a hawkish drift.

Example 3 More interestingly, consider the case α = 1, r = 0.35. In this case, the second best standard is to always re-elect, leading to θ₁ = θ₂ = 0. The PBE however, involves setting ŷ = 1.8 leading to θ₁ = 0.134 and θ₂ = 0.8. In this case the PBE exhibits a hawkish drift.

We plot in the Fig 1 below, the second best re-election standard () and the PBE standard (ŷ) against r. For reference we also plot the average policy implemented by incumbent in the range [θ₁, θ₂] under the first best. This provides a natural metric for the extent of hawkish drift under the second best and the PBE.

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Fig 1. Re-election standards under second best and PBE, and FB with α = 1.

https://doi.org/10.1371/journal.pone.0261646.g001

As we can see, when r is small (approx less than 0.225), the re-election standard under the PBE is also second best. For higher values of r, however, the PBE is not second best as it violated the incentive compatibility. In fact, for very high values of r (approx higher than 0.3) the second best involves always re-electing the incumbent.

There are a few things worth noting. First, both the second best and the PBE standards are increasing in r. Second, both the Second Best and the PBE are typically higher than the First Best. This is one type of hawkish drift. Note the hawkish drift in the θ₁, θ₂ range. Both the Second Best and the PBE involve Hawkish drift (i.e., ). The average ability of the incumbent who gets reelected drops as r goes up.

The following proposition summarizes our results.

Proposition 1 The Perfect Bayesian equilibrium re-election standard is increasing r and is weakly higher than the second best re-election standard. The two standards do not always coincide, in particular, there is a cutoff value of r at which they diverge. Moreover, both the second best and the PBE involve hawkish drift as defined above.

General case: How ŷ varies with ideology and rents

In the previous sub-section we saw how presence of rents from office (r > 0) can lead to a hawkish drift under both the second best and the PBE. We now look at how the divergence of ideology (α ≶ 0) is a further source of hawkish drift, and the reasons thereof.

First consider the case when α > 1, i.e., the politicians ideology is intrinsically more hawkish. Given any re-election standard and the value of α, as r increases, the average ability of the incumbents who meet the standard decreases. With α > 1, this leads to the voter facing a trade-off between screening, i.e., setting a higher y to re-elect a higher ability incumbents, and a higher cost of conflict due to the policy being higher than their ideal policy given the politician ability. Depending on this trade-off, the voters will set a higher or lower re-election standard as r increases. In the subsequent examples we will examine how the second best and the PBE change, for a given α > 1, when r increases.

Example 4 Consider α = 1.1, with r ≤ 0.08. In this case, the first best policy, contingent on α = 1.1, involves re-electing incumbents with ability greater than and at this threshold, the policy is . At r = 0, the voters second best re-election standard is also , which is the ideal outcome for type α = 1.1, but this is higher than first best. This outcome is also the PBE.

However, as r increases, under the second-best, the voter may find it optimal to lower the standard. For instance, when r = 0.05, the second best standard is , leading to θ₁ = θ₂ = 0.360. Thus the second best seeks to curb, to some extent, the intrinsic hawkishness of the low ability incumbents by committing to re-elect them at the standard lower than their first best. This is not a PBE, since the re-election strategy is not ex-post credible whenever an incumbents policy choice reveals his ability to be below 1.443.

In this case, the PBE involves raising the re-election standard to the point where the expected quality of the incumbents meeting it makes the re-election strategy credible. The PBE standard when r = 0.05 is ŷ = 1.665. Under the PBE we have, θ₁ = 0.374 and θ₂ = 0.513.

However, with a further increase in r, the benefit of curbing hawkishness by lowering the standard is outweighed by the cost in terms of poorer selection on ability. This leads the voter to raise the standard, as shown in the next example.

Example 5 Consider α = 1.1, with r = 0.15. In this case, the second best standard is which, while still below the first best of 1.587, is higher than the second best standard in the previous example with r = 0.05. Under this standard θ₁ = 0.214 and θ₂ = 0.369. Since the cutoff values are both below the 0.443 threshold, the second best is not a PBE. The PBE in this case is ŷ = 1.778, which induces θ₁ = 0.282 and θ₂ = 0.616.

To summarize, the two examples demonstrate the trade-offs facing a voter. A higher standard improves selection but comes at the cost of a more hawkish policy. When there are no rents from office, the voter is unable to incentivize the politician to deviate from his optimal policy. As r increases, voter can sacrifice selection to an extent by promising re-election, curbing low quality ‘hawks’. As r increases further, more and more low quality politicians want to get re-elected (i.e. θ₁ drops). In response the voter has to increase the standard again. This non monotonic feature of the second best when politicians are hawks shows the interplay between inducing better selection vs. facing higher costs of conflict. This non-monotonicity is however not credible i.e. in the absence of commitment this cannot happen. Thus, the PBE is monotonic in r, inducing increases in the standard as r increases.

We now consider the case of α < 1, i.e., the case where the incumbents ideology is dovish relative to the voter. In this case the voter does not face the trade-off he faced in the α > 1 case. The lower the α the easier it is for him to screen for a high quality by setting a high re-election standard. As the next series of examples shows, this generates a hawkish drift wherein the re-election standard is higher than not only the incumbents first best, but that of the voter as well.

Example 6 Consider α = 0.9. Suppose that r = 0. In this case the first best policy involves selecting incumbents with with the corresponding standard at this threshold to be 1.298. The second best standard, however, is leading to θ₁ = 0.484 and θ₂ = 0.732. This outcome is supported under PBE as well, since the average quality of those meeting the standard exceeds 0.443.

The above example provides an interesting insight about hawkish drift. In the above example, the hawkish policy is used to drive selection and to correct for the inherent dovish bias of the incumbent. Even though the policy is too high for even some high ability incumbents first best they prefer to implement it rather than having their ideal policy implemented by an average quality replacement. Next we examine the effect of r > 0 on the re-election standard.

Example 7 Consider α = 0.9 and r = 0.1. In this case the second best re-election standard is , leading to θ₁ = 0.388 and θ₂ = 0.901. This outcome is supported as PBE as well.

As we can see, relative to the case with r = 0, the selection is worse—(θ₁ = 0.388) vis-a-vis 0.484. This is due to fact that rents induce low ability politicians to meet the re-election standard. And the re-election standard is higher as compared to the r = 0 case. Thus, voter balances the cost of selection against a higher cost of conflict by setting a standard that allows some below average doves to get re-elected.

These examples help us understand how the second best and the PBE change as ideology (α) and rents from office (r) change. Recall the case where the politicians ideology is the same as the voter. As noted earlier, there are two opposing changes. As r increases, the divergence between the politician and the voters preferences increase. Thus, each ability type is more likely to meet a given performance standard than not meet it. To be able to screen out bad politicians, one has to choose a higher ŷ (or , as the case may be, depending on whether we are looking at the PBE or the second best). However, this comes at the cost of excessively high compared to the first best. As r increases further, the cost of excessively hawkish policy may well outweigh the gain from selection and may begin to dip. In that case we could even see the to reach a maximum and then fall. It would fall to either selecting everyone or replacing everyone out.

For our given utility function, utility is always higher from re-electing everyone than replacing everyone. Thus, the second best becomes a case of choosing between the optimal y found from maximizing the W function and comparing with re-electing everyone. Given the functional form we have chosen this is a comparison between comparing the welfare from maximizing W with 0.75.(Recall welfare from re-electing everyone is for α = 1, this is 0.75.)

As Fig 2A above shows, for α > 1, is non-monotonic in r and drops to 0 after around r = 0.3 to satisfy the V_E constraint. Fig 2B, on the other hand, represents a monotonic profile for α < 1 without the discontinuities evident in Fig 2A. Fig 2 also illustrates how the second best and the PBE vary for both hawks and doves.

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Fig 2.

A. Re-election Standards under Second Best and PBE for α ≥ 1. B. Re-election Standards under Second Best and PBE for α < 1.

https://doi.org/10.1371/journal.pone.0261646.g002

The characterization of how the voting standard changes when α is not equal to 1 is complex and the examples above provide the interesting trade-offs involved. In Appendix II in S1 File we provide a table showing the change in and ŷ, and the induced θ₁ and θ₂ for a range of values. Here, we summarize the essential features of the second best and the PBE.

Holding ability fixed, hawkish politicians find it easier to meet any standard. To get selection the voters needs a high y, but that may prove too costly in terms of welfare as it is beyond the voter’s ideal level of hawkishness even adjusting for quality. To strike the balance, y may be optimally pushed down but that ‘lower’ y may run into a credibility problem, i.e., the average of the people who bunch at the standard may be too low and are better replaced. Hence the second best is not a PBE when voters second best optimally causes y to drop for a range as r increases.

More strikingly, there is hawkish drift with politicians who are doves too. Even without any inducement from having r > 0, doves who are above average in ability may not drop out if the policy is more hawkish than their first best. They face a trade-off, suffer a more hawkish policy than they would like but implement that (by meeting the standard) at a lower cost than their ideal policy implemented by their replacement whose expected quality is lower than their own. This leads to a hawkish drift again for a range if theta and this is reinforced as r increases. Both second best and the PBE are monotone in r in this case.

We now turn to what happens when ideology as well as ability is unknown.

Model when both ideology and ability are unknown

We now consider the case where the voter cannot condition his re-election standard on ideology or ability. We then show that there is a possibility of a hawkish drift in this case as well. This result is intuitive: since we know that there exists a hawkish drift for a wide range of α, the optimal policy when α is not known will involve setting a standard that it some convex combination of the α-contingent re-election standards, and will therefore exhibit a hawkish drift. The following example is illustrative.

Example 8 Suppose r = 0.15 and the incumbent ability is either α = 0.95 or 1.05, each with probability 0.5. The second best standard is . Given this standard, if α = 0.95, we have (θ₁, θ₂) = (0.278, 0.741), and if α = 1.05, we have (θ₁, θ₂) = (0.253, 0.575). In either case, there is a hawkish drift for ability types < 0.65. Since the PBE standard is weakly higher than second best, the PBE exhibits a hawkish drift as well.

To generalize from the above example, denote by W(z, α) the maximization problem as described in Eq (9) associated with ability type α, and let denote the corresponding second best standard. Suppose α is unknown and has probability distribution F(α) over support A, then the second best standard is characterized by If each W(z, α) is concave over the relevant range, then the maximand above is also concave. Moreover, Thus, if the smallest second best standard over the set A exhibits a hawkish drift, then the standard associated with the case when α ∈ A is unknown also exhibits a hawkish drift.

We will now examine, given any performance standard, whether incumbents of a given ideology find it easier to meet the standard. In other words, we would like to know the relationship between θ₁ and α. Eq (7) gives us the relationship between any re-election standard z and θ₁. Differentiating Eq (7) we get Given that the denominator is positive, (12)

Thus we get,

Proposition 2 Given any re-election standard z such that (ln 2z − α) > 0, the marginal (as well as average) quality of incumbent politicians who get re-elected is lower the more hawkish their ideology (i.e., the greater the value of α).

It is easy to see that the condition described in the Proposition above will always hold for α < 1 for any . For α > 1, this condition will be satisfied for a sufficiently high z. In all our simulations that we based our examples on, the optimal re-election standards under the first and the second best as well as the PBE satisfy this condition. Thus, we see that asymmetric information about ideology as well as ability can lead to an endogenous bias in the electoral process. It essentially arises because both ability and hawkishness leads to a higher y, voters are unable to distinguish the two and hence the optimal standard favors ideologically hawkish politicians.