Polsci 232B · Week 5 · Detailed textbook note

Political Agency

Scott Gehlbach, Formal Models of Domestic Politics, Chapter 7, pp. 163–190

Core tension moral hazard vs. selectionInstitutions elections, coalition politics, separation of powersModels Barro–Ferejohn, career concerns, signalingSource PDF pp. 1–28 / printed pp. 163–190

1 · The chapter in one argument

Elections are an incomplete contract between voters (principals) and politicians (agents). They can discipline hidden or costly action through the threat of removal and can improve selection by retaining better types. Yet the same reelection incentive can fail because voters cannot commit or coordinate, can induce wasteful effort that merely meets expectations, and can even make well-intentioned politicians choose a policy they know is wrong.

快速直觉选举只有一个很粗的奖惩按钮：留任或下台。它既可能像“绩效工资”一样改善行为，也可能像“考试排名”一样让人只做可被观察、可被奖励的事。全章的不同模型，就是逐步改变 voters 能观察什么、politician 知道什么，以及 reelection 到底奖励行为还是类型。

Sanctioning
Promise reelection for acceptable performance.

→

Selection
Keep the candidate expected to govern better.

→

Signaling
Actions reveal type—but types imitate.

→

Pandering
Good types may mimic what voters reward.

Source scopeChapter overview and the two agency problems: printed pp. 163–164 (PDF pp. 1–2). The substantive chapter ends at printed p. 185; pp. 185–190 contain exercises.

2 · Conceptual map: what changes across models?

Model	Agency problem	Information	Why reelection changes behavior	Main pathology
Barro–Ferejohn	Moral hazard / rent extraction	Action and outcome observed; types identical	Future office value disciplines current rent	Voting rule is not credible without indifference and coordination
Conflict among voters	Collective principal problem	Targetable transfers observed	Each group tries to be cheap enough for the coalition	Competition among voters destroys accountability
Separation of powers	Joint rent extraction	Proposal and veto observed	Voters condition reelection on each officeholder’s contribution	Works only for a parameter range of outside options
Career concerns	Moral hazard + unknown competence	Neither voters nor incumbent know competence ex ante; effort hidden, outcome seen	Effort raises apparent competence and reelection probability	Equilibrium effort does not fool voters; it is a costly rat race
Signaling	Private preferences/type	Incumbent knows type and action cost; voters see action	Action changes posterior beliefs about type	Lazy types imitate diligent types
State-dependent signaling	Private information about correct policy	Incumbent knows state; voters do not	Voters interpret a visible policy as evidence of diligence	Diligent incumbent may knowingly choose the wrong policy

Analytical synthesisThe chapter is not saying that “accountability” is one thing. It separates at least three objects: lower rents, higher effort, and better policy matching. A reform can improve the first two while worsening the third.

3 · Barro–Ferejohn: reelection as an incentive contract

3.1 Players, timing, information, payoffs

Players

A continuum of identical voters (mass one), an incumbent, and a passive challenger. Incumbent and challenger have identical preferences; there is no selection problem.

Choice and outcome

The incumbent chooses rent r ∈ [0,1]. Each voter receives u_i(r) = 1 − r; the incumbent consumes r.

Future incentive

If reelected, the incumbent gets second-period office payoff R, discounted by δ. Assume δR < 1 so some rent is extracted.

Timing

(1) voters announce reservation utility ū_i; (2) incumbent chooses r; (3) voters reelect iff delivered utility meets the threshold.

Source: printed pp. 164–166 (PDF pp. 2–4).

3.2 Solve backward from the incumbent’s discrete choice

When voters coordinate on a common threshold ū, the maximum rent compatible with reelection is r̄ ≡ 1 − ū. The incumbent never chooses an interior rent below r̄ (she could take more and still win), and never chooses a rent strictly between r̄ and 1 (if losing anyway, take everything). Her real choice is therefore:

reelection: r = r̄ and payoff r̄ + δR versus exit: r = 1 and payoff 1

r̄ + δR ≥ 1. Condition 7.1; printed p. 166 / PDF p. 4.

Voters want the smallest r̄ that still makes reelection incentive-compatible. They set the constraint exactly at equality:

Equilibrium result

ū* = δR and r* = 1 − δR.

Elections produce partial, not full, accountability. The incumbent must be left an information rent equal to the discounted value she would lose by being removed.

3.3 Comparative statics and mechanism

δ ↑ ⇒ r* ↓: a more patient incumbent values tomorrow more and steals less today.
R ↑ ⇒ r* ↓: a more valuable office creates a larger bond that voters can threaten to take away.
No future value ⇒ r* = 1: a lame duck takes the full resource.

快速直觉连任价值就是 politician 留在 voters 手里的“押金”。押金越大，今天越不敢拿走全部资源。但 voters 不能把租金压到零：如果今天什么都不给 incumbent，她宁可立刻卷走全部资源。

3.4 Why this equilibrium is fragile

Critical assumptions

Coordination: all voters must select the same threshold.
Indifference at election time: because incumbent and challenger are identical, voters are willing to execute a retrospective rule that has no prospective payoff relevance.

Fearon’s objection is decisive: an arbitrarily small candidate preference makes voters abandon the announced rule. The model’s discipline comes from an equilibrium selection restriction, not from a fully credible commitment technology. Printed p. 167 / PDF p. 5.

4 · Conflict among voters: the principal is not unitary

4.1 Modification

There are N equally sized voter groups (with even N). The incumbent chooses total rent r and discriminatory transfers t₁,…,t_N summing to 1 − r. Reelection requires support from half the groups. Each group independently sets its own reservation utility.

4.2 Proof logic: underbidding for coalition membership

If the incumbent seeks reelection, she buys the N/2 cheapest groups and gives each exactly its threshold.
Suppose a putative equilibrium had r < 1 and reelection. Then at least one winning-coalition group must demand a positive transfer.
An excluded group can profitably offer a slightly lower positive threshold and replace the most expensive coalition member.
Therefore no positive-transfer coalition can be stable. In every equilibrium, the incumbent extracts the maximum rent r = 1, although she may or may not be reelected.

Central resultConflict among voters can completely eliminate accountability. The incumbent “plays groups off against one another”; the collective principal cannot commit to a demanding common standard. Printed pp. 167–169 / PDF pp. 5–7.

快速直觉每个 voter group 都怕自己被排除在 winning coalition 外，于是竞相降低要求。像劳工彼此压低工资：整体希望 politician 少拿 rent，但个体 group 有动力用更低价格换取入场。

5 · Conflict among officials: separation of powers can help

5.1 Institutional structure

Replace one incumbent with a legislature L and executive E. The legislature proposes rents r_L, r_E; the executive accepts or vetoes. After veto, outside rents are r̂_L = 0 and r̂_E ∈ (0,1). Reelection values are R_L and R_E, and δ = 1 for simplicity.

Voters reward each actor by contribution: reelect the legislature only after a zero-rent proposal; retain the executive when she accepts zero rents and when she vetoes positive rents.

5.2 Why the executive’s outside option disciplines the legislature

To get a maximal-rent proposal accepted, the legislature must give the executive at least r̂_E + R_E, because veto brings r̂_E plus reelection. The legislature then keeps at most 1 − r̂_E − R_E. It chooses zero rents and reelection when R_L is at least that amount. Yet the executive must also prefer accepting the zero-rent proposal and reelection to vetoing it, requiring R_E ≥ r̂_E.

1 − R_L − R_E ≤ r̂_E ≤ R_E

Existence conditionA zero-rent equilibrium exists when the executive’s veto payoff is large enough to make bribing her costly for the legislature, but not so large that she prefers vetoing even a clean proposal. Printed pp. 169–171 / PDF pp. 7–9.

Institutional lesson“More conflict” has opposite effects depending on where it is located. Horizontal conflict inside the electorate fragments the principal and weakens discipline; horizontal conflict inside government creates mutual checks and can strengthen it.

6 · Infinite horizon: continuation value is endogenous

The same rent game repeats forever. Voters use a stationary common threshold, an incumbent remains until defeated, and a removed politician can never return. If she complies with r̄ every period, the value of reelection is:

V = r̄ + δV = r̄/(1 − δ). Equation 7.3.

Compliance requires r̄ + δV ≥ 1. Substituting the value function gives r̄ ≥ 1 − δ. Voters choose the minimum sustainable rent:

Stationary equilibrium

r̄* = 1 − δ and V* = 1.

The two-period model is exactly recovered when its exogenous reelection prize R is set equal to the infinite-horizon continuation value V. Printed pp. 171–172 / PDF pp. 9–10.

快速直觉不是“未来无限长所以 rent 接近零”，而是 patience 决定可持续纪律：δ 越高，丢掉未来租金越痛，今天允许的 rent 越低。δ→1 时接近完全 accountability；δ→0 时纪律消失。

7 · Career concerns: prospective selection induces effort

7.1 The key informational twist

There are voters, an incumbent, and a challenger over two periods. In period 1 the incumbent chooses unobserved effort e₁ ≥ 0 at cost ½e₁². Then competence θ is realized. Crucially, neither voters nor the incumbent knew θ when effort was chosen. Voters observe only performance u₁ = θ + e₁. Competence persists if the incumbent stays; a challenger has expected competence zero. The officeholder receives wage w per period.

Do not confuseThis is not yet a signaling model. A signal is chosen by someone who knows the relevant type. Here the incumbent cannot signal θ because she does not know θ at the time of action; she can only manipulate the noisy performance measure.

7.2 Backward induction and voter inference

In period 2 there is no future election, so the winner chooses e₂ = 0.
Voters therefore care only about which candidate has higher expected competence.
Given belief ẽ₁ about equilibrium effort, they infer θ̃ = u₁ − ẽ₁.
They reelect iff θ̃ ≥ 0, the challenger’s expected competence.

7.3 Incumbent problem and equilibrium

Taking voter belief ẽ₁ as fixed, the incumbent picks effort to trade off quadratic cost against a higher chance that θ ≥ ẽ₁ − e₁:

max_e₁ −e₁²/2 + [1 − F(ẽ₁ − e₁)]δw

−e₁* + f(ẽ₁ − e₁*)δw = 0.

In equilibrium beliefs are correct, ẽ₁ = e₁^*, so the density is evaluated at zero:

Career-concerns effort

e₁* = f(0)δw. Printed p. 176 / PDF p. 14.

δ ↑ or w ↑ ⇒ effort ↑ because reelection matters more.
f(0) ↑ ⇒ effort ↑ because performance is more informative near the electoral cutoff; less noise means effort more strongly affects winning.

7.4 The apparent retrospective rule is actually prospective

Substitution yields the observable voting threshold:

reelect iff u₁ ≥ f(0)δw. Condition 7.4.

This looks like retrospective voting, but voters are not punishing low utility for its own sake. Low performance is evidence that the incumbent’s persistent competence is below the challenger’s expected competence. Unlike the Barro–Ferejohn rule, this behavior survives a small partisan bias: the cutoff merely shifts.

快速直觉这是一个 expectations treadmill。所有人都预期 incumbent 努力 e*，所以观察到好表现时 voters 会先扣掉这部分预期努力，再判断 competence。努力最终没有“骗到”任何人，但若 politician 少努力，表现就低于预期并输掉选举，因此每个人都被迫努力。

Welfare cautionThe chapter calls higher effort “accountability,” but the model does not conduct a full welfare comparison. Effort is privately costly and, because voters correctly net it out, does not improve selection conditional on the equilibrium inference rule. Whether equilibrium effort is socially valuable depends on how much voters value contemporaneous performance relative to the effort cost.

8 · Infinite-horizon career concerns: electoral cycles

Off-election periods O alternate with election periods E. Competence is θ_t = y_t + y_t−1, with serially independent shocks. Current performance reveals information useful for the next period only when an election immediately follows.

Off-election period

e_O^* = 0. Current competence information will be obsolete by the next election, so effort cannot improve reelection chances.

Election period

Effort shifts apparent current shock and therefore the probability of reelection. The continuation prize includes both next period’s wage and the discounted value of reaching another election.

V_O = w + δV_E

e_E* = g(0)δ(w + δV_E). Equation 7.5; printed p. 179 / PDF p. 17.

Political business-cycle logicEffort is zero in off-election periods and positive in election periods. Using the envelope theorem, the chapter shows ∂V_E/∂w > 0 and therefore ∂e_E^*/∂w > 0. Printed pp. 177–180 / PDF pp. 15–18.

快速直觉只有“今天的表现会影响最近一次选举”时才值得努力。模型不是假设 politicians 在 election year 突然更善良，而是信息的保质期和 electoral calendar 共同产生周期。

9 · Signaling: politicians privately know their type

9.1 Setup

Politicians are diligent (d) with prior probability π or lazy (l). Each period the officeholder chooses binary effort e_t ∈ {0,1}, observed by voters. Everyone enjoys policy benefit e_t. A diligent type has zero cost of high effort; a lazy type draws cost c_t from distribution G, with c_t > 1. Office wage satisfies w > 1. The incumbent observes her type and cost before acting.

9.2 Candidate equilibrium and beliefs

In period 2, diligent politicians choose e₂ = 1; lazy politicians choose 0.
Voters prefer the incumbent when her posterior diligence exceeds the challenger prior π.
Consider an equilibrium in which voters reelect iff e₁ = 1. Diligent incumbents always exert high effort; some low-cost lazy incumbents imitate.
Let λ ≡ Pr(e₁ = 1 | l). Bayes’ rule gives Pr(d | e₁ = 1) = π/[π + λ(1−π)] > π whenever λ < 1. Observing e₁ = 0 reveals a lazy type.

9.3 Lazy type’s cutoff

Low effort yields w + δπ: the incumbent loses, and expected period-2 policy equals the probability π that the challenger is diligent. High effort yields w + (1−c₁) + δw: she pays the net cost but is reelected. Thus a lazy incumbent mimics when:

w + (1 − c₁) + δw ≥ w + δπ ⇔ c₁ ≤ 1 + δ(w − π).

Imitation probability

λ = G(1 + δ(w − π)). Equation 7.6; printed p. 183 / PDF p. 21.

δ ↑ or w ↑ ⇒ more lazy types exert effort.
π ↑ ⇒ less effort by lazy incumbents: losing is less costly when a diligent challenger is likely to replace them.

快速直觉“对手太好”会削弱 incumbent 的自我约束：lazy incumbent 会想，反正输给 challenger 后政策也大概率不错。这里 voters 的福利与 incumbent 的 accountability 并不完全同向。

Equilibrium scopeThe chapter studies this informative equilibrium, but Exercise 6 asks for conditions supporting a pooling equilibrium in which both types choose zero and voters reelect after zero. Do not read Equation 7.6 as a uniqueness claim.

10 · State-dependent utility: when good politicians pander

10.1 The new private information

A binary state s_t ∈ {0,1} determines the correct action. Voters and politicians obtain policy payoff:

s_te_t + (1 − s_t)(1 − e_t),

so welfare is maximized by matching e_t = s_t. The incumbent observes the state; voters observe the action but neither state nor policy payoff before voting. Let η = Pr(s_t = 1).

10.2 Diligent incumbent’s dilemma when s₁ = 0

The proposed equilibrium still has voters reelect iff e₁ = 1. If s₁ = 1, a diligent type naturally chooses 1. If s₁ = 0, choosing 1 is wrong today but secures office tomorrow. The comparison is:

pander: w + 0 + δ(w + 1) ≥ correct policy: w + 1 + δ[π + (1−π)(1−η)]. Condition 7.7.

w ≥ 1/δ − (1−π)η.

Pandering conditionDiligent incumbents are more likely to knowingly choose the wrong policy when w is high, π is low, or η is high. Printed pp. 183–185 / PDF pp. 21–23.

10.3 Why these comparative statics make sense

w ↑: holding office is more valuable, so sacrificing current policy to survive is more attractive.
π ↓: replacement is more likely to be lazy; the diligent incumbent believes staying in office matters more for future policy.
η ↑: a lazy successor who always chooses zero is more likely to mismatch next period’s state, raising the future value of retaining a diligent incumbent.

快速直觉最反直觉之处：pandering 不是 good politician 不在乎政策，而是她太在乎未来政策。她今天做 voters 看得懂但错误的事，为了留下来明天做正确的事。

Normative tensionHigher wages have a double edge across the chapter: they reduce rent extraction and increase effort, but they also raise the temptation to pander. Institutional design cannot maximize “accountability” without specifying which behavioral margin and which time horizon count as welfare.

11 · Results you should be able to compare

Change	Barro–Ferejohn	Career concerns	Signaling	Pandering
Patience δ ↑	Rent r* ↓	Effort e₁* ↑	Lazy imitation λ ↑	Threshold 1/δ − (1−π)η falls; pandering easier
Office value / wage ↑	Rent ↓	Effort ↑	Lazy effort ↑	Wrong-policy pandering ↑
Noise / uncertainty ↑	Not central	Lower density near cutoff generally weakens effort incentive	Type-cost distribution changes imitation	Hidden state creates the distortion
Better challenger pool π ↑	No type difference	Challenger mean sets voting threshold	Lazy effort ↓	Pandering ↓

Unifying mechanismAll results turn on the marginal electoral return to current action. That return is high when office is valuable, voters can attribute performance to action/type, and replacement is costly to the incumbent. Whether a high return is good depends on whether the rewarded action coincides with welfare.

12 · Key evidence and intellectual lineage

This is a theory chapter, so its “evidence” consists of formal comparative statics, equilibrium constructions, and links to canonical models—not empirical estimates.

Claim supported in the chapter	Formal evidence	Canonical source named
Elections yield partial discipline even with observable action	r* = 1 − δR; stationary r* = 1 − δ	Barro (1973); Ferejohn (1986)
Discriminatory allocation can destroy accountability	Every equilibrium has maximal rent under group underbidding	Ferejohn (1986)
Checks and balances may support zero rents	1 − R_L − R_E ≤ r̂_E ≤ R_E	Persson, Roland & Tabellini (1997)
Career incentives generate costly effort and electoral cycles	e₁* = f(0)δw; e_O* = 0 < e_E*	Holmström (1982); Persson & Tabellini (2000)
Private type creates imitation	λ = G(1 + δ(w − π))	Besley (2006)
Good incumbents may choose known-wrong policy	w ≥ 1/δ − (1−π)η	Canes-Wrone, Herron & Shotts (2001); Besley (2006)

Evidence statusAll displayed equations and inequality directions above were visually checked against the assigned PDF. The chapter provides no datasets, empirical tests, or quantitative calibration.

13 · Assumptions, equilibrium discipline, and limits

Voting-rule credibility: Barro–Ferejohn sanctioning relies on voter indifference and coordinated threshold strategies. It is far more fragile than prospective selection.
Equilibrium selection: several games admit many equilibria. The chapter restricts attention to particular stationary, coordinated, or informative equilibria; central results are not blanket uniqueness theorems.
Coarse electoral instrument: voters reward or punish only through reelection. The chapter notes that mixed strategies can relax this lumpiness, but does not develop that extension.
Outcome attribution: career-concerns effort depends on the density of competence shocks around the cutoff. Large exogenous noise reduces the electoral productivity of effort.
Simplified preferences: homogeneous voters, identical challengers, binary actions/types, and quadratic costs isolate mechanisms but suppress ideology, turnout, parties, and multidimensional policy.
Welfare is not one-dimensional: lower rent, greater effort, improved selection, and correct state-contingent policy can diverge.
Private information changes meaning across sections: unknown competence (career concerns) is not the same as privately known preferences/cost/state (signaling).

Likely exam trapDo not say “elections work because voters punish bad performance.” In the career-concerns model voters are prospective; apparent punishment is Bayesian updating about persistent competence. In the Barro–Ferejohn model punishment is retrospective but credible only because voters are indifferent.

14 · Connections to the Week 5–6 readings

Fearon (1999): selection vs. sanctioning

Gehlbach uses Fearon’s critique to motivate the move away from fragile retrospective promises. Ask whether observed electoral discipline comes from threatening an incumbent or choosing a better replacement.

Ashworth (2005): reputational dynamics

Career-concerns logic supplies the baseline: actions affect beliefs about persistent type and therefore future career value. Dynamic reputations can alter effort across a longer career.

Ashworth & Bueno de Mesquita (2014)

The distinction between performance and competence is central. Electoral institutions can change both incentives to act and the information voters obtain for selection.

Canes-Wrone, Herron & Shotts (2001)

Section 7.3.2 formalizes their pandering mechanism: informed, high-quality incumbents may ignore private information to choose the publicly popular action.

Biased beliefs readings

The chapter assumes Bayesian inference. Lockwood, Levy–Razin, and Little–Schnakenberg–Turner ask what happens when citizens process the same signals through confirmation bias, correlation neglect, or motivated reasoning.

Course-wide model grammar

Map every application onto: who knows type/state, what voters observe, how action shifts beliefs, what reelection is worth, and whether the rewarded action is socially correct.

Connections are teaching analysis grounded in the assigned chapter and local Week 05–06 reading list; they are not claims that Gehlbach fully develops each later paper.

15 · Retrieval questions (click to reveal)

1. Why is the incumbent’s choice in the baseline effectively binary between r̄ and 1?

Any rent below r̄ leaves money unused while still winning; any rent above r̄ loses, so conditional on losing the incumbent takes the full resource.

2. Why is full accountability impossible in the two-period Barro–Ferejohn equilibrium?

Zero rent makes reelection worth only δR, which is below the one-shot payoff 1 under the maintained assumption δR < 1. Voters must leave a rent of 1 − δR.

3. Why does voter conflict weaken accountability while official conflict may strengthen it?

Voter groups underbid one another to enter the minimum winning coalition, fragmenting the principal. A veto player with a suitable outside option raises the price of rent extraction for the agenda setter.

4. What is the difference between retrospective appearance and prospective logic in career concerns?

The observable rule is a performance cutoff, but voters use performance only to infer persistent competence relative to the challenger. They are choosing future expected performance, not punishing the past intrinsically.

5. If equilibrium effort does not fool voters, why exert it?

Voters correctly expect effort and subtract it from observed performance. An incumbent who deviates downward then looks less competent and is less likely to win. Correct expectations sustain the costly effort race.

6. Why does more competence noise reduce effort incentives?

When the density at the electoral cutoff is low, a marginal effort increase rarely changes the election outcome; luck dominates action.

7. Why is π comparative static counterintuitive in the signaling model?

A higher π means defeat hands office to a likely diligent challenger. That improves expected policy after losing and reduces a lazy incumbent’s incentive to pay the cost of high effort.

8. Why can a diligent politician choose the wrong policy under pandering?

Choosing the publicly rewarded action secures reelection. A diligent incumbent may accept a current mismatch to prevent a likely lazy successor from making future mistakes.

9. Does a larger wage always improve voter welfare?

No. It lowers rents and raises effort in earlier models, but also makes reelection more valuable and therefore makes pandering easier in the state-dependent model.

10. What is the chapter’s most general design lesson?

Strengthening electoral incentives is not enough. One must ask what voters can observe and infer, which action the electoral reward targets, and whether that action aligns with welfare in the relevant state.