Persistence of clientelism
LLM status Partially solved unverified
D72 — Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior Economics catalogue openaigpt 6 astra ultra 50% cataloguednot recordedPartially solvedStatement
Q6 | Political economy | Editorial research problem family
Definitions and assumptions
Specify an infinite repeated game with a finite voter set $N$, parties and brokers, bounded per-period utilities, and discount factors $\delta_i\in(0,1)$. At each date, parties offer feasible benefits $b_{it}$, voter $i$ privately chooses support $v_{it}\in\{0,1\}$, and brokers receive signal $s_{it}$ with known conditional law $q(s\mid v,b,H_t)$. The public history $H_t$ contains only declared observable information. Voter utility includes material benefits, policy preferences and, if allowed, an explicitly specified reciprocity term. A policy $a$ changes ballot secrecy, broker information or access to programmatic services. Let $\mathcal E(m,a)$ be the set of sequential equilibria of the declared game. Require uniformly bounded transfers and choose an evaluation discount factor $\rho\in(0,1)$. For equilibrium $e$, define $B_m(e,a)=(1-\rho)\mathbb E_{m,e,a}[\sum_{t=0}^{\infty}\rho^t |N|^{-1}\sum_i b_{it}]$ and $V_m(e,a)=(1-\rho)\mathbb E_{m,e,a}[\sum_{t=0}^{\infty}\rho^t |N|^{-1}\sum_i v_{it}]$; the probability law depends on the model, equilibrium and policy.Formal research question
Characterize when $\mathcal E(m,a)$ contains equilibria with positive targeted transfers and a higher support probability than under the no-transfer comparison, and identify restrictions on signal informativeness, reciprocity and public-service provision that alter those outcomes. For policy evaluation, fix an equilibrium selector $\sigma(m,a)$ or report the set \[ \{(B_m(e,a),V_m(e,a),W_m(e,a)):e\in\mathcal E(m,a)\}, \] where $W_m$ uses declared welfare weights. Determine whether experimental and network data distinguish reciprocity from threats contingent on inferred voting.Interpretation and scope
Perfect ballot secrecy means that, conditional on the same prior history and offer, the broker's signal distribution does not depend on the individual vote. A sanction based only on such a signal cannot selectively punish a deviation in that vote. This does not exclude monitoring turnout, group outcomes, repeated relationships or reciprocity; those must be modeled separately. Persistence is therefore a conditional equilibrium and empirical question, not a contradiction between clientelism and secret ballots.Source audit and status
All three original references are verified. Stokes models imperfect inference, Wantchekon studies campaign appeals, and Finan--Schechter examines reciprocal targeting. They already provide mechanisms for persistence. The retained question concerns distinguishing and extending those mechanisms under specified reforms, rather than asking whether any explanation exists. The game and comparative-statics target are editorial specifications.References
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- Susan C. Stokes (2005). Perverse Accountability: A Formal Model of Machine Politics with Evidence from Argentina. American Political Science Review 99(3), 315--325.
Locator and source role: Abstract and repeated-game mechanism; imperfect inference about secret ballots rather than perfect observation of votes.
- Leonard Wantchekon (2003). Clientelism and Voting Behavior: Evidence from a Field Experiment in Benin. World Politics 55(3), 399--422.
Locator and source role: Abstract and campaign experiment; constituency-service and patronage appeals, not simply verified purchases of individual secret votes.
- Frederico Finan and Laura Schechter (2012). Vote-Buying and Reciprocity. Econometrica 80(2), 863--881.
Locator and source role: Abstract and survey/experimental reciprocity measure; an alternative mechanism supporting transfers under secrecy.
Common conventions: Source mathematical conventions
Unless an entry states otherwise, agent and firm sets are finite. State and action spaces are measurable, strategies and outcome maps are measurable, probability laws are specified, and expectations exist for the targets under discussion. Infinite-horizon discount factors lie in $(0,1)$ and discounted objectives are finite. Norms, tolerances and complexity input sizes must be specified for computational comparisons. Constants or primitives that appear locally are inputs, not empirical facts asserted by this catalogue.
Identification. A statistical model $m\in\mathcal M$ implies an observable law $P_m$ and target $\theta(m)$. At law $P$, its identified set is \[ \Theta(P;\mathcal M)=\{\theta(m):m\in\mathcal M,\ P_m=P\}. \] Point identification holds when this set is a singleton, or equivalently when $P_{m_1}=P_{m_2}$ implies $\theta(m_1)=\theta(m_2)$ for all compatible models. Sharp bounds mean bounds attained, or approached when the boundary is not attained, by compatible models. Writing this set is a definition, not a solution: the substantive task is to establish informative restrictions and derive or estimate the set. An unrestricted-confounding model may give only trivial bounds.
Inference. Identification, estimability and valid uncertainty quantification are separate questions. Fix $\alpha\in(0,1)$. A confidence procedure $C_n$ over a declared law class $\mathcal P$ has asymptotic uniform coverage at level $1-\alpha$ when \[ \liminf_{n\to\infty}\inf_{P\in\mathcal P}\Pr_P\{\theta(P)\in C_n\}\geq1-\alpha. \] For set-identified targets the coverage event must be defined separately, for example coverage of the full identified set. If an entry uses identification-indexed models instead of uniquely indexed laws, the same coverage convention is applied over those models. Pointwise limits do not establish uniform validity, and asymptotic validity does not guarantee finite-sample precision. Sample sizes, dependence structures and weak-identification sequences are part of each application.
Counterfactuals. $Y_i(a)$ is a potential outcome under a specified intervention, including its timing, implementation and versions. It is not $Y_i$ conditional on voluntarily choosing $a$. A full intervention vector permits interference; shorthand scalar treatment notation does not silently impose no interference. Assignment, selection, attrition, anticipation and measurement must be specified. A claim about an instrument's local effect is not automatically a population policy effect.
Economic equilibrium. A counterfactual model includes best responses, constraints, feasibility, market clearing, state transitions and expectations consistent with the stated information. When several equilibria exist, either a declared selector is an input or the target is set-valued. Comparisons across policy regimes must use the stated selection convention. Reduced-form relationships are not presumed invariant after an equilibrium-changing intervention.
Optimization and welfare. Optimization is over the stated feasible set. If attainment is not established, $\sup$ or $\inf$ and $\varepsilon$-optimal choices replace an asserted maximizer or minimizer. For example, with value $V=\sup_{a\in\mathcal A}W(a)<\infty$, an $\varepsilon$-optimal set is $\{a\in\mathcal A:W(a)\geq V-\varepsilon\}$ for $\varepsilon>0$. Benefits, costs, risk and health or environmental outcomes can be aggregated only using declared units and conversion weights. Interpersonal utility weights, the treatment of fiscal transfers and foreign profits, discounting, and the behavioral welfare criterion are explicit inputs. A comparative-static derivative additionally requires existence and appropriate differentiability of the selected counterfactual.
Sources. Local labels [S1], [S2], and so forth restart in every question. Locators identify the relevant abstract, model, section or result at the level actually checked; a bibliographic or abstract-level verification is not represented as inspection of an entire proof. Working papers are distinguished from later publications and changing versions. Source summaries are paraphrased. All URL checks and editorial formulations refer to the audit date stated above.
Statement licence: CC-BY-4.0 · Source file
Contributions 1
GPT 6 Astra Ultra attempt on Econ-549
Monitoring thresholds and reciprocity under ballot secrecy
Status: Partial; the full catalogue target remains unresolved.Abstract
A fully specified repeated transfer game yields an exact support-incentive threshold depending on signal informativeness and false alarms. Perfect secrecy eliminates this signal-based sanction mechanism, but a separate reciprocity game can still sustain transfers and support. False alarms also distinguish positive discounted clientelism from indefinite persistence. These mechanisms are observationally confounded without interventions separating monitoring and reciprocity.One voter and a public monitoring technology
Consider one voter, one party, and an indefinitely repeated relationship with common discount $\delta\in(0,1)$. At each date the party first pays an observable benefit $b_t\in[0,\bar b]$. The voter then privately chooses support $v_t\in\{0,1\}$. Per-period voter payoff is $b_t-dv_t$, where $d>0$ captures a preference against the party; party payoff is $Rv_t-b_t$, with $R>0$.After the vote a public broker signal is bad with probability $q_1$ under support and $q_0$ under opposition, where $0\le q_1<q_0\le1$. Signals are conditionally independent over dates given actions. The vote has no other effect on future information. This last assumption excludes turnout or group-election signals beyond the specified broker signal. Transfers are received before the vote and cannot be clawed back.
Fix a prescribed benefit $b\le\bar b$. In the good public state the party pays $b$ and the voter supports. A bad signal or any nonprescribed payment switches permanently to the bad state, where the party pays zero and the voter opposes. Thus an observed payment deviation changes the state before the current vote.
An exact equilibrium condition
Put $D=1-\delta+\delta q_1>0$. Under the prescribed strategy, good-state continuation values at the start of a period are \[ V=\frac{b-d}{D},\qquad P=\frac{R-b}{D}. \]If the party deviates to another payment, the voter enters the punishment state and opposes immediately. The party's best such deviation is zero payment, yielding zero now and thereafter. Compliance has value $P$, so it is optimal exactly when $b\le R$. The transfer cap supplies the remaining bound.
In the bad state, support would cost the voter $d$ without changing any future payoff, so opposition is optimal after any payment. The party therefore optimally pays zero. These conditions hold after every public history; there is no persistent private type requiring inference. Bellman one-period deviation inequalities bound any multistage deviation by the prescribed value, since rewards are bounded and discounted continuation tails vanish. They establish sequential optimality. Violating either incentive inequality gives the corresponding profitable one-period deviation, proving necessity within the specified class. ∎
With $q_1$ fixed, increasing $q_0$ lowers the threshold: differentiation gives $-d(1-\delta+\delta q_1)/[\delta(q_0-q_1)^2]<0$. More false alarms at fixed $q_0$ instead raise it. Informativeness and erroneous punishment are distinct aspects of monitoring.
What perfect secrecy rules out
If $q_0=q_1$, a vote deviation changes no continuation distribution in this game. Support still costs $d>0$, so no positive benefit can make support optimal after that benefit has already been paid. This conclusion does not depend on the party's resources. It follows from the equality of conditional signal laws, not merely their noisiness.The conclusion is deliberately limited. If individual support affects a public election result, broker access to turnout, household benefits, or group punishments, those additional signals must be included. Perfect individual ballot secrecy does not assert that all political actions or aggregate results are unobservable. Nor does it rule out preferences for reciprocating a benefit.
Discounted support and literal persistence
Let the evaluator discount by $\rho\in(0,1)$, possibly different from $\delta$. Starting in the good state, support and transfers occur in period $t$ with probability $(1-q_1)^t$. The normalized outcomes are therefore \[ V_{\rm eval}=\frac{1-\rho}{1-\rho(1-q_1)},\qquad B_{\rm eval}=b\,V_{\rm eval}. \tag{2} \] The geometric series proves these formulas. For the numerical example and $\rho=0.9$, normalized support is approximately $0.5263$, with normalized transfers approximately $0.8421$.If $q_1>0$, eventually a false bad signal occurs almost surely under continuing support: the probability of no bad signal through $T$ is $(1-q_1)^{T+1}$, tending to zero. Thus this equilibrium has positive discounted clientelism but not everlasting cooperation on almost every path. When $q_1=0$, no on-path bad signal occurs and support persists forever. Repairing false alarms with forgiving or finite punishment strategies is a different equilibrium construction.
A separate reciprocity mechanism
Now remove all vote information and consider a one-period game with voter utility $b-dv+\theta bv$, where $\theta>0$ represents a declared reciprocity preference. The party still obtains $Rv-b$. After a benefit the voter supports when $\theta b\ge d$, with a support tie rule. If $\bar b\ge d/\theta$ and $R\ge d/\theta$, the party can choose $b=d/\theta$ and obtain nonnegative payoff $R-d/\theta$. If that inequality is strict, buying the reciprocal support strictly dominates paying zero.This is an equilibrium mechanism under perfectly secret voting: the transfer changes the voter's current utility comparison, not a broker's ability to punish. Without a transfer the voter opposes. The model does not establish that real recipients have these preferences, and the parameter $\theta$ must not be inferred merely from observing support after benefits.
The two mechanisms can fit the same observed benefit and support rates. Separating them requires variation affecting signal informativeness while leaving benefit preferences fixed, or a defensible measure/intervention concerning reciprocity while holding monitoring fixed. Even then, general-equilibrium party responses may change benefit offers, so reduced-form support effects need not equal a direct voter incentive effect.
Remaining gap
The result characterizes one repeated public strategy, not the entire sequential-equilibrium set in a voter network. It omits competing parties, heterogeneous voter discounting, broker incentives, programmatic public services, and strategic signaling. Welfare also requires weights and real cost accounting: benefits are transfers, while exclusion from useful services and political distortions can be resource or utility losses.The broad persistence and mechanism-identification question remains unresolved. The threshold and secrecy impossibility are exact only in the specified game; the reciprocity example demonstrates why that impossibility cannot be generalized to every form of clientelism.
Completion Estimate
50%This is a post hoc, heuristic estimate for the full catalogue target. The attempt characterizes a noisy-signal grim-trigger equilibrium, computes discounted clientelism, and constructs a distinct reciprocity mechanism under ballot secrecy. Full clientelism policy sets still require the broader sequential-equilibrium correspondence, competing parties and voter networks, public-service reforms, welfare accounting, and data separating monitoring from reciprocal preferences.
References
- [fs] F. Finan and L. Schechter (2012). Vote-Buying and Reciprocity, Econometrica 80(2), 863--881. https://onlinelibrary.wiley.com/doi/10.3982/ECTA9035. The primary article motivates reciprocity as a distinct mechanism; the game and thresholds above are explicit restricted constructions.