{"id":"c9c80c33-4de2-44b9-b7b6-e8bee2724725","arxiv_id":"2607.07280","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":7,"one_line_summary":"Optimal organizational evaluation rules deliberately distort from true output, pairing with positive or negative assortative assignment depending on whether non-discretionary advantage or effort matters more for production.","lead":"This paper shows that when workers compete on networks and benefit from spillovers, the optimal performance evaluation rule should deliberately differ from true output, and worker assignment should be used as an incentive tool. A smart generalist might read it to understand why organizations should jointly design who-works-where and how-performance-is-measured, rather than treating these as separate problems.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"Assumption 2's uniformity over all assignments is the load-bearing constraint; it is most fragile exactly when type heterogeneity and spillover inequality are large—the empirically interesting case.","rationale":"The reader's identification of Assumption 2 as the load-bearing concern is correct and well-targeted. The paper's central claim (Proposition 3) depends on the closed-form equilibrium in Proposition 1, which in turn depends on Assumption 2 holding uniformly across all assignments. The authors provide mitigation in Appendix A.6, but the sufficient conditions there are themselves restrictive and the core tension—between the assumption's uniformity requirement and the planner's desire to use extreme assignments—remains. This is a real but bounded concern: the qualitative logic (that evaluation should deviate from true output to shape incentives) is robust and does not depend on the exact functional form of the equilibrium. What does depend on Assumption 2 is the clean closed-form characterization and the sharp sorting predictions. The verdict of CONDITIONAL is appropriate: the theoretical contribution is solid within its stated domain, but the domain's boundaries are not fully explored. The paper would be strengthened by either (a) a numerical robustness exercise showing that the sorting predictions survive when Assumption 2 is relaxed, or (b) a more transparent discussion of when the assumption is likely to bind in practice. I do not think the concern rises to the level of REJECT because the main economic intuition is sound and the formal analysis is careful and self-contained within its assumptions.","tokens_in":34328,"tokens_out":4010,"duration_ms":304687,"concrete_test":"Take Example 2's setup (types (0,1,2), the given M, W_L and W_H). Verify Assumption 2 holds for ALL 6 assignments at ω_I = 0.18, not just the optimal ones. Then perturb types to (0,1,10) while keeping M and W fixed, and re-check Assumption 2 for all assignments. If it fails for the negative assortative assignment, solve for the Stage-2 equilibrium numerically (allowing corner solutions) and check whether the planner still prefers negative assortative assignment with ω < s. If the sorting prediction reverses or the optimal ω shifts to the boundary, the main comparative static in Corollary 1 is not robust to the assumption.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader correctly identifies Assumption 2 as the weakest link. I agree, but want to sharpen why. Assumption 2 requires that for EVERY ω ∈ [ω_I, 1], EVERY assignment m ∈ M, and EVERY position j, the non-discretionary component Σ_k M_jk a(m)_k + α lies in the interval (0, 2σz̄(ω)) shifted by z̄(ω)q_j. This must hold for all assignments simultaneously, including the negative assortative one where the lowest type is placed in the highest-spillover position. That assignment creates the most uneven effective-advantage profile, and it is precisely the assignment the planner wants to use when s > s*. So the assumption is most binding exactly at the policy the planner most wants to implement in the effort-important regime. Appendix A.6 provides two sufficient conditions (Propositions A.1 and A.2) for restricting to [ω_I, 1] to be without loss, but these are themselves demanding: Proposition A.1 requires Ξ ≥ τ_I, which demands that every possible active subset has enough own effective advantage relative to competition pressure from inactive positions—a condition that becomes harder to satisfy when types are heterogeneous and M is unequal. The concern is not that the paper is wrong within its stated assumptions, but that the assumptions exclude the parameter region where the model's comparative statics are most interesting and empirically testable.","agreement_with_reader":"agree"},"referee_report":{"model":"glm-5.2","summary":"This paper studies the joint design of evaluation rules and worker assignment in an organization where performance depends on both effort and non-discretionary advantage. Agents are linked by two networks: a competition structure W governing benchmarking comparisons, and a spillover structure M governing how fixed types propagate into effective advantage. The planner chooses an assignment m and an evaluation weight omega to maximize total output, which depends on effort and advantage with weight s. In Stage 2, agents exert effort in a network contest. The main results characterize equilibrium effort (Proposition 1), the planner's optimal policy (Proposition 3), and the output loss from requiring pairwise stable assignments (Proposition 5). The key finding is that the optimal evaluation rule generally differs from true output: when effort is more important in production (s > s*), the planner lowers omega and uses negative assortative assignment; when advantage is more important (s < s*), the planner raises omega and uses positive assortative assignment. The paper also shows that stability loss depends on competition intensity Q, decreasing in Q when the first-best is positive assortative and increasing when it is negative assortative.","tokens_in":34843,"tokens_out":1176,"duration_ms":235850,"significance":"The paper makes a genuine contribution by jointly studying evaluation design and assignment in a networked environment with two distinct network structures. The separation of competition and spillover networks is conceptually valuable and distinguishes the model from prior work on contests on networks or assignment models alone. The closed-form equilibrium effort expression in Proposition 1, linking effort to Katz-Bonacich centrality and effective advantage, is clean and generates testable comparative statics. The main policy result—that the planner deliberately distorts evaluation away from true output and that the direction of distortion flips with the relative importance of effort—is non-obvious and well-motivated. The pairwise stability extension (Section 4) adds practical relevance by showing how decentralized assignment constraints create a measurable output loss. The full proofs in the appendix are detailed and the model is self-contained with exogenous parameters.","major_comments":[{"comment":"Assumption 2 (Interior-equilibrium region, Section 3.1) requires that for every omega in [omega_I, 1], every assignment m, and every position j, the non-discretionary component lies in a specific interval. This uniformity over all assignments is load-bearing because Proposition 1 and all downstream results depend on the closed-form all-active equilibrium. The concern is that the assumption is most binding exactly at the assignments the planner most wants to implement: when s > s*, the planner chooses negative assortative assignment, which creates the most uneven effective-advantage profile. The paper should explicitly discuss whether Assumption 2 is compatible with the negative assortative regime it characterizes, or provide a parameterized example showing that both can hold simultaneously in a non-trivial case.","section":null},{"comment":"Appendix A.6 provides two sufficient conditions (Propositions A.1 and A.2) under which restricting omega to [omega_I, 1] is without loss. However, these conditions are themselves demanding. Proposition A.1 requires Xi >= tau_I, which demands that every possible active subset has enough own effective advantage relative to competition pressure. The paper would benefit from either (a) a concrete numerical example verifying these conditions in a setting with non-trivial type heterogeneity and spillover inequality, or (b) a more transparent discussion of what economic restrictions these conditions impose and how binding they are in practice.","section":null},{"comment":"Proposition 3 characterizes the optimal policy with three cases and a cutoff s*. The cutoff formula involves eT_minus and eT_plus, which themselves depend on whether the stationary points b_omega(B) are interior or at boundary values. The resulting case structure is correct but difficult to parse. A simpler statement of the main economic intuition—perhaps through a proposition stating only the interior case under Assumption 3—would help readers separate the economic content from the technical case enumeration.","section":null}],"minor_comments":[{"comment":"The notation omega_hat(B) in the main text (e.g., around Equation 3.9) and b_omega(B) in the appendix are used interchangeably; standardizing would improve readability.","section":null},{"comment":"In Example 1 (Section 3.2), the spillover matrix M^S = I + W^S is introduced but the economic interpretation of this specific functional form is not discussed. A brief note on why this is a natural spillover structure would help.","section":null},{"comment":"The paper references 'Katz-Bonacich centrality' in the abstract but 'Katz centrality' in the body (Section 3.1). Consistent terminology would be preferable.","section":null},{"comment":"Equation (2.9) and the surrounding discussion could more explicitly state that the normalization of weights summing to one is a modeling choice and briefly note the consequence of relaxing it, rather than relegating this to a footnote.","section":null},{"comment":"The empirical implications discussed in Section 3.2 are valuable but somewhat scattered across the text. Consolidating them into a dedicated subsection or a summary table would increase their visibility.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The paper is a solid theory contribution that fits well within the journal's scope in organizational economics and network games. The main technical concern about Assumption 2 is real but does not appear to be a fatal flaw—the results are correct within their stated domain, and the domain is non-empty. The authors should be asked to clarify the restrictiveness of the assumptions, particularly in relation to the negative assortative regime, but this is a presentation/robustness issue rather than a fundamental problem. I would not expect this to require more than one round of revision."},"author_rebuttal":null,"desk_editor":{"model":"glm-5.2","letter":"The main thing to know: this paper jointly characterizes optimal evaluation distortion and assignment sorting in a two-network environment, and the central result is clean. When effort matters more for output (s > s*), the planner lowers the effort weight in evaluation and uses negative assortative assignment to create disadvantaged agents who work harder. When advantage matters more (s < s*), the planner raises the effort weight and sorts positively to exploit spillovers. The evaluation rule systematically deviates from true output, and the sign of assortative matching flips at a derived cutoff. That flipping prediction is genuinely new and testable. The Katz-centrality effort result builds on Ballester et al. (2006) but the joint design layer is the real contribution. Proofs are detailed and the equilibrium characterization (Proposition 1) is tight. The pairwise stability extension (Section 4) adds a useful decentralized-assignment constraint with a clean monotonicity result for stability loss in competition intensity. The reader's verdict of conditional with high confidence is about right. The stress-test concern about Assumption 2 is valid and well-stated. The assumption requires the non-discretionary component to stay in a specific interval for every assignment, every position, and every ω in the active-contest region. This is most binding exactly under negative assortative assignment with heterogeneous types and unequal spillover structure—which is the policy the planner wants when s > s*. So the assumption bites hardest in the empirically interesting case. Appendix A.6 gives two sufficient conditions for restricting to the interior region to be without loss, but these are themselves demanding and the paper acknowledges this. I do not think this is fatal. The results are correct within their stated domain, the authors are transparent about the restriction, and the comparative statics are still informative. But a referee should push them to either characterize what happens when the assumption fails or give a clearer sense of how large the admissible parameter region is. The model is purely theoretical with no data, but the predictions are sharp enough to motivate empirical work. The sorting-by-aggregate-spillover-value prediction (not just diagonal terms) and the stability-loss comparative statics are the most novel and falsifiable implications. This deserves a serious referee. The math is careful, the synthesis is new, and the soft spot is a technical restriction that the authors flag rather than hide.","headline":"Solid theory of joint evaluation-and-assignment design; the interior-equilibrium assumption is load-bearing but the paper is honest about it.","tokens_in":35131,"tokens_out":561,"would_cite":true,"duration_ms":81840,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"glm-5.2","headline":"Optimal evaluation deliberately distorts away from true output","keywords":["relative performance evaluation","worker assignment","organizational design","incentives","contests","network games","peer effects","spillovers"],"falsifier":"If in real organizations the non-discretionary advantage distribution is highly dispersed (some workers have overwhelming advantages or severe disadvantages), corner equilibria with zero-effort agents would arise, invalidating the closed-form characterization and the clean sorting predictions.","tokens_in":34602,"feed_emoji":"⚖️","tokens_out":1078,"duration_ms":129682,"temperature":0.7,"pith_summary":"This paper studies how an organization should jointly design two things: the rule used to evaluate workers' performance, and the assignment of workers to positions. Workers compete against peers linked by a competition network, while their non-discretionary advantages (talent, mentoring, reputation) propagate through a separate spillover network. The planner maximizes true output, which depends on both effort and advantage, but gets to choose an evaluation rule that can deliberately over- or under-weight effort relative to advantage. The central result is that the optimal evaluation rule almost never coincides with true output. When effort matters more for output, the planner should underweight effort in evaluation and assign high-ability workers to low-spillover positions (negative assortative assignment), creating disadvantage that drives agents to work harder. When advantage matters more for output, the planner should overweight effort in evaluation and assign high-ability workers to high-spillover positions (positive assortative assignment), exploiting spillovers while preventing advantaged agents from coasting. The cutoff between these two regimes depends on the intensity of competition: denser benchmarking networks push the planner toward the incentive-generating negative-sorting regime.","feed_headline":"Optimal evaluation deliberately distorts away from true output","feed_subtitle":"A planner who jointly chooses evaluation rules and worker assignment should overweight or underweight effort depending on whether incentives","key_machinery":"The model uses two networks: a competition network W governing benchmarking comparisons, and a spillover network M governing how fixed types propagate. Equilibrium effort takes a closed form involving Katz-Bonacich centrality q = (I - beta W)^{-1} 1 of the competition network and the spillover-weighted type vector. The planner's problem reduces to maximizing a one-dimensional criterion in the assignment, with the sign of (1 - s/omega) determining whether to maximize or minimize total effective advantage. A cutoff s* separates the positive-assortative regime from the negative-assortative regime. Under pairwise stability with transferable utility and symmetric M, stable assignments sort by the","core_discovery":"The paper's central mechanism is a complementarity between evaluation distortion and assignment sorting. The planner's objective decomposes into a term depending on total effort (driven by the evaluation weight and Katz-Bonacich centrality in the competition network) and a term depending on total effective advantage (driven by the assignment and the spillover network). Because equilibrium effort is decreasing in effective advantage, the planner can use assignment as an effort-inducing instrument: minimizing total advantage creates disadvantaged agents who compensate through harder work. The evaluation weight controls how strongly advantage depresses effort, so the planner tunes it jointly. A","pith_inferences":["The model implies that organizations using forced-ranking or calibration systems with many comparison links should exhibit different assignment patterns than those with sparse benchmarking, even holding worker quality fixed.","If the spillover network were endogenous to agent behavior (e.g., agents choosing to interact less with direct competitors), the planner's optimal evaluation weight would likely shift further from true output to compensate for the reduced spillover channel.","The framework could extend to dynamic settings where assignment affects learning and type evolution, potentially creating a path-dependence where early assignments lock in advantage distributions that future evaluation rules must accommodate."],"forward_implications":["Organizations with denser peer-comparison networks should be more likely to use negative assortative assignment, placing talented workers in less connected roles to create effort incentives.","Reforms that increase the weight on effort in evaluation should raise effort disproportionately among workers who previously enjoyed large non-discretionary advantages.","When workers can privately swap tasks, observed assignment sorting reflects private positional advantage rather than the organization's spillover objective, creating a measurable wedge between decentralized and optimal assignment.","The output loss from decentralized assignment constraints decreases with competition intensity when the first best uses positive assortative assignment, but increases when the first best uses negative assortative assignment.","The sign of assortative matching between worker ability and position spillover centrality should flip depending on whether the evaluation rule overweights or underweights effort relative to true production technology."],"fun_headline_variants":["Evaluation distortion and worker assignment are complementary instruments","Optimal assignment sorting depends on evaluation weight choice","Disadvantaging workers can raise equilibrium effort under optimal evaluation","Planner distorts evaluation to leverage network position and spillovers","Competition networks make effort depend on Katz-Bonacich centrality"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The model assumes that for all relevant evaluation weights, assignments, and positions, every agent's non-discretionary advantage falls in a range ensuring they all exert strictly positive effort in equilibrium. If advantage is too extreme, some agents give up entirely, the closed-form effort expression breaks down, and the planner's optimization results no longer hold.","fun_headline_variants_meta":{"raw":{"variants":["Evaluation distortion and worker assignment are complementary instruments","Optimal assignment sorting depends on evaluation weight choice","Disadvantaging workers can raise equilibrium effort under optimal evaluation","Planner distorts evaluation to leverage network position and spillovers","Competition networks make effort depend on Katz-Bonacich centrality"]},"model":"glm-5.2","effort":"low","cost_usd":0.0,"raw_usage":{"total_tokens":562,"prompt_tokens":481,"completion_tokens":81,"prompt_tokens_details":null},"tokens_in":481,"tokens_out":81,"duration_ms":65277,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-09T15:13:21.856707+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"If in real organizations the non-discretionary advantage distribution is highly dispersed (some workers have overwhelming advantages or severe disadvantages), corner equilibria with zero-effort agents would arise, invalidating the closed-form characterization and the clean sorting predictions.","supporting_citations":[],"review_version":1}