By Gaurav — 04 Jan 2026

When the Fix Is Another Distortion: Quotas as Second-Best Engineering

Chattopadhyay and Duflo (2004) (hereafter C&D) contains a formal model that builds a world where a striking normative implication becomes possible: “welfare” (in the paper’s narrow sense) can rise when you ban half the people from running for office. The paper says this pretty directly: “...reservation may make the median voter… better off...”

The model is an interesting thought experiment in the citizen-candidate tradition (Osborne–Slivinski; Besley-Coate). But like most useful thought experiments, it earns its insights by spending a lot of realism. The key question is not “is the model true?” but “what assumptions does the provocative welfare result actually require?” Once you put the assumptions on the table, the welfare claim looks less like a general lesson about quotas and more like a particular second-best possibility in a very particular political technology.

The Model

Start with a standard citizen-candidate environment. Citizens are solely motivated by the desire to implement their preferred policies. They can do so by running for office. Running has a fixed cost of entry. Payoffs depend on the distance between the implemented policy and the citizen’s ideal point. Once elected, candidates face no pressure to move toward the median voter: they do not care about rents, re-election, party advancement, reputation, or anything besides policy.

Layered on top are the more “mundane” (but still consequential) simplifications: a one dimensional policy space (0 to 1; hello American political scientists!), rational and fully informed voters, and an equilibrium driven by selective entry (since nothing forces convergence to the median).

C&D then add three key ingredients:

Gendered entry costs: women face a higher entry cost than men.
Gendered supports for ideal points: women’s ideal points are distributed on [0,W], men's on[M,1]. (This is explicitly acknowledged by the authors as “quite extreme,” and their own descriptive evidence suggests substantial overlap in preferences, with both men and women ranging from 0 to 1.)
Right-biased political capture: there is an exogenous “capture” force that biases implemented policy to the right (touché, MAGA deep state warriors!), and it is fixed and external to the institutional choice.

Given the setup, three results almost immediately fall out:

Without reservation, women may not run even if the constituency has “pro-women” preferences, because the private cost of entry is too high relative to the benefit of winning.
Reservation shifts policy left by forcing the candidate pool to be female (a direct implication of the gendered-support assumption).
Reservation can raise the median voter’s utility when the candidate closest to the median is more likely to be female, including cases where women outnumber men, and cases where reservation provides a “counterweight” to right-biased capture.

Criticism and the Growth of Knowledge

C&D’s “reservation can raise welfare” result is best understood as a second-best theorem that relies on a specific stack of assumptions. The result needs:

An entry distortion: women’s higher entry costs keep relevant women off the ballot under general elections (GEN).
A “menu effect”: gender changes the set of feasible policy types (via the restricted supports [0,W] vs. [M,1]).
Right-biased capture: μ>m, where mmm is the median voter’s ideal point.
Weak accountability / no credible commitment: elected officials implement their own ideal points rather than being disciplined toward the median.

We interrogate these assumptions and the model more generally.

C&D’s welfare narrative effectively needs gender to alter the menu of feasible candidate types. Their model accomplishes this by separating the support of men’s and women’s ideal points. But their own descriptive evidence suggests a more mixed reality, and it helps to separate two empirically plausible regimes.

Case 1: complete overlap with no meaningful gender difference in preferences. If men and women draw from essentially the same distribution of ideal points, then the “identity shifts policy” channel disappears. Reservation cannot systematically move policy left through preference differences, because gender is not informative about policy type.

Case 2: overlap, but different distributions of priorities. Men and women may want many of the same goods, yet differ in the distribution of priorities (which fits C&D’s finding that the composition of requests differs by gender). In this case, policy differences can still arise, but the provocative welfare claim—reservation can make the median voter better off by supplying a counterweight to right-biased capture—becomes harder to sustain without extra structure.

Why? If men’s support includes “left-of-m” counterweight types too, and men have lower entry costs, then under GEN one would expect those left-leaning men to be among the first to enter and win. That makes the story “reservation gives voters access to counterweights they otherwise cannot get” much harder to maintain unless you also explain why left-leaning men do not enter or cannot win. This is precisely why the restriction-of-support assumption [0,W] for women versus [M,1] for men—acknowledged as extreme—does real conceptual work in the welfare claim: it quietly prevents men from supplying the same counterweight types.

Entry Barriers: The Exclusion Story Strains Where Counterweights Should Matter Most

Proposition 1 provides sufficient conditions under which no woman runs under GEN. One of those conditions is:

$\delta_w - \sqrt{5} \delta_m > \mu - m$

Now imagine heterogeneity across constituencies in ($m$) (median voter ideology). Hold the capture point ($\mu$) roughly constant (or at least not perfectly tracking ($m$)), and recall the paper assumes $\mu > m$.

In left-leaning constituencies, ($m$) is smaller, so ($\mu - m$) is larger. That makes the inequality harder to satisfy. The “no woman runs” result, thus, becomes less plausible exactly where the median voter should value a left counterweight most.

Put differently: if capture is systematically right-biased, then the places that most want a left counterweight are the places where women should have the strongest electoral case under GEN. Keeping women out in those places requires either extremely large and rigid entry costs for women, or some additional gatekeeping structure.

Capture Is Load-Bearing, but Treated as Exogenous

Capture ($\mu$) is the lever that turns “women leaders shift policy” into “reservation can raise the median voter’s welfare.” Without a right-biased ($\mu > m$), the counterweight logic collapses.

But capture is treated as fixed and exogenous despite the paper itself listing “obvious and important limitations,” including that ($\mu$) could be influenced by reservation: when the Pradhan is a woman, it may become easier for women to influence policy ex post, shifting ($\mu$) left. So even the authors flag that “fixed, exogenous capture” is shaky. Once ($\mu$) is endogenous to leader identity, you no longer have a clean “women offset capture” story; you may instead have “reservation changes the capture process itself,” which is a different mechanism entirely.

There’s also a rhetorical issue hiding in the background. Lines like capture “moderates women… while it makes men more extreme” sound analytic but are sign-dependent: “extreme” is defined relative to the assumed ordering of men versus women on the policy line, and relative to where $m$ and $\mu$ sit. Flip the sign of capture or flip the ordering and the labels reverse. That doesn’t refute the model; it just underlines how much interpretive weight is being placed on a fixed directional wedge.

"Welfare" Here Is Median-Voter Utility, and the Result Is Second-Best by Construction

Even granting the one-dimensional setup, “welfare” here is not social welfare; it is (at best) the median voter’s utility. It is not a Pareto claim and not “efficiency” in any broad sense. If reservation shifts outcomes left, voters on the right lose. So “the median is closer to the implemented policy” is not “society is better off.” It is a narrow, median-centric comparison with distributional consequences.

More importantly, the welfare claim has an illiberal shape because it is second-best by construction. Holding fixed who is willing and able to run, reservation cannot expand the feasible set of candidate choices; it shrinks it. Therefore, reservation can only “improve welfare” in the model if GEN is assumed to fail in a very specific way: the candidates the median would like to choose under GEN do not enter, because the entry-cost wedge and equilibrium logic keep women out. That is exactly what Proposition 1 constructs: a world where the median cannot “just elect the woman anyway” because she never appears on the ballot.

C&D’s welfare result is not “quotas are good.” It is: “if the political system is already distorted (entry barriers + capture), then an additional distortion (eligibility restriction) can sometimes move the median outcome closer to ideal.” That is a second-best theorem.

Second-best theorems are famously promiscuous: change the sign of the distortion and you can justify the opposite restriction. The democratic (and, frankly, standard economic) instinct is to target the distortion directly rather than narrow political rights. In the model’s own terms, the direct interventions would be things like:

reducing the entry wedge δw (safety, campaign finance/support, childcare constraints, party recruitment reforms),
reducing capture (who attends/controls assemblies, transparency, accountability, monitoring),
and strengthening accountability/commitment mechanisms so policy is not purely a function of who enters.

Missing Politics: Accountability, Parties, Reputation, and Preference Formation

The model assumes candidates cannot credibly commit to platforms and, once elected, implement what they like. This is a common way to avoid Downsian convergence in theory, but it is highly contestable as a general representation of democracy.

Real democracies have partial commitment technologies:

repeated elections and career concerns,
party reputation and discipline (C&D note "candidates are generally nominated by political parties"; see also Cox and McCubbins 1993 and Rahn 1993)
family reputation and handoffs (C & D report "17% of women Pradhans in reserved GPs have a spouse who was previously elected to the Panchayat")
reputational punishment by voters for betrayal,
and politicians’ own motives beyond pure policy implementation.

If voters can hold representatives accountable for the policies they execute, the model’s “policy can sit away from the median with no corrective force” collapses (see Alesina 1988).

Even more fundamentally, the model treats voter preferences as exogenous—fixed external variables that candidates observe and respond to. This reduces democracy to a matching problem: given a distribution of voter ideal points, which citizens find it worthwhile to run?

In practice, successful politicians are entrepreneurs of preference. They use rhetoric, framing, and information to move the median voter, not merely locate it. Consider marriage equality: it did not succeed because a citizen-candidate finally appeared who matched pre-existing median demand. It succeeded because advocates and leaders shifted the information environment, changing what the median voter regarded as reasonable. The “center” moved; candidates didn’t just find it.

Dynamics and Rotation: Entry Costs Shouldn’t “Reset”

The paper discusses how rotation changes incentives, but rotation (reserve or not) is the policy being adopted; if it were not being adopted, the specific institutional environment motivating the analysis would not exist. Still, even under rotation—including 50/50-style alternation now common in many Indian states—discipline can persist via party reputation, future contests, family-linked candidacies and handoffs, ambitions to contest next time around, and so on.

More pointedly: if the barrier is truly an entry cost, it is hard to justify treating it as a constant wedge that resets after a quota cycle. Being forced onto the ballot under reservation plausibly changes entry costs going forward. Campaign experience, name recognition, administrative experience, training, networks, and reduced social novelty should all push toward declining marginal entry cost over time—not a permanent, rigid gap.

A dynamic extension of the model might therefore predict that the key distortion (the entry wedge) erodes with exposure, which would in turn shrink the scope for the “ban half the candidates to help the median” possibility to persist.