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 formal model builds on the citizen-candidate tradition (Osborne–Slivinski; Besley-Coate). It’s an interesting thought experiment: people are solely motivated by the desire to implement their preferred policies. They achieve it by running for office. People face a fixed cost of entry and the payoff is some function to how far the implemented policy is from their ideal point. Once elected, people face no pressure to bring their positions closer to the median voter as they do not care about anything other than policy. Along with these heroic assumptions are the relatively more mundane ones like a one dimensional policy space (0 to 1; hello American political scientists!), and that the voters are rational and fully informed. However, the conclusion that the policy can be different from the median is driven primarily by selective entry (and no pressure of the median voter).

C & D add to this setup in a few ways. First, they contend that women face a higher entry cost than men. Second, they assume that women’s ideal points are distributed on ([0,W]) and men’s on ([M,1]). (The overlap between M and W is large according to the data in the paper and if we are speaking about ranges then W is 1 and M is 0 in the data.) Third, they argue that there is some political capture by the right that biases final implemented policy to the right (touché, MAGA deep state warriors!) and is fixed and exogenous.

Given the setup, three results almost immediately fall out:

1. 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.
2. Reservation shifts policy left by forcing the candidate pool to be female (straight up implication of assumption #3).
3. Reservation raises the welfare of the median voter when the proximity to median voter ideal point is best achieved by women. (This includes all the cases where women outnumber men, etc.)

Criticism and the Growth of Knowledge

1. The welfare claim is a second-best result with an illiberal shape. Holding fixed who is willing/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 voter would like to choose under GEN do not enter (because of the gendered entry-cost wedge and the equilibrium logic that keeps women out). That’s exactly what Proposition 1 is for: it constructs a world where the median cannot “just elect the woman anyway” because she never appears on the ballot. That is not a deep theorem about quotas but a second-best fix to a postulated failure of entry. The claim is: “We can increase "welfare" by banning half the people from running for office.”
2. In more left-leaning constituencies, women should emerge without quotas. Proposition 1 gives 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
3. “Welfare” here is not social welfare; it is (at best) median-voter utility. Even taking their one-dimensional setup at face value, this is not remotely a Pareto claim. If reservation moves outcomes left, voters on the right lose. So “median voter closer to the implemented policy” is not “society is better off.” It is a narrow, median-centric comparison. The danger is rhetorical: the language makes it easy to slide into “reservation is efficient,” when what is actually shown is much narrower, and deeply distributional.
4. The entry-cost story is not identified. The paper’s formal explanation for why women rarely lead absent reservation is: women have higher entry costs, and that can keep them from running. But “women underrepresentation in leadership” can come from many mechanisms, including ones that are not well-described as distortions: different occupational preferences, different returns to political careers, differential taste for public conflict, household bargaining constraints, party gatekeeping and recruitment, etc.
5. Capture is both (i) load-bearing and (ii) 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 the paper itself immediately lists “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. Also, their rhetorical line—capture “moderates women… while it makes men more extreme”—is not a neutral analytic statement. “Extreme” is defined relative to their assumed median and the assumed ordering of men vs women on the policy line. Flip the sign of capture, or flip where the median sits, and the label reverses.
6. No credible platforms? The model assumes that candidates cannot commit to platforms and once elected, they implement what they like. As a way to avoid Downsian convergence, that assumption is common in theory. But treating it as a general representation of democracy is highly contestable because real democracies have partial commitment technologies like repeated elections, party reputation, career concerns, intra-party discipline, and voter punishment for betrayal. Politicians also want more things than executing their preferred policy. And even if they want to execute on their preferred policy, they may go about building support by persuading people and changing the ideal points before executing on the policy.
   
   If voters can hold representatives accountable for the policies they execute, the model collapses (see Alesina 1988).
   
   The paper discusses how rotation creates different incentives but remember rotation (reserve or not) is the policy being adopted. If it were not being adopted, the conditions motivating the analysis would not exist. But let's interrogate rotations:
   1. Under rotation (including 50/50-style alternation, which is now the policy in most Indian states), discipline can be imposed through party reputation and future contests (especially because "generally nominated by political parties"; pg. 1412), family-linked candidacies and “handoffs” (which the paper’s own descriptive stats suggest are nontrivial), ambitions to contest the election next time around, etc.
   2. Entry costs should not “reset” after a quota cycle. If the barrier is truly an entry cost​, then 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 constant wedge.
7. When is the citizen-candidate model a reasonable representation of democracy? The model's most fundamental limitation is treating 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 act as entrepreneurs of preference. They use rhetoric, framing, and information to move the median voter, not merely locate it. Consider marriage equality: this did not succeed because a citizen-candidate finally appeared who matched pre-existing voter 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.

Conclusion

The model’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, not a democratic ethic. And second-best theorems are famously promiscuous: change the sign of the distortion and you can justify the opposite restriction. The democratic (and might I say economic —standard pet peeve of economists) instinct is to target the distortion directly, not by narrowing political rights. In the model’s own terms, the direct interventions would be things like: reduce the entry wedge $\delta_w$​ (safety, campaign finance/support, childcare constraints, party recruitment reforms), reduce capture (change who attends/controls assemblies, transparency, accountability, monitoring), etc.

Related: https://www.gojiberries.io/first-assume-no-elections/