Measuring the Welfare Gains from Cardinal-Preference Mechanisms in School Choice

Hülya Eraslan, Jeremy Fox and YingHua He

No 35658, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: Ordinal mechanisms use rankings but not preference intensities. Cardinal mechanisms also elicit school utilities, allowing them to use students’ preferences over assignment lotteries. We compare probabilistic serial with four cardinal mechanisms that maximize the same welfare objective under successively stronger restrictions: capacity-only, ε-envy-free, envy-free, and a welfare-maximizing cardinal-preference pseudomarket. Because the feasible sets are nested, maximum welfare weakly falls as the restrictions tighten from capacity alone to approximate no-envy, exact no-envy, and equal budgets with common prices. We establish positive and negative results on large-market truthtelling. All 44 theorem parts in the paper are machine-checked in the Lean 4 proof assistant. We develop methods for computing cardinal-preference pseudomarket equilibria for Seattle’s 898 students and 11 schools. Using set-identified cardinal preferences from Seattle high-school choice data, we estimate that, under exact capacity, capacity-only raises mean welfare over probabilistic serial by 0.053, equivalent to shifting 5.3 percentage points of assignment probability from the average student’s worst school to the top school. Exact envy-freeness retains 79% of this gain; best-found pseudomarket equilibria yield a mean gain of 0.002. The estimates show both the value of cardinal information and the welfare cost of pseudomarket fairness restrictions.

JEL-codes: C78 I20 (search for similar items in EconPapers)
Date: 2026-08
Note: ED IO LS PE POL TWP
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.nber.org/papers/w35658.pdf (application/pdf)
Access to the full text is generally limited to series subscribers, however if the top level domain of the client browser is in a developing country or transition economy free access is provided. More information about subscriptions and free access is available at http://www.nber.org/wwphelp.html. Free access is also available to older working papers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberwo:35658

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/w35658
The price is Paper copy available by mail.

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().