The Cost of Proportional Representations in Electoral System Design (Economic Theory Bulletin (2024, 12:47–56)
Firms may assess prospective workers using data from markets in which the current assignment continues. Those forecasts affect which markets continue and therefore which observations shape later forecasts. A continuation conjecture is self-validating when it retains exactly the profiles that its own forecasts classify as unblocked. Removal makes exclusions permanent, whereas reassessment reconsiders the full type space after forecasts change. In one two-worker market, set-wide removal and the two pairwise orders lead to three different outcomes; from any positive-probability rectangle, every fair order of pairwise reassessment reaches the same self-validating event. In our network model, self-validation exists exactly when every feedback cycle contains a link at which candidate productivity matters less than incumbent productivity. Under a regularity condition, reassessment converges globally and is order independent. With common firm values, existence reduces to acyclicity. Within this benchmark, with strict rankings and universal acceptability, the self-validating assignments are exactly the worker-Pareto-efficient assignments.
(Part of this paper subsumes Weak and Strong Bayesian Stability which is a chapter in my dissertation.)
Allowing for any restrictions on bid spaces, we show that the first-price auction for- mat is sufficiently flexible to achieve in equilibrium any Bayesian-constrained standard objective, including maximizing or minimizing revenue, welfare, bidder surplus, and Gini mean difference as well as linear combinations of them. This first-price principle allows us to analyze problems that are beyond the scope of Myersonian mechanism design. Our further results simplify the analysis of first price auctions with arbitrary bid spaces and establish the existence of monotonic pure-strategy equilibria in these auctions.
(Part of this paper subsumes Auctions with Designed Bid Spaces, which is a chapter in my dissertation.)
Abstract: We study an optimal selection problem, such as college admissions, hiring processes, and resource distribution, where the principal seeks to maximize utility by selecting a subset of objects from different groups. The principal relies on an informed agent to assess unobservable attributes that affect the decision. We consider mechanisms in which the principal commits to a selection rule, and the agent reports the attributes of objects. We show that the optimal mechanism can be implemented through quota-based mechanisms with at most two tiers, where the principal sets quotas for objects to be selected with certainty (first tier) and via lottery (second tier), delegating the selection of objects for each quota to the agent. A single-tier quota suffices to achieve the first-best outcome when preferences are aligned. Our results demonstrate that quota-based mechanisms are not only optimal but also simple and tractable, providing a framework for characterizing optimal mechanisms across various real-world applications.
(SSRN: https://dx.doi.org/10.2139/ssrn.4031432)
Abstract: We study the impact of school choice on segregation. It shows that the popular school choice mechanisms lead to substantially different school and residential segregation, an important and overlooked aspect of choosing among school choice mechanisms. We show that open enrollment policy in public school choice program can decrease diversity of individual schools and increase segregation depending on which student allocation mechanism is used. Without open enrollment, we study the model of location choice and show that segregation is mainly associated with income. In comparing mechanisms, we show that Boston mechanism fosters segregation more than the deferred acceptance. If income and other characteristics are affiliated, the difference between BM and DA becomes more drastic. With open enrollment, another form of segregation can occur. We compare different student allocation mechanisms under open enrollment and show that Boston mechanism can worsen segregation and decrease diversity of individual schools. The deferred acceptance with multi tie breaking creates maximally diverse schools.
Abstract: This paper studies one-to-one matching environment without transfer in the presence of incomplete information on one-side. The existing notions of stability under incomplete information are studied and two alternatives are proposed. Weak Bayesian stability requires that the beliefs of the agents are derived from a common prior via Bayes’ rule and are internally consistent with the presumption that the given matching is stable. Strong Bayesian stability refines weak Bayesian stability by requiring the beliefs of agents are also externally consistent in the sense that the beliefs are narrowed down only when there is a valid reason.
Robust Mechanism for Public Goods. (with Pasha Andreyanov and Jernej Copic)
Abstract: We study mechanisms for robust allocation of a divisible public good among n agents with quasi-linear utilities, when the budget is exactly balanced. Under several additional assumptions, we prove that such mechanism is equivalent to a distribution over simple posted prices. A robustly optimal mechanism minimizes expected welfare loss among robust divisible ones. For any prior belief, we show that a simple posted prices is robustly optimal. This justifies a restriction to binary allocations commonly found in the mechanism design literature. Robustness comes at a high cost. For certain beliefs, we show that the expected welfare loss of an optimal posted price is as big as 1/2 of the expected welfare in the corresponding optimal Bayesian mechanism, independently of the size of the economy. This bound is tight for the special case of two agents.