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1. Sequential Veto Bargaining With Incomplete Information

   https://doi.org/10.3982/ECTA20658  

   Ali, S. Nageeb; Kartik, Navin; Kleiner, Andreas (January 2023, Econometrica)

   We study sequential bargaining between a proposer and a veto player. Both have single‐peaked preferences, but the proposer is uncertain about the veto player's ideal point. The proposer cannot commit to future proposals. When players are patient, there can be equilibria with Coasian dynamics: the veto player's private information can largely nullify proposer's bargaining power. Our main result, however, is that under some conditions there also are equilibria in which the proposer obtains the high payoff that he would with commitment power. The driving force is that the veto player's single‐peaked preferences give the proposer an option to “leapfrog,” that is, to secure agreement from only low‐surplus types early on to credibly extract surplus from high types later. Methodologically, we exploit the connection between sequential bargaining and static mechanism design. 

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2. Simple Delegated Choice

   Khobadahksh, A; Pountourakis, E; Taggart, S (January 2024, LivingOnTrack)

   Woodruff, D (Ed.)

   This paper studies delegation in a model of discrete choice. In the delegation problem, an uninformed principal must consult an informed agent to make a decision. Both the agent and principal have preferences over the decided-upon action which vary based on the state of the world, and which may not be aligned. The principal may commit to a mechanism, which maps reports of the agent to actions. When this mechanism is deterministic, it can take the form of a menu of actions, from which the agent simply chooses upon observing the state. In this case, the principal is said to have delegated the choice of action to the agent. We consider a setting where the decision being delegated is a choice of a utility-maximizing action from a set of several options. We assume the shared portion of the agent's and principal's utilities is drawn from a distribution known to the principal, and that utility misalignment takes the form of a known bias for or against each action. We provide tight approximation analyses for simple threshold policies under three increasingly general sets of assumptions. With independently-distributed utilities, we prove a 3-approximation. When the agent has an outside option the principal cannot rule out, the constant-approximation fails, but we prove a log ρ/ log log ρ-approximation, where ρ is the ratio of the maximum value to the optimal utility. We also give a weaker but tight bound that holds for correlated values, and complement our upper bounds with hardness results. One special case of our model is utility-based assortment optimization, for which our results are new. 

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3. Simple Delegated Choice

   Khodabakhsh, Ali; Pountourakis, Emmanouil; Taggart, Samuel (January 2024, Society for Industrial and Applied Mathematics)

   This paper studies delegation in a model of discrete choice. In the delegation problem, an uninformed principal must consult an informed agent to make a decision. Both the agent and principal have preferences over the decided-upon action which vary based on the state of the world, and which may not be aligned. The principal may commit to a mechanism, which maps reports of the agent to actions. When this mechanism is deterministic, it can take the form of a menu of actions, from which the agent simply chooses upon observing the state. In this case, the principal is said to have delegated the choice of action to the agent. We consider a setting where the decision being delegated is a choice of a utility-maximizing action from a set of several options. We assume the shared portion of the agent's and principal's utilities is drawn from a distribution known to the principal, and that utility misalignment takes the form of a known bias for or against each action. We provide tight approximation analyses for simple threshold policies under three increasingly general sets of assumptions. With independently-distributed utilities, we prove a 3-approximation. When the agent has an outside option the principal cannot rule out, the constant-approximation fails, but we prove a log ρ/ log log ρ-approximation, where ρ is the ratio of the maximum value to the optimal utility. We also give a weaker but tight bound that holds for correlated values, and complement our upper bounds with hardness results. One special case of our model is utility-based assortment optimization, for which our results are new. 

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4. Anonymous and Copy-Robust Delegations for Liquid Democracy

   Utke, Markus; Schmidt-Kraepelin, Ulrike (January 2023, Advances in neural information processing systems)

   Oh, A; Naumann, T; Globerson, A; Saenko, K; Hardt, M; Levine, S (Ed.)

   Liquid democracy with ranked delegations is a novel voting scheme that unites the practicability of representative democracy with the idealistic appeal of direct democracy: Every voter decides between casting their vote on a question at hand or delegating their voting weight to some other, trusted agent. Delegations are transitive, and since voters may end up in a delegation cycle, they are encouraged to indicate not only a single delegate, but a set of potential delegates and a ranking among them. Based on the delegation preferences of all voters, a delegation rule selects one representative per voter. Previous work has revealed a trade-off between two properties of delegation rules called anonymity and copy-robustness. To overcome this issue we study two fractional delegation rules: Mixed Borda branching, which generalizes a rule satisfying copy-robustness, and the random walk rule, which satisfies anonymity. Using the Markov chain tree theorem, we show that the two rules are in fact equivalent, and simultaneously satisfy generalized versions of the two properties. Combining the same theorem with Fulkerson's algorithm, we develop a polynomial-time algorithm for computing the outcome of the studied delegation rule. This algorithm is of independent interest, having applications in semi-supervised learning and graph theory. 

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5. Veto Threat Bargaining with a Bicameral Congress

   https://doi.org/10.1177/1065912920925917  

   Guenther, Scott_M; Kernell, Samuel (June 2020, Political Research Quarterly)

   According to the conventional view, presidents are largely bereft of influence with an opposition-controlled Congress. Congress sends them legislation with a “take it or leave it” choice that maximizes the preferences of the opposition majority while minimizing presidents’ preferences. To extricate themselves from this bind, presidents threaten vetoes. Past research suggests that their efforts largely fail, however, for two model-driven reasons: first, veto threats amount to minimally informative “cheap talk,” and second, Congress is a unitary actor with firm control over its agenda. We relax both assumptions, bringing veto rhetoric into a setting more closely resembling real-world conditions. Presidents transmit credible veto threats to a heterogeneous, bicameral Congress where chamber rules enable the minority party to wield some influence over legislation. Examining the legislative histories of all veto-threatened bills passed between 1985 and 2016, we confirm that veto threats ward off about half of veto-targeted legislative provisions—a far greater share than for comparable unthreatened provisions. The House of Representatives is more likely to introduce and pass legislation objectionable to presidents and the Senate is more likely to accommodate presidents, findings consistent with the textbook description of the modern bicameral Congress. 

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