There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Lecture Notes in Economics and Mathematical Systems

A unifying theme in the literature on organizations such as public bureaucracies and private nonprofits is the importance of mission, as opposed to profit, as an organizational goal. Such mission-oriented organizations are frequently staffed by motivated agents who subscribe to the mission. This paper studies incentives in such contexts and emphasizes the role of matching the mission preferences of principals and agents in increasing organizational efficiency. Matching economizes on the need for high-powered incentives. It can also, however, entrench bureaucratic conservatism and resistance to innovations. The framework developed in this paper is applied to school competition, incentives in the public sector and in private nonprofits, and the interdependence of incentives and productivity between the private for-profit sector and the mission-oriented sector through occupational choice. (JEL D23, D73, H41, L31) The late twentieth century witnessed a historic high in the march of market capitalism, with unbridled optimism in the role of the profit motive in promoting welfare in the production of private goods. Moreover, this generated a broad consensus on the optimal organization of private good production through privately owned competitive firms. When it comes to the provision of collective goods, no such consensus has emerged.' Debates about the relative merits of public and private provision still dominate. This paper suggests a contracting approach to the provision of collective goods. It focuses on two key issues: how to structure incentives, and the role of competition between providers. At its heart is the idea that organizations that provide collective goods cohere around a mission.2 Thus production of collective goods can be viewed as mission-oriented.

/pdf/competition-and-incentives-with-motivated-agents-x931r05hsc.pdf

Competition and Incentives with Motivated Agents

The widely publicized finding that "aid promotes growth in a good policy environment" is not robust to the inclusion of new data or alternative definitions of "aid," "policy" or "growth." The idea that "aid buys growth" is on shaky ground theoretically and empirically. It doesn't help that aid agencies face poor incentives to deliver results and underinvest in enforcing aid conditions and performing scientific evaluations. Aid should set more modest goals, like helping some of the people some of the time, rather than trying to be the catalyst for society-wide transformation.

/pdf/can-foreign-aid-buy-growth-52to66diyl.pdf

Can Foreign Aid Buy Growth

Two people, 1 and 2, are said to have common knowledge of an event E if both know it, 1 knows that 2 knows it, 2 knows that 1 knows it, 1 knows that 2 knows that 1 knows it, and so on.

Agreeing to disagree.

Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. The Shapley framework for explainability has strength in its general applicability combined with its precise, rigorous foundation: it provides a common, model-agnostic language for AI explainability and uniquely satisfies a set of intuitive mathematical axioms. However, Shapley values are too restrictive in one significant regard: they ignore all causal structure in the data. We introduce a less restrictive framework, Asymmetric Shapley values (ASVs), which are rigorously founded on a set of axioms, applicable to any AI system, and flexible enough to incorporate any causal structure known to be respected by the data. We demonstrate that ASVs can (i) improve model explanations by incorporating causal information, (ii) provide an unambiguous test for unfair discrimination in model predictions, (iii) enable sequentially incremental explanations in time-series models, and (iv) support feature-selection studies without the need for model retraining.

Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability

Markets from Networks: Socioeconomic Models of Production

/pdf/asymmetric-shapley-values-incorporating-causal-knowledge-4v507et7fl.pdf

Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability.

This paper models aid agencies as financial intermediaries that do not make a financial return to depositors, whose concern is to transfer resources to investor-beneficiaries. This leads to a problem of verifying that the agency is using donations as intended. One solution to this problem is for an agency to employ altruistic workers at below-market wages: altruistic workers, who can monitor the agency's activities, would not work at below-market rates unless it were genuinely transferring resources to beneficiaries. We consider conditions for this solution to be incentive compatible. In a model with pure moral hazard, observability of wages makes incorporation as a not-for-profit firm redundant as a commitment device. In a model with both moral hazard and adverse selection, incorporation as a not-for-profit firm can serve as a costly commitment mechanism reassuring donors against misuse of their funds. Hiring a worker of low ability can also be a valuable commitment device against fraud.

Intermediation by aid agencies

Novel auction schemes are constantly being designed. Their design has significant consequences for the allocation of goods and the revenues generated. But how to tell whether a new design has the desired properties, such as efficiency, i.e. allocating goods to those bidders who value them most? We say: by formal, machine-checked proofs. We investigated the suitability of the Isabelle, Theorema, Mizar, and Hets/CASL/TPTP theorem provers for reproducing a key result of auction theory: Vickrey's 1961 theorem on the properties of second-price auctions. Based on our formalisation experience, taking an auction designer's perspective, we give recommendations on what system to use for formalising auctions, and outline further steps towards a complete auction theory toolbox.

A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory

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