Optimal Impartial Selection

This is the final version of the article. It first appeared from Society for Industrial and Applied Mathematics via http://dx.doi.org/10.1137/140995775We study a fundamental problem in social choice theory, the selection of a member of a set of agents based on impartial nominations by agents from that set. Studied previously by Alon et al. [Proceedings of TARK, 2011, pp. 101--110] and by Holzman and Moulin [Econometrica, 81 (2013), pp. 173--196], this problem arises when representatives are selected from within a group or when publishing or funding decisions are made based on a process of peer review. Our main result concerns a randomized mechanism that in expectation selects an agent with at least half the maximum number of nominations. This is best possible subject to impartiality and resolves a conjecture of Alon et al. Further results are given for the case where some agent receives many nominations and the case where each agent casts at least one nomination

A Near-Optimal Mechanism for Impartial Selection

We examine strategy-proof elections to select a winner amongst a set of agents, each of whom cares only about winning. This impartial selection problem was introduced independently by Holzman and Moulin and Alon et al. Fisher and Klimm showed that the permutation mechanism is impartial and $1/2$-optimal, that is, it selects an agent who gains, in expectation, at least half the number of votes of most popular agent. Furthermore, they showed the mechanism is $7/12$-optimal if agents cannot abstain in the election. We show that a better guarantee is possible, provided the most popular agent receives at least a large enough, but constant, number of votes. Specifically, we prove that, for any $\epsilon>0$, there is a constant $N_{\epsilon}$ (independent of the number $n$ of voters) such that, if the maximum number of votes of the most popular agent is at least $N_{\epsilon}$ then the permutation mechanism is $(\frac{3}{4}-\epsilon)$-optimal. This result is tight. Furthermore, in our main result, we prove that near-optimal impartial mechanisms exist. In particular, there is an impartial mechanism that is $(1-\epsilon)$-optimal, for any $\epsilon>0$, provided that the maximum number of votes of the most popular agent is at least a constant $M_{\epsilon}$

Deterministic Impartial Selection with Weights

In the impartial selection problem, a subset of agents up to a fixed size $k$ among a group of $n$ is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of being selected by changing its vote. It is $\alpha$-optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of $\alpha$ of the votes received by the subset of size $k$ with the highest number of votes. We study deterministic impartial mechanisms in a more general setting with arbitrarily weighted votes and provide the first approximation guarantee, roughly $1/\lceil 2n/k\rceil$. When the number of agents to select is large enough compared to the total number of agents, this yields an improvement on the previously best known approximation ratio of $1/k$ for the unweighted setting. We further show that our mechanism can be adapted to the impartial assignment problem, in which multiple sets of up to $k$ agents are to be selected, with a loss in the approximation ratio of $1/2$.Comment: To appear in the Proceedings of the 19th Conference on Web and Internet Economics (WINE 2023

A robust approach to model-based classification based on trimming and constraints

In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations, namely outliers and data with incorrect labels, can strongly undermine the classifier performance, especially if the training size is small. The present work introduces a robust modification to the Model-Based Classification framework, employing impartial trimming and constraints on the ratio between the maximum and the minimum eigenvalue of the group scatter matrices. The proposed method effectively handles noise presence in both response and exploratory variables, providing reliable classification even when dealing with contaminated datasets. A robust information criterion is proposed for model selection. Experiments on real and simulated data, artificially adulterated, are provided to underline the benefits of the proposed method

Money, Politics, and Impartial Justice

A centuries-old controversy asks whether judicial elections are inconsistent with impartial justice. The debate is especially important because more than 90 percent of the United States\u27 judicial business is handled by state courts, and approximately nine in ten of all state court judges face the voters in some type of election. Using a stunning new data set of virtually all state supreme court decisions from 1995 to 1998, this paper provides empirical evidence that elected state supreme court judges routinely adjust their rulings to attract votes and campaign money. I find that judges who must be reelected by Republican voters, especially in partisan elections, tend to decide cases in accord with standard Republican policy: they are more likely to vote for businesses over individuals, for employers in labor disputes, for doctors and hospitals in medical malpractice cases, for businesses in products liability cases and tort cases generally, and against criminals in criminal appeals. Judicial behavior is correspondingly liberal for judges facing reelection by Democrats. Moreover, I find evidence that judges change their rulings when the political preferences of the voters change. In addition, my analysis finds a strong relationship between campaign contributions and judges\u27 rulings. Contributions from pro-business groups, pro-labor groups, doctor groups, insurance companies, and lawyer groups increase the probability that judges will vote for the litigants favored by those interest groups. The results suggest that recent trends in judicial elections-elections becoming more contested, competitive, and expensive-may have upset the delicate balance between judicial independence and accountability. I discuss various policy solutions for reforming states\u27 systems

Decision rules and information provision: monitoring versus manipulation

The paper focuses on the organization of institutions designed to resolve disputes between two parties, when some information is not veri…able and decision makers may have vested preferences. It shows that the choice of how much discretional power to grant to the decision maker and who provides the information are intrinsically related. Direct involvement of the interested parties in the supply of information enhances monitoring over the decision maker, although at the cost of higher manipulation. Thus, it is desirable when the decision maker is granted high discretion. On the contrary, when the decision maker has limited discretional power, information provision is better assigned to an agent with no direct stake. The analysis helps to rationalize some organizational arrangements that are commonly observed in the context of judicial and antitrust decision-makin

A Theory of Advocates: Trading Advice for Inuence

An advocate for a special interest provides information to an uninformed planner for her to consider in making a sequence of important decisions. Although the advocate may have valuable information for the planner, it is is also known that the advocate is biased and will distort her advice if necessary to ináuence the plannerís decision. Each time she repeats the problem, however, the planner learns about the accuracy of the advocateís recommendation, mitigating some of the advocateís incentive to act in a self-serving manner. We propose a theory of advocacy to explain why planners do sometimes rely on information provided by advocates in making decisions. The interaction takes place in two stages, a cheap talk recommendation from the advocate, followed by decisions and learning by the planner. The theory predicts conditions under which an advocateís advice will be ignored and when it will ináuence a plannerís decision, when planners will prefer the advice of an advocate to the advice of a neutral adviser and, Önally, how an advocate gains ináuence with a decision maker by making his preferences for action unpredictable. Applications of our theory are used to explain why regulated enterprises are sometimes delegated authority to determine how they are monitored and why some consumers of Önancial services give Önancial advisors who beneÖt from their business such great latitude in managing their investments and Önances.Advocates, Advocacy, Learning, Cheap Talk, Dynamic Contract