Quantum voting and violation of Arrow's Impossibility Theorem

We propose a quantum voting system, in the spirit of quantum games such as the quantum Prisoner's Dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's Impossibility Theorem. Arrow's Theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's Theorem. A quantum version of majority rule, we show, violates this Quantum Arrow Conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.Comment: Version accepted by Phys. Rev. A. Added background and references about game theory and about Arrow's Theorem. Added an opportunity for further research. For citation purposes: The second author's family name is "Yunger Halpern" (not "Halpern"

Problems and Models in Strategic Air Traffic Flow Management

The thesis comprises of three essays. The first essay is titled "Do more US airports need slot controls? A welfare based approach to determine slot levels." It analyzes the welfare effects of slot controls on major US airports. We consider the fundamental trade-off between benefits from queuing delay reduction and costs due to simultaneous schedule delay increase to passengers while imposing slot limits at airports. A set of quantitative models and simulation procedures are developed to explore the possible airline scheduling responses through reallocating and trimming flights. We find that, of the 35 major US airports, a more widespread use of slot controls would improve travelers' welfare. The results from our analyses suggest that slot caps at the four airports that currently have slot controls (Washington Reagan, Newark, New York LaGuardia, New York John F. Kennedy) are set too high. Further slot reduction by removing some of the flights at these airports could generate additional benefits to passengers. Slot controls can potentially reduce two thirds of the total system delays caused by congestion. A number of implementation and design issues related to the use of slot controls are also discussed in the paper. The second essay is titled "Designing the Noah's Ark: A Multi-objective Multi-stakeholder Consensus Building Method." A significant challenge of effective air traffic flow management (ATFM) is to allow for various competing airlines to collaborate with an air navigation service provider (ANSP) in determining flow management initiatives. This challenge has led over the past 15 years to the development of a broad approach to ATFM known as collaborative decision making (CDM). A set of CDM principles has evolved to guide the development of specific tools that support ATFM resource allocation. However, these principles have not been extended to cover the problem of providing strategic advice to an ANSP in the initial planning stages of traffic management initiatives. In the second essay, we describe a mechanism whereby competing airlines provide ``consensus'' advice to an ANSP using a voting mechanism. It is based on the recently developed Majority Judgment voting procedure. The result of the procedure is a consensus real-valued vector that must satisfy a set of constraints imposed by the weather and traffic conditions of the day in question. While we developed and modeled this problem based on specific ATFM features, it appears to be highly generic and amenable to a much broader set of applications. Our analysis of this problem involves several interesting sub-problems, including a type of column generation process that creates candidate vectors for input to the voting process. The third essay is titled "Strategic Opportunity Analysis in COuNSEL -- A Consensus-Building Mechanism for Setting Service Level Expectations." The consensus-building mechanism described in the second essay has been accepted as a technically viable solution for the stated problem -- although many practical challenges still remain before it may be deployed in operations. A key issue worthy of further investigation is its strong strategy-resistance -- as claimed by the authors of Majority Judgment, the voting procedure embedded in COuNSEL. Using the broad ideas of Nash Equilibria, we characterize the necessary and sufficient conditions for an airline to benefit from unilaterally deviating from truthfully grading one or more candidates. The framework provides the airline with all the other airlines' grades on a set of candidates, and allows it an opportunity to present new grades. The analysis is repeated over multiple instances, and likelihood of beneficial strategic opportunity is presented

Decision by sampling: the role of the decision environment in risky choice

Decision by sampling (DbS) is a theory about how our environment shapes the decisions that we make. Here, I review the application of DbS to risky decision making. According to classical theories of risky decision making, people make stable transformations between outcomes and probabilities and their subjective counterparts using fixed psychoeconomic functions. DbS offers a quite different account. In DbS, the subjective value of an outcome or probability is derived from a series of binary, ordinal comparisons with a sample of other outcomes or probabilities from the decision environment. In this way, the distribution of attribute values in the environment determines the subjective valuations of outcomes and probabilities. I show how DbS interacts with the real-world distributions of gains, losses, and probabilities to produce the classical psychoeconomic functions. I extend DbS to account for preferences in benchmark data sets. Finally, in a challenge to the classical notion of stable subjective valuations, I review evidence that manipulating the distribution of attribute values in the environment changes our subjective valuations just as DbS predicts

Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions

Judgement aggregation is a model of social choice where the space of social alternatives is the set of consistent evaluations (`views') on a family of logically interconnected propositions, or yes/no-issues. Unfortunately, simply complying with the majority opinion in each issue often yields a logically inconsistent collection of judgements. Thus, we consider the Condorcet set: the set of logically consistent views which agree with the majority in as many issues as possible. Any element of this set can be obtained through a process of diachronic judgement aggregation, where the evaluations of the individual issues are decided through a sequence of majority votes unfolding over time, with earlier decisions possibly imposing logical constraints on later decisions. Thus, for a fixed profile of votes, the ultimate social choice can depend on the order in which the issues are decided; this is called path dependence. We investigate the size and structure of the Condorcet set ---and hence the scope and severity of path-dependence ---for several important classes of judgement aggregation problems.judgement aggregation; diachronic; path-dependence; indeterminacy; Condorcet; median rule; majoritarian

Affective Decision Making and the Ellsberg Paradox

Affective decision-making is a strategic model of choice under risk and uncertainty where we posit two cognitive processes -- the "rational" and the "emotional" process. Observed choice is the result of equilibrium in this intrapersonal game. As an example, we present applications of affective decision-making in insurance markets, where the risk perceptions of consumers are endogenous. We derive the axiomatic foundation of affective decision making, and show that affective decision making is a model of ambiguity-seeking behavior consistent with the Ellsberg paradox.Affective choice, Endogenous risk perception, Insurance, Ellsberg paradox, Variational preferences, Ambiguity-seeking

Measuring the Compactness of Political Districting Plans

The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans. We propose a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable -- which we coin the relative proximity index. We prove that any compactness measure which satisfies three desirable properties (anonymity of voters, efficient clustering, and invariance to scale, population density, and number of districts) ranks districting plans identically to our index. We then calculate the relative proximity index for the 106th Congress, requiring us to solve for each state's maximal compactness; an NP-hard problem. Using two properties of maximally compact districts, we prove they are power diagrams and develop an algorithm based on these insights. The correlation between our index and the commonly-used measures of dispersion and perimeter is -.22 and -.06, respectively. We conclude by estimating seat-vote curves under maximally compact districts for several large states. The fraction of additional seats a party obtains when their average vote increases is significantly greater under maximally compact districting plans, relative to the existing plans.