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Öğe Approval compatible voting rules(Springer, 2026) Terzopoulou, Zoi; Lang, Jerome; Zwicker, William S.Suppose voters are asked to submit approval ballots for a certain set of alternatives, with approval voting applied to determine a winning alternative. The same voters are then asked to report rankings over these alternatives, and some voting rule intended for ranked ballots is applied. If voters are sincere, can an approval winner possibly win this second election? Can an approval loser lose that election, or all approval co-winners be co-winners of the election? These questions give rise to three notions of approval compatibility for voting rules: positive, negative, and uniform positive approval compatibility (PAC, NAC, and UPAC). We find that NAC is a very weak notion and UPAC is a very strong one. Moreover, PAC, a stronger variant of it called OPAC, and a weaker variant of UPAC called FUPAC divide usual voting rules into four families: Condorcet-consistent rules satisfy all of them; K-approval rules for K >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K\ge 2$$\end{document} satisfy none; plurality, plurality with runoff and STV satisfy OPAC but fail FUPAC; and Borda satisfies FUPAC and PAC but fails OPAC.Öğe Monotonicity properties and their adaptation to irresolute social choice rules(Springer, 2012) Sanver, M. Remzi; Zwicker, William S.What is a monotonicity property? How should such a property be recast, so as to apply to voting rules that allow ties in the outcome? Our original interest was in the second question, as applied to six related properties for voting rules: monotonicity, participation, one-way monotonicity, half-way monotonicity, Maskin monotonicity, and strategy-proofness. This question has been considered for some of these properties: by Peleg and BarberA for monotonicity, by Moulin and P,rez et al, for participation, and by many authors for strategy-proofness. Our approach, however, is comparative; we examine the behavior of all six properties, under three general methods for handling ties: applying a set extension principle (in particular, Gardenfors' sure-thing principle), using a tie-breaking agenda to break ties, and rephrasing properties via the t-a-t approach, so that only two alternatives are considered at a time. In attempting to explain the patterns of similarities and differences we discovered, we found ourselves obliged to confront the issue of what it is, exactly, that identifies these properties as a class. We propose a distinction between two such classes: the tame monotonicity properties (which include participation, half-way monotonicity, and strategy proofness) and the strictly broader class of normal monotonicity properties (which include monotonicity and one-way monotonicity, but not Maskin monotonicity). We explain why the tie-breaking agenda, t-a-t, and Gardenfors methods are equivalent for tame monotonicities, and how, for properties that are normal but not tame, set-extension methods can fail to be equivalent to the other two (and may fail to make sense at all).Öğe Nash's bargaining problem and the scale-invariant Hirsch citation index(Springer, 2025) Freixas, Josep; Hoerl, Roger; Zwicker, William S.A number of citation indices have been proposed for measuring and ranking the research publication records of scholars. Some of the best known indices, such as those proposed by Hirsch and Woeginger, are designed to reward most highly those records that strike some balance between productivity (number of papers published) and impact (frequency with which those papers are cited). A large number of rarely cited publications will not score well, nor will a very small number of heavily cited papers. We discuss three new citation indices, one of which was independently proposed in Fenner et al. (PLOS ONE 13(7): e0200098, 2018). Each rests on the notion of scale invariance, fundamental to John Nash's solution of the two-person bargaining problem. Our main focus is on one of these-a scale-invariant version of the Hirsch index. We argue that it has advantages over the original; it produces fairer rankings within subdisciplines, is more decisive (discriminates more finely, yielding fewer ties) and more dynamic (growing over time via more frequent, smaller increments), and exhibits enhanced centrality and tail balancedness. Simulations suggest that scale invariance improves robustness under Poisson noise, with increased decisiveness having no cost in terms of the number of accidental reversals, wherein random irregularities cause researcher A to receive a lower index value than B, although A's productivity and impact are both slightly higher than B's. Moreover, we provide an axiomatic characterization of the scale-invariant Hirsch index, via axioms that bear a close relationship, in discrete analogue, to those used by Nash (Econometrica 18(2):155-162, 1950). This argues for the mathematical naturality of the new index.Öğe One-way monotonicity as a form of strategy-proofness(Springer Heidelberg, 2009) Sanver, M. Remzi; Zwicker, William S.Suppose that a vote consists of a linear ranking of alternatives, and that in a certain profile some single pivotal voter v is able to change the outcome of an election from s alone to t alone, by changing her vote from P-v to P'(v). A voting rule F is two-way monotonic if such an effect is only possible when v moves to from below s (according to P-v) to above s (according to P'(v)). One-way monotonicity is the strictly weaker requirement forbidding this effect when v makes the opposite switch, by moving s from below t to above t. Two-way monotonicity is very strong-equivalent over any domain to strategy proofness. One-way monotonicity holds for all sensible voting rules, a broad class including the scoring rules, but no Condorcet extension for four or more alternatives is one-way monotonic. These monotonicities have interpretations in terms of strategy-proofness. For a one-way monotonic rule F, each manipulation is paired with a positive response, in which F offers the pivotal voter a strictly better result when she votes sincerely.Öğe Position: Social Choice Should Guide AI Alignment in Dealing with Diverse Human Feedback(ML Research Press, 2024) Conitzer, Vincent; Freedman, Rachel; Heitzig, Jobst; Holliday, Wesley H.; Jacobs, Bob M.; Lambert, Nathan; Zwicker, William S.Foundation models such as GPT-4 are fine-tuned to avoid unsafe or otherwise problematic behavior, such as helping to commit crimes or producing racist text. One approach to fine-tuning, called reinforcement learning from human feedback, learns from humans' expressed preferences over multiple outputs. Another approach is constitutional AI, in which the input from humans is a list of high-level principles. But how do we deal with potentially diverging input from humans? How can we aggregate the input into consistent data about “collective” preferences or otherwise use it to make collective choices about model behavior? In this paper, we argue that the field of social choice is well positioned to address these questions, and we discuss ways forward for this agenda, drawing on discussions in a recent workshop on Social Choice for AI Ethics and Safety held in Berkeley, CA, USA in December 2023. Copyright 2024 by the author(s)
