Robustness among multiwinner voting rules

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p263.pdf **Abstract:** We simulate voting rules for multiwinner elections in a model of judgment aggregation that distinguishes between rationality and feasibility constraints. These constraints restrict the structure of the individual judgments and of the collective outcome computed by the rule, respectively. We extend known results regarding the simulation of single-winner voting rules to the multiwinner setting, both for elections with ordinal preferences and for elections with approval-based preferences. This not only provides us with a new tool to analyse multiwinner elections, but it also suggests the definition of new judgment aggregation rules, by generalising some of the principles at the core of well-known multiwinner voting rules to this richer setting. We explore this opportunity with regards to the principle of proportionality. Finally, in view of the computational difficulty associated with many judgment aggregation rules, we investigate the computational complexity of our embeddings and of the new judgment aggregation rules we put forward.

The concept of distance rationalizability of voting rules has been explored in recent years by several authors. Roughly speaking, we first choose a consensus set of elections (defined via preferences of voters over candidates) for which the result is specified a priori (intuitively, these are elections on which all voters can easily agree on the result). We also choose a measure of distance between elections. The result of an election outside the consensus set is defined to be the result of the closest consensual election under the distance measure. Most previous work has dealt with a definition in terms of preference profiles. However, most voting rules in common use are anonymous and homogeneous. In this case there is a much more succinct representation (using the voting simplex) of the inputs to the rule. This representation has been widely used in the voting literature, but rarely in the context of distance rationalizability. We show exactly how to connect distance rationalizability on profiles for anonymous and homogeneous rules to geometry in the simplex. We develop the connection for the important special case of votewise distances, recently introduced and studied by Elkind, Faliszewski and Slinko in several papers. This yields a direct interpretation in terms of well-developed mathematical concepts not seen before in the voting literature, namely Kantorovich (also called Wasserstein) distances and the geometry of Minkowski spaces. As an application of this approach, we prove some positive and some negative results about the decisiveness of distance rationalizable anonymous and homogeneous rules. The positive results connect with the recent theory of hyperplane rules, while the negative ones deal with distances that are not metrics, controversial notions of consensus, and the fact that the $\ell^1$-norm is not strictly convex.

Explaining the outcome of an election is a crucial task to address, especially in the case of complex voting rules. For those without a background in social choice, understanding the result of an election with a complex voting rule can be difficult. One possible way of explaining a voting rule is by using a decision tree structure, allowing the reader to follow the reasoning behind the outcome. This work proposes a methodology for explaining voting rules using decision-tree-based classifiers. Using simple features, the classifiers can be trained to a high accuracy while maintaining a human-readable size. We test this framework with well-established voting rules -- Copeland, Kemeny-Young, Ranked Pairs and Schulze -- to generate explanations for each election's outcome. We experiment with different decision tree algorithms on a synthetic dataset to generate explanations for the election outcome. We find that Copeland and Schulze under three candidates can be learned perfectly using an optimized decision tree algorithm, while cases of other rules have high accuracy experimentally.

Voting rules are powerful tools that allow multiple agents to aggregate their preferences in order to reach joint decisions. A common flaw of some voting rules, known as the no-show paradox, is that agents may obtain a more preferred outcome by abstaining an election. Whenever a rule does not suffer from this paradox, it is said to satisfy participation. In this paper, we initiate the study of participation in probabilistic social choice, i.e., for voting rules that yield probability distributions over alternatives. We consider three degrees of participation based on expected utility, the strongest of which even requires that an agent is strictly better off by participating at an election. While the latter condition is prohibitive in non-probabilistic social choice, we show that it can be met by reasonable probabilistic functions. More generally, we study to which extent participation and Pareto efficiency are compatible. To the best of our knowledge, this is the first work in this direction.

We use preference data from the 2015 parliament election in the Austrian federal state of Styria to analyze different voting rules. An exit poll right after the election collected data on ordinal and cardinal preferences from approximately 1000 actual voters. Our analysis is threefold. First, we determine the hypothetical social outcomes under different voting rules; second, we investigate the stability of the outcomes under those rules. Finally, we provide a categorization of different types of parties and analyze the impact of certain voting rules (Plurality Rule, Plurality Run Off, Hare System, Condorcet Method, Approval Voting, Borda Rule, Evaluative Voting, and Majority Judgment) on the performances of parties in those scenarios.

We introduce a general problem about bribery in voting systems. In the $\mathcal{R}$-Multi-Bribery problem, the goal is to bribe a set of voters at minimum cost such that a desired candidate wins the perturbed election under the voting rule R. Voters assign prices for withdrawing their vote, for swapping the positions of two consecutive candidates in their preference order, and for perturbing their approval count to favour candidates. As our main result, we show that $\mathcal{R}$-Multi-Bribery is fixed-parameter tractable parameterized by the number of candidates for many natural voting rules $\mathcal{R}$, including Kemeny rule, all scoring protocols, maximin rule, Bucklin rule, fallback rule, SP-AV, and any C1 rule. In particular, our result resolves the parameterized complexity of $\mathcal{R}$-Swap Bribery for all those voting rules, thereby solving a long-standing open problem and "Challenge #2" of the "Nine Research Challenges in Computational Social Choice" by Bredereck et al. Further, our algorithm runs in single-exponential time for arbitrary cost; it thus improves the earlier double-exponential time algorithm by Dorn and Schlotter that is restricted to the uniform-cost case for all scoring protocols, the maximin rule, and Bucklin rule.

Suppose you want to design a voting rule that can be used to elect a committee or parliament by asking each voter to approve of a subset of the candidates standing. There are several properties you may want that rule to satisfy. First, voters should enjoy some form of proportional representation. Second, voters should not have an incentive to misrepresent their preferences. Third, outcomes should be Pareto efficient. We show that it is impossible to design a voting rule that satisfies all three properties. We also explore what possibilities there are when we weaken our requirements. Of special interest is the methodology we use, as a significant part of the proof is outsourced to a SAT solver. While prior work has considered similar questions for the special case of resolute voting rules, which do not allow for ties between outcomes, we focus on the fact that, in practice, most voting rules allow for the possibility of such ties.

In this paper, we attempt to explain the underlying strategic incentives confronting individuals when they must make a collective decision over a set of alternatives and each has information that is decision-relevant for others. A significant literature has emerged in formal political theory over the past several years that focuses on such problems, paying particular attention, first, to the extent to which voting can be expected to aggregate committee members' information and, second, to the role of communication among committee members prior to voting. Inter alia, this literature reveals a surprisingly subtle interaction between the voting rules used to make decisions and the incentives for committee members to share information prior to voting.

When Do Conflicting Parties Share Political Power? An Experimental Study

Background Multiple mobility-related challenges frequently appear with aging. As a result, many older adults have difficulty getting around, to go, for example, to doctors’ appointments or leisure activities. Although various means of transportation are currently available, older adults do not necessarily use them, partly because they do not know which ones are adapted to their needs and preferences. To foster older adults’ autonomy and freedom in their decision-making about transportation, it is crucial to help them make informed decisions about the means that suit them best.ObjectiveOur aim is to develop Mobilainés, a one-stop platform transportation planning service combining different transport modes and services to help older adults move around in their community where, when, and how they wish. More specifically, we aim to (1) define older adults’ mobility needs and preferences in order to conceptualize a one-stop platform; (2) cocreate a prototype of the one-stop platform; and (3) test the prototype with users in a real-life context.MethodsThis ongoing study uses a “Living Lab” co-design approach. This approach differs from traditional research on aging by facilitating intersectoral knowledge sharing and innovative solutions by and with older adults themselves. A steering committee of 8 stakeholders from the public, scientific, and private sectors, as well as older citizens, will meet quarterly throughout the study. The design comprises three phases, each with several iterative subphases. Phase 1 is exploration: through co-design workshops and literature reviews, members of the intersectoral committee will define older adults’ mobility needs and preferences to support the conceptualization of the one-stop platform. Phase 2 is experimentation: 4 personas will be produced that reflect the different needs and preferences of typical older adult end users of the platform; for development of a prototype, scenarios and mockups (static designs of the web application) will be created through co-design sessions with older adults (N=12) embodying these personas. Phase 3 is evaluation: we will test the usability of the prototype and document changes in mobility, such as the ability to move around satisfactorily and to participate in meaningful activities, by and with older adults (N=30) who use the prototype. The steering committee will identify ways to support the adoption, implementation, and scaling up of Mobilainés to ensure its sustainability. Qualitative and quantitative data will be triangulated according to each subphase objective.Results The first phase began in September 2019. The study is scheduled for completion by mid-2023.Conclusions This innovative transportation planning service will merge existing transportation options in one place. By meeting a wide variety of older adults’ needs and preferences, Mobilainés will help them feel comfortable and safe when moving around, which should increase their participation in meaningful activities and reduce the risk of social isolation.International Registered Report Identifier (IRRID)DERR1-10.2196/33894

<h3>Objective:</h3> To determine the effect of changing the criteria from faculty vote to a blinded clinical case report on reducing bias in a neurology resident award. <h3>Background:</h3> Women are under-represented in the field of Neurology, especially at the leadership level. Awards can play an important role in career advancement. In the absence of a well-designed process for identifying award winners, there is a risk that the demographics of awardees will reflect those of voters. We hypothesized that a blinded merit-based approach for a junior neurology resident award could reduce bias and result a more balanced gender-profile for awardees. <h3>Design/Methods:</h3> In our program, an annual named award is given to PGY-2 residents who exemplify clinical excellence. From 2003–2018 this award was determined by votes from clinical faculty. In 2019 the award changed to a submitted case report that was independently reviewed by 5 faculty, using a structured scoring rubric. Committee members were blinded to the identity of the submitting resident. We compiled gender data for clinical faculty, residents, and award recipients from 2003 to 2022 and compared recipient gender profiles before and after the change. <h3>Results:</h3> From 2003–2018, 12/16 (75%) of award winners were male, more closely reflecting the gender distribution of voting faculty (77.9% male) than resident demographics (55.3% male). After the change in selection criteria, 0/8 winners were male (p&lt;0.001). The proportion of male residents was significantly lower in 2019–22 (37.5% vs 55.3%, p=0.02), which could partially account for the decrease in male award winners. <h3>Conclusions:</h3> Despite relatively small changes in the gender balance of faculty and residents there was a significant change in the gender balance of award winners when the process became blinded. Moving forward, utilizing a blinded process and more transparent selection criteria could lead to an increase in diversity of award winners in neurology residency programs. <b>Disclosure:</b> Dr. Lambert has nothing to disclose. Dr. Cooper has nothing to disclose. An immediate family member of Dr. Narula has received personal compensation in the range of $5,000-$9,999 for serving as a Consultant for abbot vascular. The institution of an immediate family member of Dr. Narula has received research support from Abbot Vascular Inc.. The institution of an immediate family member of Dr. Narula has received research support from US Food and Drug Administration . The institution of an immediate family member of Dr. Narula has received research support from Women’s Health Research at Yale. Dr. Moeller has received publishing royalties from a publication relating to health care.

Fierce debate continues over Taiwan's 2004 presidential election. The election-eve shooting of President Chen Shui-bian and Vice President Annette Lu is the pivotal factor in these discussions. Most analyses of the shooting incident have been more focussed on inferring the truth about this criminal case, and debate about whether or not the incumbent president benefited from this shooting. (1) However, when solving a criminal case without significant and direct evidence, any hypothetic deductive logic is just one possibility. The opposition, which lost the presidential election by 0.2 per cent of the vote, accused the incumbent bloc of using the shooting incident to mislead voters into sympathising with Chen Shui-bian. (2) These contentions inevitably caused the legitimacy of the 2004 Taiwanese presidential election results to be questioned. The concept of legitimacy contrasts with the concept of legality. As a great deal of the classic literature in politics and jurisprudence has already discussed these concepts, no attempt is made in this article to discuss them in detail. The focus here is on forward-looking thinking--how to reduce the possibility that any such incident like the 2004 election-eve shooting could occur in the future. (3) The article begins by considering the normative aspect: Should any legitimacy be given to the outcome of the presidential election? Then the positive aspect is examined: How do we redeem the legitimacy of the presidential election results? How do we avert doubts about the legitimacy of future presidential elections? Accordingly, the specific purposes of this article are: firstly, to show the difficulty in resolving the current dissension over the legitimacy of the 2004 Taiwanese presidential election results during the process of seeking answers for the normative and positive questions; and secondly, to remind researchers of the importance of the forward-looking aspect of this serious issue. Methodology The focus here is on the benchmark approach abstracted from Ronald Coase by Bingyuang Hsiung. (4) Coase's approach can be summarised as follows: setting a reference point, treating this point as a benchmark and then comparing and contrasting this benchmark with the selected topics. Hsiung also suggests: we apply the benchmark approach, we have to consider why to choose this benchmark point but not the others. (5) In economics, benefit and cost are mentioned in the same breath, and cost-benefit analysis is also a useful tool in many studies. For example, if the expected benefits of a specific policy are greater than the expected costs, then implementing the policy will add to total social welfare. Nonetheless, the benefit of Taiwan's presidential election results without legitimacy problems may not be easy to measure. For individuals, the benefits of legitimacy are highly subjective. When the outcome of an election is legitimate, some people may be quite satisfied with it, but others may not care. How can we compare, for different people, the degree of benefit in having no legitimacy problem; or how can we use a measurable index to make comparisons? Even if some indirect measurements are used, the results of comparison may not be clear. When the outcome of an election lacks legitimacy and needs resolution, using the concept of costs is clear and objective. In the case of the 2004 presidential election in Taiwan, if a re-vote is one method to redeem its legitimacy, then the functional expenses that Taiwan's Central Election Commission (CEC) would pay for holding the re-vote is a definite cost. If a multi-party political consultation is another method to redeem the legitimacy of the presidential election results, then the resources that the two rival blocs need to invest in the consultation are measurable costs. For instance, each bloc may need to hold its own plenary session to reach common consent, and the two blocs may negotiate many times with each other about confirming the legitimacy of the presidential election results. …

In Memoriam

Poll Illiteracy: How the Public Misunderstands Polls

Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to look towards the single transferable vote (STV) rule as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open problem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. In this paper, we first present a taxonomy of proportional representation axioms for general weak order preferences, some of which generalise and strengthen previously introduced concepts. We then present a rule called the expanding approvals rule (EAR) that satisfies properties stronger than the central PR axiom satisfied by STV, can handle indifferences in a convenient and computationally efficient manner, and also satisfies better candidate monotonicity properties. In view of this, our proposed rule seems to be a compelling solution for achieving proportional representation in voting settings.