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Electing a committee of size k from m candidates ( k < m ) is an interesting problem under multi-winner voting situations. In this paper, we propose a new committee selection rule based on cooperative game theoretic tools, where voters can approve both individuals and groups of candidates simultaneously. This flexibility of approving groups of candidates allows the voters to assess the candidates' compatibility to work in a group. In many situations, the k-elected candidates have no particular status as a group and voters in such multi-winner elections are presumably concerned about the personal qualities of the candidates. However, many committees function in unison and therefore, their productivity also depends on the compatibility of the members to accomplish a task together. We assume that the voters have prior beliefs about this compatibility. The profile of summed approval votes constitutes the characteristic function of a cooperative game. The Shapley value of this game is calculated to measure the candidates' expected marginal contributions in accomplishing the group task as perceived by the voters. The top k-ranked candidates prescribed by the Shapley value are selected to form the desired committee. The Shapley value as a committee selection rule is characterized by a set of intuitive axioms. We explore several properties of the committee selection rule. [ABSTRACT FROM AUTHOR]

We study how voting rules shape voter coordination in large three-candidate elections. We consider three rules, that differ on the number of candidates that voters can support: Plurality (one), Anti-Plurality (two) and Approval Voting (one or two). We show that the Condorcet winner is always elected at some equilibrium under Approval Voting, and that this rule provides better welfare guarantees than Plurality. We then numerically study a dynamic process of political tâtonnement which delivers rich insights. The Condorcet winner is virtually always elected under Approval Voting, but not under the other rules. The dominance of Approval Voting is robust to several alternative welfare criteria and the introduction of expressive voters. [ABSTRACT FROM AUTHOR]

Recent attempts to provide a viable account of decision making under normative uncertainty through the use of voting procedures seem promising, but incomparable options pose a challenge. This paper focuses on the so-called Borda approach to decision making under normative uncertainty (MacAskill, Mind 125(500):967–1004, 2016; MacAskill et al., Moral uncertainty, Oxford University Press, 2020) and illustrates how an extended version of it aimed at accommodating incomplete preference orderings associated with normative theories fails. I propose a different account for proponents fond of the voter-theoretic approach that is grounded by approval voting, which sufficiently addresses the problem of option incomparability and is pragmatically compelling due to its simpler structure. [ABSTRACT FROM AUTHOR]

In this paper, we consider those voting situations in which each voter decides whether he or she approves each candidate. Given a list of such approvals, a "social preference function" picks a ranking of the candidates. We are interested in finding out which social preference functions are non-manipulable. We show that a particular social preference function, referred to as approval ranking , is more decisive than any other social preference functions satisfying completeness , neutrality , anonymity , and non-manipulability. In addition, we show that approval ranking is axiomatized by these four axioms and tie-breakability. • Approval voting is characterized in terms of manipulability and decisiveness. • Approval voting is characterized in terms of manipulability and tie-breakability. • May's theorem and classical axioms have connections with approval voting. [ABSTRACT FROM AUTHOR]

In the high-stakes race for scalability, some blockchains have turned to committee-based consensus (CBC), whereby the chain's recordkeeping rights are entrusted to a committee of block producers elected via approval voting. Smaller committees boost speed and scalability but can compromise security when voters have limited information. In this environment, voting strategies are naturally nonlinear, and equilibria can become intractable. Despite this, we show that elections converge to optimality asymptotically (in voter numbers), exponentially quickly, and under relatively weak informational requirements. Compared to popular stake-weighted lottery and single-vote protocols used in practice, we find that CBC, when paired with approval voting, can offer meaningful efficiency and robustness gains if enough voters are engaged. This paper was accepted by Will Cong, Special Section of Management Science: Blockchains and Crypto Economics. Funding: This work was funded by The Hogeg Blockchain Research Institute. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2022.03177. [ABSTRACT FROM AUTHOR]

The majority judgment (MJ) voting method works well in theory and in practice. Not only does MJ avoid the classical Condorcet and Arrow paradoxes, but it also overcomes the domination paradox, from which paired comparisons by majority rule, approval voting, and all Condorcet consistent methods suffer. This article also shows why MJ best reduces the impact of strategic manipulation and minimizes ties to the extreme. The article illustrates the resistance of MJ to manipulations in a real example, discusses other salient properties of MJ, and summarizes several recent applications that show MJ to be, despite its newness, the right basis of electoral reform. [ABSTRACT FROM AUTHOR]

Preference approval voting (PAV) and fallback voting (FV) are two voting rules that combine approval and preferences, first introduced by Brams and Sanver (in: Brams, Gehrlein and Roberts (eds) The mathematics of preference, choice and order, Springer, Berlin, 2009). Under PAV, voters rank the candidates and indicate which ones they approve of; with FV, they rank only those candidates they approve of. In this paper, we further develop the work of Brams and Sanver (2009) by exploring some other normative properties of FV and PAV. We show among other things that FV and PAV satisfy and fail the same criteria; they possess two properties that AV does not: Pareto optimality and the fact of always electing the absolute Condorcet winner when he exists. To provide a practical comparison, we evaluate the probabilities of satisfying the Condorcet majority criteria for three-candidate elections and a considerably large electorate, examining FV and PAV alongside other voting rules. Our findings indicate that PAV outperforms the Borda rule in this regard. Furthermore, we observe that in terms of agreement, FV and PAV align more closely with scoring rules than with approval voting. Our analysis is performed under the impartial anonymous culture assumption. [ABSTRACT FROM AUTHOR]

In a controlled laboratory experiment we investigate whether time pressure influences voting decisions, and in particular the degree of strategic (insincere) voting. We find that participants under time constraints are more sincere when using the widely-employed Plurality Voting method. That is, time pressure might reduce strategic voting and hence misrepresentation of preferences. However, there are no effects for Approval Voting, in line with arguments that this method provides no incentives for strategic voting.

A preference–approval on a set of alternatives consists of a weak order on that set and, additionally, a cut-off line that separates acceptable and unacceptable alternatives. In this paper, we propose a new method for defining the distance between preference–approvals taking into account jointly the disagreements in preferences and approvals for each pair of alternatives. The proposed distance is compared to the existing distance functions to deal with clustering problems. Specifically, we prove that our metric improves the estimated clusters in terms of both stability and accuracy. [ABSTRACT FROM AUTHOR]

In a controlled laboratory experiment we investigate whether time pressure influences voting decisions, and in particular the degree of strategic (insincere) voting. We find that participants under time constraints are more sincere when using the widely-employed Plurality Voting method. That is, time pressure might reduce strategic voting and hence misrepresentation of preferences. However, there are no effects for Approval Voting, in line with arguments that this method provides no incentives for strategic voting. [ABSTRACT FROM AUTHOR]

We characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON. [ABSTRACT FROM AUTHOR]

We examine the mechanical effect of a multiple vote, proportional representation electoral system on party vote share in n dimensions. In one dimension, Cox (1990) has proven that such a system is centripetal: it drives parties to the center of the political spectrum. However, as populism has swept across Western Europe and the United States, the importance of multiple policy dimensions has grown considerably. We use simulations to examine how a multiple vote system could alter electoral outcomes in all possible parliamentary systems. We find that multiple vote systems act centripetally in multiple dimensions too, though weakly in extreme cases where parties are sorted into ideological clusters at opposite corners of the ideological space. Even in these cases, though, we find that a slight disturbance of the conditions (by introducing an additional party- even if it is very small) strengthens the centripetal properties of the multiple vote system. [ABSTRACT FROM AUTHOR]

The two main criticisms by approval voting (AV) supporters have been that majority judgment (MJ) is not "Condorcet" and that it admits the no-show paradox. That MJ is not Condorcet consistent is a good property shared with AV: the domination paradox shows that majority rule may well err in an election between two. Whereas the no-show paradox is in theory possible with MJ, it is as a practical matter impossible. Moreover, it is proven that MJ with three grades does not admit the no-show paradox. In contrast, AV suffers from serious drawbacks. With AV, voters cannot express their opinions adequately; experiments show that Approve is not the opposite of Disapprove and that AV does not admit the no-show paradox—it admits the very closely allied no-show syndrome. Two grades are simply too few! The debate must concern three or more grades. Majority judgment (MJ) and approval voting (AV) are compared in theory and practice. Criticisms of MJ and claims that AV is superior are refuted. The two primary criticisms have been that MJ is not "Condorcet consistent" and that it admits the "no-show paradox." That MJ is not Condorcet consistent is a good property shared with AV: the domination paradox shows that majority rule may well err in an election between two. Whereas the no-show paradox is in theory possible with MJ, it is as a practical matter impossible. For those who believe that this extremely rare phenomenon is important, it is proven that MJ with three grades cannot admit the no-show paradox. In contrast, AV suffers from serious drawbacks because voters can only "tick" or "approve" candidates—at best, only Approve or Disapprove each candidate. With AV, voters cannot express their opinions adequately; experiments show that Approve is not the opposite of Disapprove, and although AV does not admit the no-show paradox, it admits the very closely allied no-show syndrome and "insensitivity." Two are too few. Substantive debate must concern three or more grades. [ABSTRACT FROM AUTHOR]

In this study, we propose a new direction of research on the axiomatic analysis of approval voting, which is a common democratic decision method. Its novelty is to examine an infinite population setting, which includes an application to intergenerational problems. In particular, we assume that the set of the population is countably infinite. We provide several extensions of the method of approval voting for this setting. As our main result, axiomatic characterizations of the extensions are offered by revealing a direct link between approval voting and the Borda rule. The characterized methods are natural extensions of the standard approval voting method for the finite-population case and are regarded as minimum requirements for other possible infinite-population extensions, which are reasonably democratic. [ABSTRACT FROM AUTHOR]

We study how payoff valence affects voting behavior on the distribution of monetary outcomes framed as gains or losses in a group when using standard plurality voting (PV) procedures and when using approval voting (AV). The latter method allows the subjects to approve of as many alternatives as they wish and has been shown to eliminate the incentives to vote strategically. For both methods, we observe that voters express higher support for egalitarian allocations (and lower support for selfish options) when sharing gains than when sharing losses. Moreover, the average number of approved alternatives per ballot is higher when distributions are framed in terms of gains than when they are framed in terms of losses. We also discuss under which circumstances the shift in voting behavior is more likely to produce changes in the electoral outcome. The results suggest that framing manipulations (payoff valence) can significantly impact voting behavior. [ABSTRACT FROM AUTHOR]

Voting algorithms are used to choose candidates by an electorate. However, voter participation is variable and uncertain, and projections from polls or past elections are uncertain because voter preferences may change. Furthermore, electoral victory margins are often slim. Variable voter participation or preferences, and slim margins of decision, have implications for choosing a voting algorithm. We focus on approval voting (AV) and compare it to plurality voting (PV), regarding their robustness to uncertainty in voting outcomes. We ask: by how much can voting outcomes change without altering the election outcomes? We see fairly consistent empirical differences between AV and PV. In single-winner elections, PV tends to be more robust to vote uncertainty than AV in races with large victory margins, while AV tends to be more robust at low victory margins. Two conflicting concepts—approval flattening and approval magnification—explain this tendency for reversal of robust dominance between PV and AV. We also examine the robustness to vote uncertainty of PV in elections for proportional representation of parties. [ABSTRACT FROM AUTHOR]

We study how payoff valence affects voting behavior on the distribution of monetary outcomes framed as gains or losses in a group when using standard plurality voting (PV) procedures and when using approval voting (AV). The latter method allows the subjects to approve of as many alternatives as they wish and has been shown to eliminate the incentives to vote strategically. For both methods, we observe that voters express higher support for egalitarian allocations (and lower support for selfish options) when sharing gains than when sharing losses. Moreover, the average number of approved alternatives per ballot is higher when distributions are framed in terms of gains than when they are framed in terms of losses. We also discuss under which circumstances the shift in voting behavior is more likely to produce changes in the electoral outcome. The results suggest that framing manipulations (payoff valence) can significantly impact voting behavior.

I assume that voters mark ballots exclusively to express their true preferences among parties, leaving aside any considerations about an election's possible outcome. The paper then analyzes the resulting voting behavior. In particular, it studies how effective different voting systems such as plurality rule, approval voting, and range voting are in fostering high turnout rates of such expressive voters. [ABSTRACT FROM AUTHOR]

We axiomatically study voting rules without making any assumption on the ballots that voters are allowed to cast. In this setting, we characterize the family of "endorsement rules," which includes approval voting and the plurality rule, via the imposition of three normative conditions. The first condition is the well known social‐theoretic principle of consistency; the second one, unbiasedness, roughly requires social outcomes not to be biased toward particular candidates or voters; the last one, dubbed no single voter overrides, demands that the addition of a voter to an electorate cannot radically change the social outcome. Building on this result, we provide the first axiomatic characterization of approval voting without the approval balloting assumption. The informational basis of approval voting as well as its aggregative rationale are jointly derived from a set of conditions that can be defined on most of the ballot spaces studied in the literature. [ABSTRACT FROM AUTHOR]

The aim of this study is evaluate various single winner voting systems with the help of computer aided simulations. The impact of phenomena such as strategic voting, spoiler effect and centre squeeze are studied on various election systems such as First Past the Post, Ranked voting, Approval voting and Score voting. The democratic process gives great moral legitimacy to the winner as they are deemed to be chosen by the people, ergo the election system too needs to accurately reflect the will of all the people. Single winner systems or "winner takes all" systems have the advantage of decisive governments as compared to proportional systems but by its construct exclude parliamentary representation to a large percentage of voters who ended up on the losing side. It is therefore even more important that the single winner system mirror the voters mandate as accurately as possible. I conclude after evaluation that alternate systems such as Instant Runoff or Approval voting could be considered in lieu of the FPTP systems as they have fewer flaws and are more likely to give a truer representation of electorate's choice. [ABSTRACT FROM AUTHOR]

Approval voting allows electors to list any number of candidates and their final scores are obtained by summing the votes cast in their favor. Equal-and-even cumulative voting instead follows the One-person-one-vote principle by endowing each elector with a single vote that may be distributed evenly among several candidates. It corresponds to satisfaction approval voting, introduced by Brams and Kilgour (in: Fara et al (eds) Voting power and procedures. Essays in honor of Dan Fesenthal and Moshé Machover, Springer, Heidelberg, 2014) as an extension of approval voting to a multiwinner election. It also corresponds to the concept of Shapley ranking, introduced by Ginsburgh and Zang (J Wine Econ 7:169–180, 2012) as the Shapley value of a cooperative game with transferable utility. In the present paper, we provide an axiomatic foundation for Shapley ranking and analyze the properties of the resulting social welfare function. [ABSTRACT FROM AUTHOR]

Doodle polls allow people to schedule meetings or events based on time preferences of participants. Each participant indicates on a web-based poll form which time slots they find acceptable and a time slot with the most votes is chosen. This is a social choice mechanism known as approval voting , in which a standard assumption is that all voters vote sincerely —no one votes "no" on a time slot they prefer to a time slot they have voted "yes" on. We take a game-theoretic approach to understanding what happens in approval voting assuming participants vote sincerely. While our instances are framed in the context of the Doodle poll application, the results apply more broadly to approval voting. First we characterize Doodle poll instances where sincere pure Nash Equilibria (NE) exist, under lexicographic tie-breaking, random candidate, and random voter tie-breaking. We then study the quality of such NE voting profiles in Doodle polls, showing the price of anarchy and price of stability are both unbounded, even when a time slot that many participants vote yes for is selected. Finally, we find some reasonable conditions under which the quality of the NE (and strong NE) is good. • Many approval voting instances (e.g. Doodle polls) admit sincere pure Nash Equilibria. • Both price of anarchy and price of stability are unbounded in approval voting. • Many realistic approval voting scenarios have a price of stability of 1. [ABSTRACT FROM AUTHOR]

We investigate the propensity of evaluative voting (2, 1, 0) to fulfill Condorcet majority conditions in a framework where preferences are supposed to be trichotomous and only three candidates are in contention. In this framework, we also compare evaluative voting to other voting rules, including Borda rule, plurality rule and approval voting. [ABSTRACT FROM AUTHOR]

Although two-round voting procedures are common, the theoretical voting literature rarely discusses any such rules beyond the traditional plurality runoff rule. Therefore, using four criteria in conjunction with two data-generating processes, we define and evaluate nine "runoff pair selection rules" that comprise two rounds of voting, two candidates in the second round, and a single final winner. The four criteria are: social utility from the expected runoff winner (UEW), social utility from the expected runoff loser (UEL), representativeness of the runoff pair (Rep), and resistance to strategy (RS). We examine three rules from each of three categories: plurality rules, utilitarian rules and Condorcet rules. We find that the utilitarian rules provide relatively high UEW and UEL, but low Rep and RS. Conversely, the plurality rules provide high Rep and RS, but low UEW and UEL. Finally, the Condorcet rules provide high UEW, high RS, and a combination of UEL and Rep that depends which Condorcet rule is used. [ABSTRACT FROM AUTHOR]

Under approval voting (AV), each voter just distinguishes the candidates he approves of from those appearing as unacceptable. The preference approval voting (PAV) is a hybrid version of the approval voting first introduced by Brams and Sanver (in: Brams, Gehrlein, Roberts (eds) The mathematics of preference, choice and order. Springer, Berlin, pp 215–237, 2009). Under PAV, each voter ranks all the candidates and then indicates the ones he approves. In this paper, we provide an analytical representation of the limiting probability that PAV elects the Condorcet winner (resp. the Condorcet loser) when she exists in three-candidate elections. We perform our analysis by assuming the assumption of the Extended Impartial Culture. The aim is to measure at which extend PAV performs better than AV both on the propensity of electing the Condorcet winner and on that of the non-election of the Condorcet loser. For this purpose, we also provide an analytical representation of the limiting probability that AV elects the Condorcet winner (resp. the Condorcet loser) when she exists in three-candidate elections. Our representation of the limiting probability that AV elects the Condorcet winner is more general than that provided by Diss et al. (in: Laslier and Sanver (eds) Handbook on approval voting. Springer, Berlin, pp 255–283, 2010) and it leads to the same figures as the representation provided by Gehrlein and Lepelley (Group Decis Negot 24:243–269, 2015). [ABSTRACT FROM AUTHOR]