Drawing on the so-called “doctrinal paradox”, List and Pettit (2002) have shown that, given an unrestricted domain condition, there exists no procedure for aggregating individual sets of judgments over multiple interconnected propositions into corresponding collective ones, where the procedure satisfies some minimal conditions similar to the conditions of Arrow’s theorem. I prove that we can avoid the paradox and the associated impossibility result by introducing an appropriate domain restriction: a structure condition, called unidimensional alignment, is shown to open up (...) a possibility result, similar in spirit to Black’s median voter theorem. Specifically, I prove that, given unidimensional alignment, propositionwise majority voting is the unique procedure for aggregating individual sets of judgments into collective ones in accordance with the above mentioned minimal conditions. (shrink)

We study experimentally in the laboratory the situation when individuals have to report their private information about a variable to a public authority that then makes inference about the true values given a known variable using a regression technique. It is assumed that individuals prefer this predicted value to be as close as possible to their true value. Consistent with the theoretical literature, we show that subjects misrepresent their private information more when an ordinary least squares regression is implemented than (...) when the so-called resistant line estimator is employed. The latter extends the median voter theorem to the two-dimensional setting and belongs to the family of robust estimation techniques. In fact, we find that OLS involves serious biases but the RL estimation is empirically unbiased. Furthermore, subjects never earn less when the RL is applied. (shrink)

Panels, boards, and committees throughout society evaluate all manner of things by grading them, first individually and then collectively. Thus risks are prioritized, research proposals are funded, and candidates are shortlisted for jobs. It is not usual to pick winners in political elections by grading the candidates, but there are examples in history. This article takes up a question about the quality of judgments and decisions made by grading: under which conditions are they likely to be right? An answer comes (...) in the form of a jury theorem for median grading. Here, the collective grade for a thing is the median of its individually assigned grades—the one in the middle, when all of them are listed from "top" to "bottom." A second objective of this article is to suggest a solution to problems of voter ignorance in democracies. The idea is for democratic assemblies to use voting methods that make more of people's limited knowledge than do commonly used methods, such as majority voting. It turns out that in theory anyway, and perhaps also in practice, median grading can enable unenlightened assemblies to “track the truth”—even as majority voting would run them off the rails. (shrink)

The two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote (...) these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect. (shrink)

In online social networks, the audience size commanded by an organization or an individual is a critical measure of that entity’s popularity and this measure has important economic and/or political implications. Such efforts to measure popularity of users or exploit knowledge about their audience are complicated by the presence of fake profiles on these networks. In this study, analysis of 62 million publicly available Twitter user profiles was conducted and a strategy to identify automatically generated fake profiles was established. Using (...) a combination of a pattern-matching algorithm on screen-names and an analysis of update times, a reasonable number of highly reliable fake user accounts were identified. Analysis of profile creation times and URLs of these fake accounts revealed their distinct behavior relative to a ground truth data set. The characteristics of friends and followers of users in the two data sets further revealed the very different nature of the two groups. The ratio of number of followers-to-friends for ground truth users was ∼1, consistent with past observations, while the fake profiles had a median ratio ∼30, indicating that the fake users we identified were primarily focused on gathering friends. An analysis of the temporal evolution of accounts over 2 years showed that the friends-to-followers ratio increased over time for fake profiles while they decreased for ground truth users. Our results, thus, suggest that a profile-based approach can be used for identifying a core set of fake online social network users in a time-efficient manner. (shrink)

This chapter explores the relationship between Goldman's thesis and the classical jury theorem. It identifies the minimal modification needed in order to recover Goldman's thesis in a Condorcetian framework. Goldman's thesis can be recast as a generalization of the classical Condorcet jury theorem. The central move needed to recover Goldman's thesis from a generalized jury theorem is to replace Condorcet's assumption that there is a single truth to be tracked with the assumption of multiple such truths: one (...) for each voter. In Goldman's picture, there is still an indirect, derivative sense in which there exists an 'overall' truth about the correct outcome for the electorate in aggregate. This 'overall' truth is determined, of course, by the profile of voter‐specific truths and therefore depends on the identity of the electorate. The chapter also provides some numerical examples to illustrate the implications of the generalized jury theorem. (shrink)

Many political theorists and philosophers use Condorcet's Jury Theorem to defend democracy. This paper illustrates an uncomfortable implication of Condorcet's Jury Theorem. Realistically, when the conditions of Condorcet’s Jury Theorem hold, even in very high stakes elections, having more than 100,000 citizens vote does no significant good in securing good political outcomes. On the Condorcet model, unless voters enjoy voting, or unless they produce some other value by voting, then the cost to most voters of voting exceeds (...) the expected epistemic benefits to the common good of their casting a vote. Anyone who is committed to democracy on the basis of the Jury Theorem ought also to hold that widespread voting is wasteful, at least unless she can provide some further justification of mass democratic participation. (shrink)

Depending on how people respond to it, a constitution can cause suffering on a vast scale or lay the foundation for a nation’s liberty, prosperity, and equality. As currently practiced, constitutional theory and interpretation especially concern the meaning, history, and philosophy of constitutional texts. These approaches cannot predict the responses of people to constitutions. Constitutional consequentialism, which I advocate, is a research program that aims to predict the effect of alternative forms and interpretations of constitutions on policy values, especially liberty, (...) prosperity, and equality. This paper discusses two constitutional processes. “Median democracy,” which empowers the median voter, is implemented by referenda and ballot initiatives, special districts, and winner-take-all elections. “Bargain democracy,” which lubricates bargaining among factions and regions, is implemented by legislatures, comprehensive governments, and proportional representation. I show that median democracy causes stability, whereas bargain democracy ideally causes efficiency and often causes corruption or instability. (shrink)

In recent years, the receipt and the perception of information has changed in ways which have fueled fears about the fates of our democracies. However, real information on these possibilities or the direction of these changes does not exist. Into this gap, Hahn and colleagues bring the power of Condorcet's (1785) Jury Theorem to show that changes in our information networks have affected voter inter‐dependence so that it is likely that voters are now collectively more ignorant even if (...) individual voter competence remains unchanged. (shrink)

We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (...) (ii) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (shrink)

Procedural justifications of democracy emphasize inclusiveness and respect and by doing so come into conflict with instrumental justifications that depend on voters’ competence. This conflict raises questions about jury theorems and makes their standing in democratic theory contested. We show that a type of no-regret learning called meta-induction can help to satisfy the competence assumption without excluding voters or diverse opinion leaders on an a priori basis. Meta-induction assigns weights to opinion leaders based on their past predictive performance to determine (...) the level of their inclusion in recommendations for voters. The weighting minimizes the difference between the performance of meta-induction and the best opinion leader in hindsight. The difference represents the regret of meta-induction whose minimization ensures that the recommendations are optimal in supporting voters’ competence. Meta-induction has optimal truth-tracking properties that support voters’ competence even if it is targeted by mis/disinformation and should be considered a tool for supporting democracy in hyper-plurality. (shrink)

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.

The purpose of this paper is to assess the emergence of the pirate movements in the European Union. Our goal is to sketch the steps towards a research agenda for this grassroots political movement which gained momentum since 2009. To attain our goal we showed the re-signification of the concept of piracy in the debate around intellectual property and its institutional settlement. Afterwards we analysed the big political themes of several European Pirate Parties and their struggle to follow the preferences (...) of the median voter. We concluded with a set of hypotheses of which the most important is that the pirates will inscribe neither to the left nor to the right part of the political spectrum. (shrink)

In the basic model of Condorcet’s jury theorem and in the literature that follows, an odd-numbered group of voters is assumed so that the simple majority rule can be used. We show that this assumption is not necessary either in Condorcet’s basic model or in the general framework of dichotomous choice. We first apply simple majority rule to an even-numbered homogeneous fixed-size committee. We then provide a justification for using simple majority rule for an even-numbered heterogeneous fixed-size committee when (...) the competence structure of the committee members is not common knowledge. (shrink)

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore (...) suggest restricting independence to premises, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent. (shrink)

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set (...) of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem. (Published Online July 11 2006) Footnotes1 Much of this article was written while the author was a fellow at the Swedish Collegium for Advanced Study in the Social Sciences (SCASSS) in Uppsala. I want to thank the Collegium for providing me with excellent working conditions. Wlodek Rabinowicz and other fellows gave me valuable comments at a seminar at SCASSS when an early version of the paper was presented. I also want to thank Luc Bovens, Franz Dietrich, Christian List and an anonymous referee for their excellent comments on a later version. The final version was prepared during a stay at Oxford University for which I am grateful to the British Academy. (shrink)

May's theorem famously shows that, in social decisions between two options, simple majority rule uniquely satisfies four appealing conditions. Although this result is often cited in support of majority rule, it has never been extended beyond decisions based on pairwise comparisons of options. We generalize May's theorem to many-option decisions where voters each cast one vote. Surprisingly, plurality rule uniquely satisfies May's conditions. This suggests a conditional defense of plurality rule: If a society's balloting procedure collects only a (...) single vote from each voter, then plurality rule is the uniquely compelling electoral procedure. To illustrate the conditional nature of this claim, we also identify a richer informational environment in which approval voting, not plurality rule, is supported by a May-style argument. (shrink)

In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning to losing. In this note, we prove a new impossibility theorem concerning this axiom: there is no ordinal voting method satisfying positive involvement that also satisfies the Condorcet winner and loser criteria, resolvability, and a common invariance property for Condorcet methods, (...) namely that the choice of winners depends only on the ordering of majority margins by size. (shrink)

The Condorcet jury theorem (CJT) is based on the assumption of homogeneous voters who imperfectly know the correct policy. We reassess the validity of the CJT when voters are homogeneous and each knows the correct decision with an average probability of more than a half.

In general, analyses of voting power are performed through the notion of a simple voting game (SVG) in which every voter can choose between two options: ‘yes’ or ‘no’. Felsenthal and Machover [Felsenthal, D.S. and Machover, M. (1997), International Journal of Game Theory 26, 335–351.] introduced the concept of ternary voting games (TVGs) which recognizes abstention alongside. They derive appropriate generalizations of the Shapley–Shubik and Banzhaf indices in TVGs. Braham and Steffen [Braham, M. and Steffen, F. (2002), in Holler, (...) et al. (eds.), Power and Fairness, Jahrbuch für Neue Politische Ökonomie 20, Mohr Siebeck, pp. 333–348.] argued that the decision-making structure of a TVG may not be justified. They propose a sequential structure in which voters first decide between participation and abstention and then between ‘yes’ or ‘no’. The purpose of this paper is two-fold. First, we compare the two approaches and show how the probabilistic interpretation of power provides a unifying characterization of analogues of the Banzhaf (Bz) measure. Second, using the probabilistic approach we shall prove a special case of Penrose’s Limit Theorem (PLT). This theorem deals with an asymptotic property in weighted voting games with an increasing number of voters. It says that under certain conditions the ratio between the voting power of any two voters (according to various measures of voting power) approaches the ratio between their weights. We show that PLT holds in TVGs for analogues of Bz measures, irrespective of the particular nature of abstention. (shrink)

The purpose of this paper is to illustrate, formally, an ambiguity in the exercise of political influence. To wit: A voter might exert influence with an eye toward maximizing the probability that the political system (1) obtains the correct (e.g. just) outcome, or (2) obtains the outcome that he judges to be correct (just). And these are two very different things. A variant of Condorcet's Jury Theorem which incorporates the effect of influence on group competence and interdependence is (...) developed. Analytic and numerical results are obtained, the most important of which is that it is never optimal--from the point-of-view of collective accuracy--for a voter to exert influence without limit. He ought to either refrain from influencing other voters or else exert a finite amount of influence, depending on circumstance. Philosophical lessons are drawn from the model, to include a solution to Wollheim's "Paradox in the Theory of Democracy". (shrink)

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: (i) whether a premise is justi…ed depends on the notion of probability considered; (ii) none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.

LS Penrose was the first to propose a measure of voting power (which later came to be known as ‘the [absolute] Banzhaf index’). His limit theorem – which is implicit in Penrose (1952) and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while the quota is pegged at half the total weight, then – under certain conditions – the ratio between the voting powers (as measured (...) by him) of any two voters converges to the ratio between their weights. We conjecture that the theorem holds, under rather general conditions, for large classes of variously defined weighted voting games, other values of the quota, and other measures of voting power. We provide proofs for some special cases. (shrink)

Sen's classic social choice result supposedly demonstrates a conflict between Pareto and even minimal forms of liberalism. By providing the first direct mathematical proof of this seminal result, we underscore a significantly different interpretation: rather than conflicts among rights, Sen's result occurs because the liberalism assumption negates the assumption that voters have transitive preferences. This explanation enriches interpretations of Sen's conclusion by including radically new kinds of societal conflicts, it suggests ways to sidestep these difficulties, and it explains earlier approaches (...) to avoid the difficulties. (shrink)

The dramatic rise in inequality in the United States over the past generation has occasioned considerable attention from economists, but strikingly little from students of American politics. This has started to change: in recent years, a small but growing body of political science research on rising inequality has challenged standard economic accounts that emphasize apolitical processes of economic change. For all the sophistication of this new scholarship, however, it too fails to provide a compelling account of the political sources and (...) effects of rising inequality. In particular, these studies share with dominant economic accounts three weaknesses: they downplay the distinctive feature of American inequality —namely, the extreme concentration of income gains at the top of the economic ladder; they miss the profound role of government policy in creating this “winner-take-all” pattern; and they give little attention or weight to the dramatic long-term transformation of the organizational landscape of American politics that lies behind these changes in policy. These weaknesses are interrelated, stemming ultimately from a conception of politics that emphasizes the sway of the “median voter” in electoral politics, rather than the influence of organized interests in the process of policy making. A perspective centered on organizational and policy change —one that identifies the major policy shifts that have bolstered the economic standing of those at the top and then links those shifts to concrete organizational efforts by resourceful private interests —fares much better at explaining why the American political economy has become distinctively winner-take-all. (shrink)

There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we report on the development of a framework for formalizing voting theory in the Lean theorem prover, which we have applied to verify properties of a recently studied voting method. While previous applications of interactive theorem proving to social choice have (...) focused on the verification of impossibility theorems, we aim to cover a variety of results ranging from impossibility theorems to the verification of properties of specific voting methods. In order to formalize voting theoretic axioms concerning adding or removing candidates and voters, we work in a variable-election setting whose formalization makes use of dependent types in Lean. (shrink)

L S Penrose’s Limit Theorem – which is implicit in Penrose [7, p. 72] and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely and the relative quota is pegged, then – under certain conditions – the ratio between the voting powers of any two voters converges to the ratio between their weights. Lindner and Machover [4] prove some special cases of Penrose’s Limit Theorem. They (...) give a simple counter-example showing that the theorem does not hold in general even under the conditions assumed by Penrose; but they conjecture, in effect, that under rather general conditions it holds ‘almost always’ – that is with probability 1 – for large classes of weighted voting games, for various values of the quota, and with respect to several measures of voting power. We use simulation to test this conjecture. It is corroborated with respect to the Penrose–Banzhaf index for a quota of 50% but not for other values; with respect to the Shapley–Shubik index the conjecture is corroborated for all values of the quota. (shrink)

Set theoretic formulation of Arrow's theorem, viewedin light of a taxonomy of transitive relations,serves to unmask the theorem's understatedgenerality. Under the impress of the independenceof irrelevant alternatives, the antipode of ceteris paribus reasoning, a purported compilerfunction either breaches some other rationalitypremise or produces the effet Condorcet. Types of cycles, each the seeming handiwork of avirtual voter disdaining transitivity, arerigorously defined. Arrow's theorem erects adilemma between cyclic indecision anddictatorship. Maneuvers responsive theretoare explicable in set theoretic terms. None (...) ofthese gambits rival in simplicity the unassistedescape of strict linear orderings, which, by virtueof the Arrow–Sen reflexivity premise, are notcaptured by the theorem. Yet these are therelations among whose n-tuples the effetCondorcet is most frequent. A generalization andstronger theorem encompasses these and all otherlinear orderings and total tierings. Revisions tothe Arrow–Sen definitions of `choice set' and`rationalization' similarly enable one to generalizeSen's demonstration that some rational choicefunction always exists. Similarly may onegeneralize Debreu's theorems establishing conditionsunder which a binary relation may be represented bya continuous real-valued order homomorphism. (shrink)

In many democracies, voter turnout is low and getting lower. If the people choose not to govern themselves, should they be forced to do so? For Jason Brennan, compulsory voting is unjust and a petty violation of citizens' liberty. The median non-voter is less informed and rational, as well as more biased, than the median voter. According to Lisa Hill, compulsory voting is a reasonable imposition on personal liberty. Hill points to the discernible benefits of (...) compulsory voting and argues that high turnout elections are more democratically legitimate. The authors - both well-known for their work on voting and civic engagement - debate questions such as: • Do citizens have a duty to vote, and is it an enforceable duty? • Does compulsory voting violate citizens' liberty? If so, is this sufficient grounds to oppose it? Or is it a justifiable violation? Might it instead promote liberty on the whole? • Is low turnout a problem or a blessing? (shrink)

The paradox of mass voting is not, generally speaking, matched by a paradoxical mass attempt to be politically well informed. As Converse underscored, most people are grossly politically ignorant—just as they would be if, as rational‐ignorance theory holds, they realized that their votes don't matter. Yet many millions of them contradict the theory by voting. This contradiction, and the illogical reasons people offer for voting, suggest that the logic of collective action does not come naturally to people. To equate public (...) ignorance with “rational ignorance,” then, attributes too much theoretical self‐consciousness to people. Even if their ignorance is not based on a grasp of the collective‐action problem, however, people's political ignorance is “rational”: but it is less a matter of calculating the low benefit likely to flow from one vote in a sea of millions, than of encountering the much higher cost of being well informed as compared to voting. As the high cost of becoming well informed appears likely to grow, it may be advisable to move off of the political agenda issues that have no clear continuum toward which a mostly ignorant median voter may gravitate. (shrink)

This is the first book in welfare economics to be primarily intended for undergraduates and non-specialists. Concepts such as Pareto optimality in a market economy, the compensation criterion, and the social welfare function are explored in detail. Market failures are analysed by using different ways of measuring welfare changes. The book also examines public choice, and the issues of provision of public goods, median voter equilibrium, government failures, efficient and optimal taxation, and intergenerational equity. The three final chapters (...) are devoted to applied welfare economics: methods for revealing people's preferences, cost-benefit analysis, and project evaluation in a risky world. The book is intended for introductory and intermediate courses in welfare economics, microeconomics, and public economics. It will also be suitable for courses in health economics, environmental economics, and cost-benefit analysis, as well as those undertaking project evaluations in government agencies and private firms. (shrink)

In response to widespread voter ignorance, Jason Brennan argues for a voting ethics that can be summarized as one negative duty: do not vote badly. The implication that abstaining is always permissible entails no incentive for citizens to become competent voters or to vote once competent. Following the Condorcet Jury Theorem, this can lead to suboptimal outcomes, suggesting that voter turnout should concern instrumentalist epistemic accounts of democratic legitimacy. This could be addressed by adding two positive voting (...) duties: to make an effort to become a competent voter; and, once competent, to vote. (shrink)

Under the assumptions of the standard Condorcet Jury Theorem, majority verdicts are virtually certain to be correct if the competence of voters is greater than one-half, and virtually certain to be incorrect if voter competence is less than one-half. But which is the case? Here we turn the Jury Theorem on its head, to provide one way of addressing that question. The same logic implies that, if the outcome saw 60 percent of voters supporting one proposition and (...) 40 percent the other, then average voter competence must either be 0.60 or 0.40. We still have to decide which, but limiting the choice to those two values is a considerable aid in that. Key Words: Condorcet Jury Theorem • epistemic democracy • voter competence. (shrink)

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This (...) class='Hi'>theorem rehabilitates the importance of deliberation and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (shrink)

Epistemic democracy aims to show, often by appeal to the Condorcet Jury Theorem, that democracy has a high chance of reaching correct decisions. It has been argued that epistemic democracy is compatible with various metaethical accounts, such as moral realism, conventionalism and majoritarianism. This paper casts doubt on that thesis and reveals the following metaethical dilemma: if we adopt moral realism, it is doubtful that voters are, on average, more than 0.5 likely to track moral facts and identify the (...) correct alternative. By contrast, if we adopt conventionalism or majoritarianism, we cannot expect that voters are both competent and sincere. Either way, the conditions for the application of Condorcet’s theorem are not met. (shrink)

The Federalist, justifying the Electoral College to elect the president, claimed that a small group of more informed individuals would make a better decision than the general mass. But the Condorcet Jury Theorem tells us that the more independent, better-than-random voters there are, the more likely it will be that the majority among them will be correct. The question thus arises as to how much better, on average, members of the smaller group would have to be to compensate for (...) the epistemic costs of making decisions on the basis of that many fewer votes. This question is explored in the contexts of referendum democracy, delegate-style representative democracy, and trustee-style representative democracy. (shrink)

We are thankful to Gerhard Schurz for his response (Schurz 2023) to our paper (Spelda et al. 2023). Spelda et al. (2023) shows how a variant of no-regret learning called meta-induction (Schurz 2008; 2019) can be used for optimal selection from available political alternatives and, as a result, also for increasing voter competence that has come under attack from mis/disinformation. Since our paper takes a first step in applying meta-induction to long-standing issues in Democratic Theory (e.g., the usefulness of (...) jury theorems for justifying democracy), we are grateful to Gerhard Schurz for highlighting some of the conditions that need to be met for the development of practical applications. (shrink)

In his classic monograph, Social Choice and Individual Values, Arrow introduced the notion of a decisive coalition of voters as part of his mathematical framework for social choice theory. The subsequent literature on Arrow’s Impossibility Theorem has shown the importance for social choice theory of reasoning about coalitions of voters with different grades of decisiveness. The goal of this paper is a fine-grained analysis of reasoning about decisive coalitions, formalizing how the concept of a decisive coalition gives rise to (...) a social choice theoretic language and logic all of its own. We show that given Arrow’s axioms of the Independence of Irrelevant Alternatives and Universal Domain, rationality postulates for social preference correspond to strong axioms about decisive coalitions. We demonstrate this correspondence with results of a kind familiar in economics—representation theorems—as well as results of a kind coming from mathematical logic—completeness theorems. We present a complete logic for reasoning about decisive coalitions, along with formal proofs of Arrow’s and Wilson’s theorems. In addition, we prove the correctness of an algorithm for calculating, given any social rationality postulate of a certain form in the language of binary preference, the corresponding axiom in the language of decisive coalitions. These results suggest for social choice theory new perspectives and tools from logic. (shrink)

BackgroundWinning funding for health and medical research usually involves a lengthy application process. With success rates under 20%, much of the time spent by 80% of applicants could have been better used on actual research. An alternative funding system that could save time is using democracy to award the most deserving researchers based on votes from the research community. We aimed to pilot how such a system could work and examine some potential biases.MethodsWe used an online survey with a convenience (...) sample of Australian researchers. Researchers were asked to name the 10 scientists currently working in Australia that they thought most deserved funding for future research. For comparison, we used recent winners from large national fellowship schemes that used traditional peer review.ResultsVoting took a median of 5 min (inter-quartile range 3 to 10 min). Extrapolating to a national voting scheme, we estimate 599 working days of voting time (95% CI 490 to 728), compared with 827 working days for the current peer review system for fellowships. The gender ratio in the votes was a more equal 45:55 (female to male) compared with 34:66 in recent fellowship winners, although this could be explained by Simpson’s paradox. Voters were biased towards their own institution, with an additional 1.6 votes per ballot (inter-quartile range 0.8 to 2.2) above the expected number. Respondents raised many concerns about the idea of using democracy to fund research, including vote rigging, lobbying and it becoming a popularity contest.ConclusionsThis is a preliminary study of using voting that does not investigate many of the concerns about how a voting system would work. We were able to show that voting would take less time than traditional peer review and would spread the workload over many more reviewers. Further studies of alternative funding systems are needed as well as a wide discussion with the research community about potential changes. (shrink)

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis : 865–895, 2016) shows that when voters have ambiguous prior beliefs—a set of priors—and follow maxmin expected utility, such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead (...) to posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error. In a classical model, Feddersen and Pesendorfer :23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis : 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals. (shrink)

Suppose a committee or a jury confronts a complex question, the answer to which requires attending to several sub-questions. Two different voting procedures can be used. On one, the committee members vote on each sub-question and the voting results are used as premises for the committee’s conclusion on the main issue. This premise-based procedure can be contrasted with the conclusion-based approach, which requires the members to directly vote on the conclusion, with the vote of each member being guided by her (...) views on the relevant sub-questions. The two procedures are not equivalent: There may be a majority of voters supporting each of the premises, but if these majorities do not significantly overlap, there will be a majority against the conclusion. Pettit (2001) connects the choice between the two procedures with the discussion of deliberative democracy. The problem we want to examine instead concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. Which of them is better when it comes to tracking truth? As it turns out, the answer is not univocal. On the basis of Condorcet’s jury theorem, the premise-based procedure can be shown to be superior if the objective is reach truth for the right reasons, without making any mistakes on the way. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be cases in which using the conclusion-based procedure turns out to be more reliable, even though, for the most part, the premise-based procedure will retain its superiority. (shrink)

We introduce a new theorem in social choice theory built on a path integral approach which will show that, under some reasonable conditions, there is a unique way to aggregate individual preferences based on fuzzy sets into a social preference based on probabilities, and that this way is invariant under any permutation of alternatives. We then apply this theorem to the case of democratic decision making with data of the behaviour and voting preferences of voting agents and show (...) that there is a tradeoff between fairness and efficiency and that no voting system can achieve both simultaneously. (shrink)

Antonio Quesada (Public Choice 130:395–400, 2007) argues that a dictator has no more than two to three times the ‘average power’ of a non-dictatorial voter. If Quesada is correct, then his argument has major consequences for social choice theory; for instance, it warrants reconsidering the significance of Arrow’s Theorem. If Quesada is incorrect, however, then his position is dangerously misleading. This paper argues that Quesada is wrong. His argument depends on his own formal account of power, an account (...) that is implausible because it disregards a basic insight common to the standard characterisations of voting power: the idea that one has power over an outcome to the extent that one is able to change that outcome. Claims about power have a counterfactual component; to assert that an individual actually has determined an outcome is also to make an assertion about what would have been the case had that individual acted differently. We can employ David Lewis’s influential account of counterfactuals to show, contra Quesada, that in a dictatorship, nondictatorial individuals and groups cannot possibly determine a social preference. In short, Quesada is fundamentally mistaken about power, and thus also about the distribution of power in a dictatorship. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:138 In 2010 the city of Colorado Springs was strapped for cash. Government officials announced that they would either have to raise revenue through increased taxation or cut public services—­ in some cases rather severely—­ including, perhaps, police and fire protection, and even more basic bits of municipal infrastructure. The city shut down one-­ third of residential streetlights and closed public restrooms. Citi­ zens were outraged, but a majority (...) of voters had recently defeated a proposed tax increase. It’s tempting to suppose that the city was trying to teach its citizens a lesson: if you want public services, you have to be willing to pay for them. Colorado Springs is, and has been for some time now, a died-­in-­the-­wool small-­government, anti-­tax-­increase, fiscally conservative town. As Colorado Springs resident Bo Sharifi put it, “As soon as I hear government [say] ‘Oh, we need more money’... I guess I kind of automatically assume there’s probably some other things you could probably cut before firemen, policemen, city lights and that sort of thing.”1 On the surface, that seems reasonable. So... what comes to mind? How about food stamps? What about WIC? Of course these are federal services, not funded by Coloradans alone. There’s government, and then there’s government. Well, how about... well... what? Doesn’t the government spend money on all sorts of things we could very easily do without? Perhaps. Isn’t it part of our job to know or to decide which things these are? If we don’t trust government, even more obviously we don’t trust it with our money, though we pretty clearly have no idea how public funds are actually allocated or spent. When asked whether he remembered the proposed tax increase that the city had voted against, Sharifi replied, “maybe.” Bo and his wife were charged $125 to have Connected: How Trains, Genes, Pineapples, Piano Keys, and a Few Disasters Transformed Americans at the Dawn of the Twentieth Century By Steven Cassedy Stanford: Stanford University Press, 2014 JOHN MARIANA Book Reviews 139 their streetlight turned back on. Bo’s wife Sara viewed this as extortion. “By shoveling out a hundred dollars to turn on a streetlight that we kind of felt was supposed to be on anyway, that it was giving them what they wanted,” she said. They who? One resident wrote the city of Colorado Springs a check for $300 to turn the lights on for his entire neighborhood. City Councilwoman Jan Martin pointed out to him that the total cost to the individual Colorado Springs taxpayer to keep the streetlights on—­and to fund the maintenance of public parks and medians, as well as community centers and pre-­recession-­level police and fire services—­by approving the tax increase would have been: $200. He replied that he would never vote for a tax increase. In other words, as the reporter who covered the story (Robert Smith) observed, he would rather pay more to keep the streetlights on in his own neighborhood than to pay for all city services combined. Smith remarked that “Colorado Springs was stepping away from one of the things that we take for granted in most American cities: that we’re all in it together—­ at least when it comes to basic services.”2 As near as I can tell, this is the moral of Steven Cassedy’s exceptionally timely Connected: that we’re all in it together. For much of the book Cassedy merely traces the history of the emergence in the consciousness of ordinary Americans of the concept of the social network, but he is not so much talking about the notion of a network society as such, as I understand him. Or, at any rate, the network society as such is not really his main concern. He is talking about the idea of social, political, national, and ultimately global and universal human interconnectedness that was a distinct product of the complex networked structures (both concrete and abstract) that came to constitute modern American life in the twentieth century (and of course life pretty much everywhere ), and about our understanding of ourselves as so networked.3 On this... (shrink)

This book represents a considerable revision and expansion of Public Choice II. Six new chapters have been added, and several chapters from the previous edition have been extensively revised. The discussion of empirical work in public choice has been greatly expanded. As in the previous editions, all of the major topics of public choice are covered. These include: why the state exists, voting rules, federalism, the theory of clubs, two-party and multiparty electoral systems, rent seeking, bureaucracy, interest groups, dictatorship, the (...) size of government, voter participation, and political business cycles. Normative issues in public choice are also examined including a normative analysis of the simple majority rule, Bergson–Samuelson social welfare functions, the Arrow and Sen impossibility theorems, Rawls's social contract theory and the constitutional political economy of Buchanan and Tullock. (shrink)

I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is at least in some cases to identify which of several policy proposals will best promote the public good. To support this view I first briefly investigate several notions of the kind of public good that public policy should promote. Then I examine the probability logic of voting as embodied in two very robust versions of the Condorcet Jury Theorem and some related (...) results. These theorems show that if the number of voters or legislators is sufficiently large and the average of their individual propensities to select the better of two policy proposals is a little above random chance, and if each person votes his or her own best judgment (rather than in alliance with a block or faction), then the majority is extremely likely to select the better alternative. Here ‘better alternative’ means that policy or law that will best promote the public good. I also explicate a Convincing Majorities Theorem, which shows the extent to which the majority vote should provide evidence that the better policy has been selected. Finally, I show how to extend all of these results to judgments among multiple alternatives through the kind of sequential balloting typical of the legislative amendment process. (shrink)

Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg- Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer (...) based on the following insight: we can view Legg-Hutter agents as candidates in an election, whose voters are environments, letting each environment vote (via its rewards) which agent (if either) is more intelligent. This leads to an abstract family of comparators simple enough that we can prove some structural theorems about them. It is an open question whether these structural theorems apply to more practical intelligence measures. (shrink)

It is not uncommon to be frustrated by the outcome of an election or a decision in voting, law, economics, engineering, and other fields. Does this 'bad' result reflect poor data or poorly informed voters? Or does the disturbing conclusion reflect the choice of the decision/election procedure? Nobel Laureate Kenneth Arrow's famed theorem has been interpreted to mean 'no decision procedure is without flaws'. Similarly, Nobel Laureate Amartya Sen dashes hope for individual liberties by showing their incompatibility with societal (...) needs. This highly accessible book offers a new, different interpretation and resolution of Arrow's and Sen's theorems. Using simple mathematics, it shows that these negative conclusions arise because, in each case, some of their assumptions negate other crucial assumptions. Once this is understood, not only do the conclusions become expected, but a wide class of other phenomena can also be anticipated. (shrink)

Proposals to lower the age of voting, to 15 for example, are regularly met with worries that people that age are not sufficiently ‘competent’. Notice however that we allow people that age to sign binding legal contracts, provided that those contracts are co-signed by their parents. Notice, further, that in a democracy voters are collectively ‘joint authors’ of the laws that they enact. Enfranchising some less competent voters is no worry, the Condorcet Jury Theorem assures us, so long as (...) the electorate's competence averaging across all voters remains better-than-random. (shrink)