Jury voting without objective probability

© 2015, Springer-Verlag Berlin Heidelberg. Unlike in the standard jury voting experiment, the voting environment in practice has no explicit signal structure. Voters then need to conceptualize the information structure in order to update their beliefs based on “pivotal reasoning”. This paper investigates whether voters can play a strategic voting under a “detail-free” environment. We obtain non-parametric predictions in terms of the differences in voting behaviors under majority and unanimity rule. Our experimental results suggest that voters can still play the strategic voting as in the existing experiments

Plural Voting for the Twenty-First Century

Recent political developments cast doubt on the wisdom of democratic decision-making. Brexit, the Colombian people's (initial) rejection of peace with the FARC, and the election of Donald Trump suggest that the time is right to explore alternatives to democracy. In this essay, I describe and defend the epistocratic system of government which is, given current theoretical and empirical knowledge, most likely to produce optimal political outcomes—or at least better outcomes than democracy produces. To wit, we should expand the suffrage as wide as possible and weight citizens’ votes in accordance with their competence. As it turns out, the optimal system is closely related to J. S. Mill's plural voting proposal. I also explain how voters’ competences can be precisely determined, without reference to an objective standard of correctness and without generating invidious comparisons between voters

Jury Theorems

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’

Whom to Ask? Jury Selection for Decision Making Tasks on Micro-blog Services

It is universal to see people obtain knowledge on micro-blog services by asking others decision making questions. In this paper, we study the Jury Selection Problem(JSP) by utilizing crowdsourcing for decision making tasks on micro-blog services. Specifically, the problem is to enroll a subset of crowd under a limited budget, whose aggregated wisdom via Majority Voting scheme has the lowest probability of drawing a wrong answer(Jury Error Rate-JER). Due to various individual error-rates of the crowd, the calculation of JER is non-trivial. Firstly, we explicitly state that JER is the probability when the number of wrong jurors is larger than half of the size of a jury. To avoid the exponentially increasing calculation of JER, we propose two efficient algorithms and an effective bounding technique. Furthermore, we study the Jury Selection Problem on two crowdsourcing models, one is for altruistic users(AltrM) and the other is for incentive-requiring users(PayM) who require extra payment when enrolled into a task. For the AltrM model, we prove the monotonicity of JER on individual error rate and propose an efficient exact algorithm for JSP. For the PayM model, we prove the NP-hardness of JSP on PayM and propose an efficient greedy-based heuristic algorithm. Finally, we conduct a series of experiments to investigate the traits of JSP, and validate the efficiency and effectiveness of our proposed algorithms on both synthetic and real micro-blog data.Comment: VLDB201

Theoretical Aspects of Collective Decision Making - Survey of the Economic Literature

The article aims at surveying the economic literature related to collective decision making. In order to do so it proposes a coherent framework allowing for a structured analysis of the factors influencing the works of a committee. These factors are divided into external ( shaped outside of the committee e.g. by law) and internal ones (related to the composition of the committee and interactions between its members). The survey of the general economic literature related to collective decision making presented within the proposed framework yields interesting suggestions for further research, including the consequences for the shape of monetary policy committeesArtykuł ma na celu dokonanie przeglądu literatury ekonomicznej z zakresu kolektywnego podejmowania decyzji. W tym celu zaproponowano ramy pozwalające na ustrukturyzowaną analizę czynników wpływających na pracę organu kolektywnego (rady). Dokonano podziału tych czynników na zewnętrzne (tzn. kształtowane poza samą radą, np. przez wymogi prawne) oraz wewnętrzne (związane ze składem rady oraz interakcjami między jej członkami). Dokonany w ramach zaproponowanej struktury przegląd literatury ogólnoekonomicznej dotyczącej kolektywnego podejmowania decyzji pozwala na zaproponowanie interesujących kierunków dalszych badań, w tym konsekwencji dla kształtu rad polityki pieniężnej

The Premises of Condorcet's Jury Theorem Are Not Simultaneously Justified

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 justified depends on the notion of probability considered; (ii) none of the notions renders both premises simultaneously justified. Under the perhaps most interesting notions, the independence assumption should be weakened.mathematical economics;

Information acquisition and decision making in committees: a survey

JEL Classification: D71, E52Committees, costly information acquisition, monetary policy committees, strategic voting

A Bayesian Model of Voting in Juries

We take a game-theoretic approach to the analysis of juries by modelling voting as a game of incomplete information. Rather than the usual assumption of two possible signals (one indicating guilt, the other innocence), we allow jurors to perceive a full spectrum of signals. Given any voting rule requiring a fixed fraction of votes to convict, we characterize the unique symmetric equilibrium of the game, and we consider the possibility of asymmetric equilibria: we give a condition under which no asymmetric equilibria exist and show that, without under which no asymmetric equilibria exist and show that, without it, asymmetric equilibria may exist. We offer a condition under which unanimity rule exhibits a bias toward convicting the innocent, regardless of the size of the jury, and we exhibit an example showing this bias can be reversed. And we prove a "jury theorem" for our general model: as the size of the jury increases, the probability of a mistaken judgment goes to zero for every voting rule, except unanimity rule; for unanimity rule, we give a condition under which the probability of a mistake is bounded strictly above zero, and we show that, without this condition, the probability of a mistake may go to zero.

Judgment aggregation in search for the truth

We analyze the problem of aggregating judgments over multiple issues from the perspective of whether aggregate judgments manage to efficiently use all voters' private information. While new in judgment aggregation theory, this perspective is familiar in a different body of literature about voting between two alternatives where voters' disagreements stem from conflicts of information rather than of interest. Combining the two bodies of literature, we consider a simple judgment aggregation problem and model the private information underlying voters' judgments. Assuming that voters share a preference for true collective judgments, we analyze the resulting strategic incentives and determine which voting rules efficiently use all private information. We find that in certain, but not all cases a quota rule should be used, which decides on each issue according to whether the proportion of ‘yes’ votes exceeds a particular quota