12,838 research outputs found
Scoring rules for judgment aggregation
This paper studies a class of judgment aggregation rules, to be called 'scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total 'score' across the individuals, subject to the judgments having to be rational. Depending on how we define 'scores', we obtain several (old and new) solutions to the judgment aggregation problem, such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a generalization of Borda rule to judgment aggregation. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory
Scoring rules for judgment aggregation
This paper studies a class of judgment aggregation rules, to be called `scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total `score' across the individuals, subject to the judgments having to be rational. Depending on how we define `scores', we obtain several (old and new) solutions to the judgment aggregation problem,such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a Borda-type rule. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory
Scoring rules for judgment aggregation
This paper studies a class of judgment aggregation rules, to be called `scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total `score' across the individuals, subject to the judgments having to be rational. Depending on how we define `scores', we obtain several (old and new) solutions to the judgment aggregation problem,such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a Borda-type rule. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory
Scoring rules for judgment aggregation
This paper studies a class of judgment aggregation rules, to be called `scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total `score' across the individuals, subject to the judgments having to be rational. Depending on how we define `scores', we obtain several (old and new) solutions to the judgment aggregation problem,such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a Borda-type rule. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory
A partial taxonomy of judgment aggregation rules, and their properties
The literature on judgment aggregation is moving from studying impossibility
results regarding aggregation rules towards studying specific judgment
aggregation rules. Here we give a structured list of most rules that have been
proposed and studied recently in the literature, together with various
properties of such rules. We first focus on the majority-preservation property,
which generalizes Condorcet-consistency, and identify which of the rules
satisfy it. We study the inclusion relationships that hold between the rules.
Finally, we consider two forms of unanimity, monotonicity, homogeneity, and
reinforcement, and we identify which of the rules satisfy these properties
A non-proposition-wise variant of majority voting for aggregating judgments
Majority voting is commonly used in aggregating judgments. The literature to date on judgment
aggregation (JA) has focused primarily on proposition-wise majority voting (PMV). Given a set of issues
on which a group is trying to make collective judgments, PMV aggregates individual judgments issue by
issue, and satisfies a salient property of JA rules—independence. This paper introduces a variant of
majority voting called holistic majority voting (HMV). This new variant also meets the condition of
independence. However, instead of aggregating judgments issue by issue, it aggregates individual
judgments en bloc. A salient and straightforward feature of HMV is that it guarantees the logical
consistency of the propositions expressing collective judgments, provided that the individual points of
view are consistent. This feature contrasts with the known inability of PMV to guarantee the consistency
of the collective outcome. Analogously, while PMV may present a set of judgments that have been
rejected by everyone in the group as collectively accepted, the collective judgments returned by HMV
have been accepted by a majority of individuals in the group and, therefore, rejected by a minority of
them at most. In addition, HMV satisfies a large set of appealing properties, as PMV also does. However,
HMV may not return any complete proposition expressing the judgments of the group on all the issues at
stake, even in cases where PMV does. Moreover, demanding completeness from HMV leads to
impossibility results similar to the known impossibilities on PMV and on proposition-wise JA rules in
genera
On the Accuracy of Group Credences
to appear in Szabó Gendler, T. & J. Hawthorne (eds.) Oxford Studies in Epistemology volume 6
We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular group in question? According to the credal judgment aggregation principle, Linear Pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this paper, I give an argument for Linear Pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle
Voting rules as statistical estimators
We adopt an `epistemic' interpretation of social decisions: there is an objectively correct choice, each voter receives a `noisy signal' of the correct choice, and the social objective is to aggregate these signals to make the best possible guess about the correct choice. One epistemic method is to fix a probability model and compute the maximum likelihood estimator (MLE), maximum a posteriori estimator (MAP) or expected utility maximizer (EUM), given the data provided by the voters. We first show that an abstract voting rule can be interpreted as MLE or MAP if and only if it is a scoring rule. We then specialize to the case of distance-based voting rules, in particular, the use of the median rule in judgement aggregation. Finally, we show how several common `quasiutilitarian' voting rules can be interpreted as EUM.voting; maximum likelihood estimator; maximum a priori estimator; expected utility maximizer; statistics; epistemic democracy; Condorcet jury theorem; scoring rule
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