22 research outputs found
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
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
Jury Theorems
We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcetâs (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 âwisdom of crowdsâ. In particular, we argue (i) that there is a fundamental tension between votersâ independence and votersâ competence, hence between the two premises of most jury theorems; (ii) that the (asymptotic) conclusion that âhuge groups are infallibleâ, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that âlarger groups are more reliableâ, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the âwisdom of crowdsâ
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 âyesâ votes exceeds a particular quota
Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers
We introduce a new Condorcet consistent voting method, called Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying independence of clones and the Pareto principle. Unlike other methods in this family, Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, relative to other clone-independent Paretian methods, Split Cycle mitigates âspoiler effectsâ and âstrong no show paradoxes.
Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers
We propose a Condorcet consistent voting method that we call Split Cycle.
Split Cycle belongs to the small family of known voting methods that
significantly narrow the choice of winners in the presence of majority cycles
while also satisfying independence of clones. In this family, only Split Cycle
satisfies a new criterion we call immunity to spoilers, which concerns adding
candidates to elections, as well as the known criteria of positive involvement
and negative involvement, which concern adding voters to elections. Thus, in
contrast to other clone-independent methods, Split Cycle mitigates both
"spoiler effects" and "strong no show paradoxes."Comment: 71 pages, 15 figures. Added a new explanation of Split Cycle in
Section 1, updated the caption to Figure 2, the discussion in Section 3.3,
and Remark 4.11, and strengthened Proposition 6.20 to Theorem 6.20 to cover
single-voter resolvability in addition to asymptotic resolvability. Thanks to
Nicolaus Tideman for helpful discussio
Jury Theorems
We give a review of jury theorems, including Condorcet's (1785) classic theorem and several later refinements and departures. The review comes with a critique of jury theorems from a social-epistemology perspective. We assess the plausibility of the theorems' conclusions and premises and the potential of jury 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 typical 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 (non-asymptotic) 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'
A Statistical Decision-Theoretic Framework for Social Choice
In this paper, we take a statistical decision-theoretic viewpoint on social choice, putting a focus on the decision to be made on behalf of a system of agents. In our framework, we are given a statistical ranking model, a decision space, and a loss function defined on (parameter, decision) pairs, and formulate social choice mechanisms as decision rules that minimize expected loss. This suggests a general framework for the design and analysis of new social choice mechanisms. We compare Bayesian estimators, which minimize Bayesian expected loss, for the Mallows model and the Condorcet model respectively, and the Kemeny rule. We consider various normative properties, in addition to computational complexity and asymptotic behavior. In particular, we show that the Bayesian estimator for the Condorcet model satisfies some desired properties such as anonymity, neutrality, and monotonicity, can be computed in polynomial time, and is asymptotically different from the other two rules when the data are generated from the Condorcet model for some ground truth parameter.Engineering and Applied Science