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When do noisy votes reveal the truth? (2013).
| Content Provider | CiteSeerX |
|---|---|
| Author | Caragiannis, Ioannis Procaccia, Ariel D. Shah, Nisarg |
| Abstract | A well-studied approach to the design of voting rules views them as maximum likelihood estimators; given votes that are seen as noisy estimates of a true ranking of the alternatives, the rule must reconstruct the most likely true ranking. We argue that this is too stringent a requirement, and instead ask: How many votes does a voting rule need to reconstruct the true ranking? We define the family of pairwise-majority consistent rules, and show that for all rules in this family the number of samples required from the Mallows noise model is logarithmic in the number of alternatives, and that no rule can do asymptotically better (while some rules like plurality do much worse). Taking a more normative point of view, we consider voting rules that surely return the true ranking as the number of samples tends to infinity (we call this property accuracy in the limit); this allows us to move to a higher level of abstraction. We study families of noise models that are parametrized by distance functions, and find voting rules that are accurate in the limit for all noise models in such general families. We characterize the distance functions that induce noise models for which pairwise-majority consistent rules are accurate in the limit, and provide a similar result for another novel family of position-dominance consistent rules. These characterizations capture three well-known distance functions. |
| File Format | |
| Publisher Date | 2013-01-01 |
| Access Restriction | Open |
| Subject Keyword | Noisy Vote Reveal True Ranking Voting Rule Noise Model Distance Function Pairwise-majority Consistent Rule Many Vote Well-known Distance Function Novel Family Normative Point Position-dominance Consistent Rule Property Accuracy Similar Result Noisy Estimate Mallow Noise Model Maximum Likelihood Estimator General Family Likely True Ranking Sample Tends Well-studied Approach |
| Content Type | Text |
