NDLI: Voting with Limited Information and Many Alternatives

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Voting with Limited Information and Many Alternatives

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kleinberg, Jon Chierichetti, Flavio
Copyright Year	2014
Abstract	The traditional axiomatic approach to voting is motivated by the problem of reconciling differences in subjective preferences. In contrast, an important line of work in the theory of voting has considered a different kind of scenario, also fundamental to voting, in which there is a genuinely best outcome that voters would agree on if they only had enough information. This type of scenario has its roots in the classical Condorcet jury theorem; it includes cases such as jurors in a criminal trial who all want to reach the correct verdict but disagree in their inferences from the available evidence, or a corporate board of directors who all want to improve the company's revenue but who have different information that favors different options. This style of voting leads to a natural set of questions: each voter has a private signal that provides probabilistic information about which option is best, and a central question is whether a simple plurality voting system, which tabulates votes for different options, can cause the group decision to arrive at the correct option. We show that plurality voting is powerful enough to achieve this: there is a way for voters to map their signals into votes for options in such a way that---with sufficiently many voters---the correct option receives the greatest number of votes with high probability. We show further, however, that any process for achieving this is inherently expensive in the number of voters it requires: succeeding in identifying the correct option with probability at least $1 - \eta$ requires $\Omega(n^3 \epsilon^{-2} \log \eta^{-1})$ voters, where $n$ is the number of options and $\epsilon$ is a distributional measure of the minimum difference between the options.
Starting Page	1615
Ending Page	1653
Page Count	39
File Format	PDF
ISSN	00975397
DOI	10.1137/130936592
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	43
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-09-17
Access Restriction	Subscribed
Subject Keyword	Voting theory sampling voting systems
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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