18,697 research outputs found
Information-Theoretic Study of Voting Systems
The typical paradigm in voting theory involves n
voters and m candidates. Every voter ranks the candidates resulting
in a permutation of the m candidates. A key problem is
to derive the aggregate result of the voting. A popular method
for vote aggregation is based on the Condorcet criterion. The
Condorcet winner is the candidate who wins every other candidate
by pairwise majority. However, the main disadvantage of
this approach, known as the Condorcet paradox, is that such a
winner does not necessarily exist since this criterion does not admit
transitivity. This paradox is mathematically likely (if voters
assign rankings uniformly at random, then with probability approaching
one with the number of candidates, there will not be
a Condorcet winner), however, in real life scenarios such as elections,
it is not likely to encounter the Condorcet paradox. In this
paper we attempt to improve our intuition regarding the gap between
the mathematics and reality of voting systems. We study a
special case where there is global intransitivity between all candidates.
We introduce tools from information theory and derive
an entropy-based characterization of global intransitivity. In addition,
we tighten this characterization by assuming that votes
tend to be similar; in particular they can be modeled as permutations
that are confined to a sphere defined by the Kendalls Ï„
distance
Tuning the Diversity of Open-Ended Responses from the Crowd
Crowdsourcing can solve problems that current fully automated systems cannot.
Its effectiveness depends on the reliability, accuracy, and speed of the crowd
workers that drive it. These objectives are frequently at odds with one
another. For instance, how much time should workers be given to discover and
propose new solutions versus deliberate over those currently proposed? How do
we determine if discovering a new answer is appropriate at all? And how do we
manage workers who lack the expertise or attention needed to provide useful
input to a given task? We present a mechanism that uses distinct payoffs for
three possible worker actions---propose,vote, or abstain---to provide workers
with the necessary incentives to guarantee an effective (or even optimal)
balance between searching for new answers, assessing those currently available,
and, when they have insufficient expertise or insight for the task at hand,
abstaining. We provide a novel game theoretic analysis for this mechanism and
test it experimentally on an image---labeling problem and show that it allows a
system to reliably control the balance betweendiscovering new answers and
converging to existing ones
On Rational Delegations in Liquid Democracy
Liquid democracy is a proxy voting method where proxies are delegable. We
propose and study a game-theoretic model of liquid democracy to address the
following question: when is it rational for a voter to delegate her vote? We
study the existence of pure-strategy Nash equilibria in this model, and how
group accuracy is affected by them. We complement these theoretical results by
means of agent-based simulations to study the effects of delegations on group's
accuracy on variously structured social networks.Comment: 17 pages, 3 figures. This paper (without Appendix) appears in the
proceedings of AAAI'1
Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data
We consider learning, from strictly behavioral data, the structure and
parameters of linear influence games (LIGs), a class of parametric graphical
games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic
inference (CSI): Making inferences from causal interventions on stable behavior
in strategic settings. Applications include the identification of the most
influential individuals in large (social) networks. Such tasks can also support
policy-making analysis. Motivated by the computational work on LIGs, we cast
the learning problem as maximum-likelihood estimation (MLE) of a generative
model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation
uncovers the fundamental interplay between goodness-of-fit and model
complexity: good models capture equilibrium behavior within the data while
controlling the true number of equilibria, including those unobserved. We
provide a generalization bound establishing the sample complexity for MLE in
our framework. We propose several algorithms including convex loss minimization
(CLM) and sigmoidal approximations. We prove that the number of exact PSNE in
LIGs is small, with high probability; thus, CLM is sound. We illustrate our
approach on synthetic data and real-world U.S. congressional voting records. We
briefly discuss our learning framework's generality and potential applicability
to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending
publication.) Last conference version: submitted March 30, 2012 to UAI 2012.
First conference version: entitled, Learning Influence Games, initially
submitted on June 1, 2010 to NIPS 201
Haplotype Assembly: An Information Theoretic View
This paper studies the haplotype assembly problem from an information
theoretic perspective. A haplotype is a sequence of nucleotide bases on a
chromosome, often conveniently represented by a binary string, that differ from
the bases in the corresponding positions on the other chromosome in a
homologous pair. Information about the order of bases in a genome is readily
inferred using short reads provided by high-throughput DNA sequencing
technologies. In this paper, the recovery of the target pair of haplotype
sequences using short reads is rephrased as a joint source-channel coding
problem. Two messages, representing haplotypes and chromosome memberships of
reads, are encoded and transmitted over a channel with erasures and errors,
where the channel model reflects salient features of high-throughput
sequencing. The focus of this paper is on the required number of reads for
reliable haplotype reconstruction, and both the necessary and sufficient
conditions are presented with order-wise optimal bounds.Comment: 30 pages, 5 figures, 1 tabel, journa
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