1,704 research outputs found
Randomized strategies for the plurality problem
AbstractWe consider a game played by two players, Paul and Carol. At the beginning of the game, Carol fixes a coloring of n balls. At each turn, Paul chooses a pair of the balls and asks Carol whether the balls have the same color. Carol truthfully answers his question. Paul’s goal is to determine the most frequent (plurality) color in the coloring by asking as few questions as possible. The game is studied in the probabilistic setting when Paul is allowed to choose his next question randomly.We give asymptotically tight bounds both for the case of two colors and many colors. For the balls colored by k colors, we prove a lower bound Ω(kn) on the expected number of questions; this is asymptotically optimal. For the balls colored by two colors, we provide a strategy for Paul to determine the plurality color with the expected number of 2n/3+O(nlogn) questions; this almost matches the lower bound 2n/3−O(n)
The Complexity of Manipulating -Approval Elections
An important problem in computational social choice theory is the complexity
of undesirable behavior among agents, such as control, manipulation, and
bribery in election systems. These kinds of voting strategies are often
tempting at the individual level but disastrous for the agents as a whole.
Creating election systems where the determination of such strategies is
difficult is thus an important goal.
An interesting set of elections is that of scoring protocols. Previous work
in this area has demonstrated the complexity of misuse in cases involving a
fixed number of candidates, and of specific election systems on unbounded
number of candidates such as Borda. In contrast, we take the first step in
generalizing the results of computational complexity of election misuse to
cases of infinitely many scoring protocols on an unbounded number of
candidates. Interesting families of systems include -approval and -veto
elections, in which voters distinguish candidates from the candidate set.
Our main result is to partition the problems of these families based on their
complexity. We do so by showing they are polynomial-time computable, NP-hard,
or polynomial-time equivalent to another problem of interest. We also
demonstrate a surprising connection between manipulation in election systems
and some graph theory problems
A Local-Dominance Theory of Voting Equilibria
It is well known that no reasonable voting rule is strategyproof. Moreover,
the common Plurality rule is particularly prone to strategic behavior of the
voters and empirical studies show that people often vote strategically in
practice. Multiple game-theoretic models have been proposed to better
understand and predict such behavior and the outcomes it induces. However,
these models often make unrealistic assumptions regarding voters' behavior and
the information on which they base their vote.
We suggest a new model for strategic voting that takes into account voters'
bounded rationality, as well as their limited access to reliable information.
We introduce a simple behavioral heuristic based on \emph{local dominance},
where each voter considers a set of possible world states without assigning
probabilities to them. This set is constructed based on prospective candidates'
scores (e.g., available from an inaccurate poll). In a \emph{voting
equilibrium}, all voters vote for candidates not dominated within the set of
possible states.
We prove that these voting equilibria exist in the Plurality rule for a broad
class of local dominance relations (that is, different ways to decide which
states are possible). Furthermore, we show that in an iterative setting where
voters may repeatedly change their vote, local dominance-based dynamics quickly
converge to an equilibrium if voters start from the truthful state. Weaker
convergence guarantees in more general settings are also provided.
Using extensive simulations of strategic voting on generated and real
preference profiles, we show that convergence is fast and robust, that emerging
equilibria are consistent across various starting conditions, and that they
replicate widely known patterns of human voting behavior such as Duverger's
law. Further, strategic voting generally improves the quality of the winner
compared to truthful voting
Computing Majority with Triple Queries
Consider a bin containing balls colored with two colors. In a -query,
balls are selected by a questioner and the oracle's reply is related
(depending on the computation model being considered) to the distribution of
colors of the balls in this -tuple; however, the oracle never reveals the
colors of the individual balls. Following a number of queries the questioner is
said to determine the majority color if it can output a ball of the majority
color if it exists, and can prove that there is no majority if it does not
exist. We investigate two computation models (depending on the type of replies
being allowed). We give algorithms to compute the minimum number of 3-queries
which are needed so that the questioner can determine the majority color and
provide tight and almost tight upper and lower bounds on the number of queries
needed in each case.Comment: 22 pages, 1 figure, conference version to appear in proceedings of
the 17th Annual International Computing and Combinatorics Conference (COCOON
2011
Most Expected Winner: An Interpretation of Winners over Uncertain Voter Preferences
It remains an open question how to determine the winner of an election when
voter preferences are incomplete or uncertain. One option is to assume some
probability space over the voting profile and select the Most Probable Winner
(MPW) -- the candidate or candidates with the best chance of winning. In this
paper, we propose an alternative winner interpretation, selecting the Most
Expected Winner (MEW) according to the expected performance of the candidates.
We separate the uncertainty in voter preferences into the generation step and
the observation step, which gives rise to a unified voting profile combining
both incomplete and probabilistic voting profiles. We use this framework to
establish the theoretical hardness of \mew over incomplete voter preferences,
and then identify a collection of tractable cases for a variety of voting
profiles, including those based on the popular Repeated Insertion Model (RIM)
and its special case, the Mallows model. We develop solvers customized for
various voter preference types to quantify the candidate performance for the
individual voters, and propose a pruning strategy that optimizes computation.
The performance of the proposed solvers and pruning strategy is evaluated
extensively on real and synthetic benchmarks, showing that our methods are
practical.Comment: This is the technical report of the following paper: Haoyue Ping and
Julia Stoyanovich. 2023. Most Expected Winner: An Interpretation of Winners
over Uncertain Voter Preferences. Proc. ACM Manag. Data, 1, N1, Article 22
(May 2023), 33 pages. https://doi.org/10.1145/358870
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