12 research outputs found
How many candidates are needed to make elections hard to manipulate?
In multiagent settings where the agents have different preferences,
preference aggregation is a central issue. Voting is a general method for
preference aggregation, but seminal results have shown that all general voting
protocols are manipulable. One could try to avoid manipulation by using voting
protocols where determining a beneficial manipulation is hard computationally.
The complexity of manipulating realistic elections where the number of
candidates is a small constant was recently studied (Conitzer 2002), but the
emphasis was on the question of whether or not a protocol becomes hard to
manipulate for some constant number of candidates. That work, in many cases,
left open the question: How many candidates are needed to make elections hard
to manipulate? This is a crucial question when comparing the relative
manipulability of different voting protocols. In this paper we answer that
question for the voting protocols of the earlier study: plurality, Borda, STV,
Copeland, maximin, regular cup, and randomized cup. We also answer that
question for two voting protocols for which no results on the complexity of
manipulation have been derived before: veto and plurality with runoff. It turns
out that the voting protocols under study become hard to manipulate at 3
candidates, 4 candidates, 7 candidates, or never
Computer Science and Game Theory: A Brief Survey
There has been a remarkable increase in work at the interface of computer
science and game theory in the past decade. In this article I survey some of
the main themes of work in the area, with a focus on the work in computer
science. Given the length constraints, I make no attempt at being
comprehensive, especially since other surveys are also available, and a
comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic
Dichotomy for voting systems
AbstractScoring protocols are a broad class of voting systems. Each is defined by a vector (α1,α2,…,αm), α1⩾α2⩾⋯⩾αm, of integers such that each voter contributes α1 points to his/her first choice, α2 points to his/her second choice, and so on, and any candidate receiving the most points is a winner.What is it about scoring-protocol election systems that makes some have the desirable property of being NP-complete to manipulate, while others can be manipulated in polynomial time? We find the complete, dichotomizing answer: Diversity of dislike. Every scoring-protocol election system having two or more point values assigned to candidates other than the favorite—i.e., having ‖{αi|2⩽i⩽m}‖⩾2—is NP-complete to manipulate. Every other scoring-protocol election system can be manipulated in polynomial time. In effect, we show that—other than trivial systems (where all candidates alway tie), plurality voting, and plurality voting's transparently disguised translations—every scoring-protocol election system is NP-complete to manipulate
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
Anyone but Him: The Complexity of Precluding an Alternative
Preference aggregation in a multiagent setting is a central issue in both
human and computer contexts. In this paper, we study in terms of complexity the
vulnerability of preference aggregation to destructive control. That is, we
study the ability of an election's chair to, through such mechanisms as
voter/candidate addition/suppression/partition, ensure that a particular
candidate (equivalently, alternative) does not win. And we study the extent to
which election systems can make it impossible, or computationally costly
(NP-complete), for the chair to execute such control. Among the systems we
study--plurality, Condorcet, and approval voting--we find cases where systems
immune or computationally resistant to a chair choosing the winner nonetheless
are vulnerable to the chair blocking a victory. Beyond that, we see that among
our studied systems no one system offers the best protection against
destructive control. Rather, the choice of a preference aggregation system will
depend closely on which types of control one wishes to be protected against. We
also find concrete cases where the complexity of or susceptibility to control
varies dramatically based on the choice among natural tie-handling rules.Comment: Preliminary version appeared in AAAI '05. Also appears as
URCS-TR-2005-87