4 research outputs found
Local Distance Restricted Bribery in Voting
Studying complexity of various bribery problems has been one of the main
research focus in computational social choice. In all the models of bribery
studied so far, the briber has to pay every voter some amount of money
depending on what the briber wants the voter to report and the briber has some
budget at her disposal. Although these models successfully capture many real
world applications, in many other scenarios, the voters may be unwilling to
deviate too much from their true preferences. In this paper, we study the
computational complexity of the problem of finding a preference profile which
is as close to the true preference profile as possible and still achieves the
briber's goal subject to budget constraints. We call this problem Optimal
Bribery. We consider three important measures of distances, namely, swap
distance, footrule distance, and maximum displacement distance, and resolve the
complexity of the optimal bribery problem for many common voting rules. We show
that the problem is polynomial time solvable for the plurality and veto voting
rules for all the three measures of distance. On the other hand, we prove that
the problem is NP-complete for a class of scoring rules which includes the
Borda voting rule, maximin, Copeland for any , and
Bucklin voting rules for all the three measures of distance even when the
distance allowed per voter is for the swap and maximum displacement
distances and for the footrule distance even without the budget constraints
(which corresponds to having an infinite budget). For the -approval voting
rule for any constant and the simplified Bucklin voting rule, we show
that the problem is NP-complete for the swap distance even when the distance
allowed is and for the footrule distance even when the distance allowed is
even without the budget constraints.Comment: Accepted as an extended abstract in AAMAS 201
Multi-Party Campaigning
We study a social choice setting of manipulation in elections and extend the
usual model in two major ways: first, instead of considering a single
manipulating agent, in our setting there are several, possibly competing ones;
second, instead of evaluating an election after the first manipulative action,
we allow several back-and-forth rounds to take place. We show that in certain
situations, such as in elections with only a few candidates, optimal strategies
for each of the manipulating agents can be computed efficiently.
Our algorithmic results rely on formulating the problem of finding an optimal
strategy as sentences of Presburger arithmetic that are short and only involve
small coefficients, which we show is fixed-parameter tractable -- indeed, one
of our contributions is a general result regarding fixed-parameter tractability
of Presburger arithmetic that might be useful in other settings. Following our
general theorem, we design quite general algorithms; in particular, we describe
how to design efficient algorithms for various settings, including settings in
which we model diffusion of opinions in a social network, complex budgeting
schemes available to the manipulating agents, and various realistic
restrictions on adversary actions
Opinion Diffusion and Campaigning on Society Graphs
We study the effects of campaigning, where the society is partitioned into
voter clusters and a diffusion process propagates opinions in a network
connecting the clusters. Our model is very powerful and can incorporate many
campaigning actions, various partitions of the society into clusters, and very
general diffusion processes. Perhaps surprisingly, we show that computing the
cheapest campaign for rigging a given election can usually be done efficiently,
even with arbitrarily-many voters. Moreover, we report on certain computational
simulations
A Unifying Framework for Manipulation Problems
Manipulation models for electoral systems are a core research theme in social
choice theory; they include bribery (unweighted, weighted, swap, shift, ...),
control (by adding or deleting voters or candidates), lobbying in referenda and
others.
We develop a unifying framework for manipulation models with few types of
people, one of the most commonly studied scenarios. A critical insight of our
framework is to separate the descriptive complexity of the voting rule R from
the number of types of people. This allows us to finally settle the
computational complexity of R-Swap Bribery, one of the most fundamental
manipulation problems. In particular, we prove that R-Swap Bribery is
fixed-parameter tractable when R is Dodgson's rule and Young's rule, when
parameterized by the number of candidates. This way, we resolve a long-standing
open question from 2007 which was explicitly asked by Faliszewski et al. [JAIR
40, 2011].
Our algorithms reveal that the true hardness of bribery problems often stems
from the complexity of the voting rules. On one hand, we give a fixed-parameter
algorithm parameterized by number of types of people for complex voting rules.
Thus, we reveal that R-Swap Bribery with Dodgson's rule is much harder than
with Condorcet's rule, which can be expressed by a conjunction of linear
inequalities, while Dodson's rule requires quantifier alternation and a bounded
number of disjunctions of linear systems. On the other hand, we give an
algorithm for quantifier-free voting rules which is parameterized only by the
number of conjunctions of the voting rule and runs in time polynomial in the
number of types of people. This way, our framework explains why Shift Bribery
is polynomial-time solvable for the plurality voting rule, making explicit that
the rule is simple in that it can be expressed with a single linear inequality,
and that the number of voter types is polynomial.Comment: 15 pages, accepted to AAMAS 201