18 research outputs found
Schulze and Ranked-Pairs Voting are Fixed-Parameter Tractable to Bribe, Manipulate, and Control
Schulze and ranked-pairs elections have received much attention recently, and
the former has quickly become a quite widely used election system. For many
cases these systems have been proven resistant to bribery, control, or
manipulation, with ranked pairs being particularly praised for being NP-hard
for all three of those. Nonetheless, the present paper shows that with respect
to the number of candidates, Schulze and ranked-pairs elections are
fixed-parameter tractable to bribe, control, and manipulate: we obtain uniform,
polynomial-time algorithms whose degree does not depend on the number of
candidates. We also provide such algorithms for some weighted variants of these
problems
Solving Hard Control Problems in Voting Systems via Integer Programming
Voting problems are central in the area of social choice. In this article, we
investigate various voting systems and types of control of elections. We
present integer linear programming (ILP) formulations for a wide range of
NP-hard control problems. Our ILP formulations are flexible in the sense that
they can work with an arbitrary number of candidates and voters. Using the
off-the-shelf solver Cplex, we show that our approaches can manipulate
elections with a large number of voters and candidates efficiently
Fine-Grained Complexity and Algorithms for the Schulze Voting Method
We study computational aspects of a well-known single-winner voting rule
called the Schulze method [Schulze, 2003] which is used broadly in practice. In
this method the voters give (weak) ordinal preference ballots which are used to
define the weighted majority graph (WMG) of direct comparisons between pairs of
candidates. The choice of the winner comes from indirect comparisons in the
graph, and more specifically from considering directed paths instead of direct
comparisons between candidates.
When the input is the WMG, to our knowledge, the fastest algorithm for
computing all winners in the Schulze method uses a folklore reduction to the
All-Pairs Bottleneck Paths problem and runs in time, where is
the number of candidates. It is an interesting open question whether this can
be improved. Our first result is a combinatorial algorithm with a nearly
quadratic running time for computing all winners. This running time is
essentially optimal. If the input to the Schulze winners problem is not the WMG
but the preference profile, then constructing the WMG is a bottleneck that
increases the running time significantly; in the special case when there are
candidates and voters, the running time is , or
if there is a nearly-linear time algorithm for multiplying dense
square matrices. To address this bottleneck, we prove a formal equivalence
between the well-studied Dominance Product problem and the problem of computing
the WMG. We prove a similar connection between the so called Dominating Pairs
problem and the problem of finding a winner in the Schulze method.
Our paper is the first to bring fine-grained complexity into the field of
computational social choice. Using it we can identify voting protocols that are
unlikely to be practical for large numbers of candidates and/or voters, as
their complexity is likely, say at least cubic.Comment: 19 pages, 2 algorithms, 2 tables. A previous version of this work
appears in EC 2021. In this version we strengthen Theorem 6.2 which now holds
also for the problem of finding a Schulze winne
Search versus Search for Collapsing Electoral Control Types
Electoral control types are ways of trying to change the outcome of elections
by altering aspects of their composition and structure [BTT92]. We say two
compatible (i.e., having the same input types) control types that are about the
same election system E form a collapsing pair if for every possible input
(which typically consists of a candidate set, a vote set, a focus candidate,
and sometimes other parameters related to the nature of the attempted
alteration), either both or neither of the attempted attacks can be
successfully carried out [HHM20]. For each of the seven general (i.e., holding
for all election systems) electoral control type collapsing pairs found by
Hemaspaandra, Hemaspaandra, and Menton [HHM20] and for each of the additional
electoral control type collapsing pairs of Carleton et al. [CCH+ 22] for veto
and approval (and many other election systems in light of that paper's Theorems
3.6 and 3.9), both members of the collapsing pair have the same complexity
since as sets they are the same set. However, having the same complexity (as
sets) is not enough to guarantee that as search problems they have the same
complexity. In this paper, we explore the relationships between the search
versions of collapsing pairs. For each of the collapsing pairs of Hemaspaandra,
Hemaspaandra, and Menton [HHM20] and Carleton et al. [CCH+ 22], we prove that
the pair's members' search-version complexities are polynomially related (given
access, for cases when the winner problem itself is not in polynomial time, to
an oracle for the winner problem). Beyond that, we give efficient reductions
that from a solution to one compute a solution to the other. For the concrete
systems plurality, veto, and approval, we completely determine which of their
(due to our results) polynomially-related collapsing search-problem pairs are
polynomial-time computable and which are NP-hard.Comment: The metadata's abstract is abridged due to arXiv.org's
abstract-length limit. The paper itself has the unabridged (i.e., full)
abstrac
Public Evidence from Secret Ballots
Elections seem simple---aren't they just counting? But they have a unique,
challenging combination of security and privacy requirements. The stakes are
high; the context is adversarial; the electorate needs to be convinced that the
results are correct; and the secrecy of the ballot must be ensured. And they
have practical constraints: time is of the essence, and voting systems need to
be affordable and maintainable, and usable by voters, election officials, and
pollworkers. It is thus not surprising that voting is a rich research area
spanning theory, applied cryptography, practical systems analysis, usable
security, and statistics. Election integrity involves two key concepts:
convincing evidence that outcomes are correct and privacy, which amounts to
convincing assurance that there is no evidence about how any given person
voted. These are obviously in tension. We examine how current systems walk this
tightrope.Comment: To appear in E-Vote-Id '1