81 research outputs found
Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers
We propose a Condorcet consistent voting method that we call Split Cycle.
Split Cycle belongs to the small family of known voting methods that
significantly narrow the choice of winners in the presence of majority cycles
while also satisfying independence of clones. In this family, only Split Cycle
satisfies a new criterion we call immunity to spoilers, which concerns adding
candidates to elections, as well as the known criteria of positive involvement
and negative involvement, which concern adding voters to elections. Thus, in
contrast to other clone-independent methods, Split Cycle mitigates both
"spoiler effects" and "strong no show paradoxes."Comment: 71 pages, 15 figures. Added a new explanation of Split Cycle in
Section 1, updated the caption to Figure 2, the discussion in Section 3.3,
and Remark 4.11, and strengthened Proposition 6.20 to Theorem 6.20 to cover
single-voter resolvability in addition to asymptotic resolvability. Thanks to
Nicolaus Tideman for helpful discussio
Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers
We introduce a new Condorcet consistent voting method, called Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying independence of clones and the Pareto principle. Unlike other methods in this family, Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, relative to other clone-independent Paretian methods, Split Cycle mitigates “spoiler effects” and “strong no show paradoxes.
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A Complexity-of-Strategic-Behavior Comparison Between Schulze's Rule and Ranked Pairs
Schulze's rule and ranked pairs are two Condorcet methods that both satisfy many natural axiomatic properties. Schulze's rule is used in the elections of many organizations, including the Wikimedia Foundation, the Pirate Party of Sweden and Germany, the Debian project, and the Gento Project. Both rules are immune to control by cloning alternatives, but little is otherwise known about their strategic robustness, including resistance to manipulation by one or more voters, control by adding or deleting alternatives, adding or deleting votes, and bribery. Considering computational barriers, we show that these types of strategic behavior are NP-hard for ranked pairs (both constructive, in making an alternative a winner, and destructive, in precluding an alternative from being a winner). Schulze's rule, in comparison, remains vulnerable at least to constructive manipulation by a single voter and destructive manipulation by a coalition. As the first such polynomial-time rule known to resist all such manipulations, and considering also the broad axiomatic support, ranked pairs seems worthwhile to consider for practical applications.Engineering and Applied Science
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
Manipulation and Control Complexity of Schulze Voting
Schulze voting is a recently introduced voting system enjoying unusual
popularity and a high degree of real-world use, with users including the
Wikimedia foundation, several branches of the Pirate Party, and MTV. It is a
Condorcet voting system that determines the winners of an election using
information about paths in a graph representation of the election. We resolve
the complexity of many electoral control cases for Schulze voting. We find that
it falls short of the best known voting systems in terms of control resistance,
demonstrating vulnerabilities of concern to some prospective users of the
system
Obvious Independence of Clones
The Independence of Clones (IoC) criterion for social choice functions
(voting rules) measures a function's robustness to strategic nomination.
However, prior literature has established empirically that individuals cannot
always recognize whether or not a mechanism is strategy-proof and may still
submit costly, distortionary misreports even in strategy-proof settings. The
intersection of these issues motivates the search for mechanisms which are
Obviously Independent of Clones (OIoC): where strategic nomination or strategic
exiting of clones obviously have no effect on the outcome of the election. We
examine three IoC ranked-choice voting mechanisms and the pre-existing proofs
that they are independent of clones: Single Transferable Vote (STV), Ranked
Pairs, and the Schulze method. We construct a formal definition of a voting
system being Obviously Independent of Clones based on a reduction to a clocked
election by considering a bounded agent. Finally, we show that STV and Ranked
Pairs are OIoC, whereas we prove an impossibility result for the Schulze method
showing that this voting system is not OIoC
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