7 research outputs found
Strategyproofness and Proportionality in Party-Approval Multiwinner Elections
In party-approval multiwinner elections the goal is to allocate the seats of
a fixed-size committee to parties based on the approval ballots of the voters
over the parties. In particular, each voter can approve multiple parties and
each party can be assigned multiple seats. Two central requirements in this
setting are proportional representation and strategyproofness. Intuitively,
proportional representation requires that every sufficiently large group of
voters with similar preferences is represented in the committee.
Strategyproofness demands that no voter can benefit by misreporting her true
preferences. We show that these two axioms are incompatible for anonymous
party-approval multiwinner voting rules, thus proving a far-reaching
impossibility theorem. The proof of this result is obtained by formulating the
problem in propositional logic and then letting a SAT solver show that the
formula is unsatisfiable. Additionally, we demonstrate how to circumvent this
impossibility by considering a weakening of strategy\-proofness which requires
that only voters who do not approve any elected party cannot manipulate. While
most common voting rules fail even this weak notion of strategyproofness, we
characterize Chamberlin--Courant approval voting within the class of Thiele
rules based on this strategyproofness notion.Comment: Appears in the 37th AAAI Conference on Artificial Intelligence
(AAAI), 202
Démocratie à géométrie variable (à l'usage des algorithmes)
International audienceDe nombreux problèmes, par exemple en décision, ne peuvent se résoudre de manière exacte et font appel à des heuristiques qui attribuent des scores aux différents choix possibles. Ces heuristiques peuvent être nombreuses et plus ou moins corrélées : par exemple, en variant les hyperparamètres d'un algorithme, on peut générer toute une famille d'heuristiques fortement corrélées mais de qualité variable. Plutôt que de chercher la meilleure heuristique, cet article propose d'agréger les scores de manière intelligente. Notre solution, qui utilise les corrélations entre heuristiques, est plus efficace que l'agrégation triviale et plus robuste qu'une approche basée sur le maximum de vraisemblance
Measuring a Priori Voting Power -- Taking Delegations Seriously
We introduce new power indices to measure the a priori voting power of voters
in liquid democracy elections where an underlying network restricts
delegations. We argue that our power indices are natural extensions of the
standard Penrose-Banzhaf index in simple voting games. We show that computing
the criticality of a voter is #P-hard even when voting weights are
polynomially-bounded in the size of the instance. However, for specific
settings, such as when the underlying network is a bipartite or complete graph,
recursive formulas can compute these indices for weighted voting games in
pseudo-polynomial time. We highlight their theoretical properties and provide
numerical results to illustrate how restricting the possible delegations can
alter voters' voting power.Comment: 34 pages, 8 figure
Measuring a Priori Voting Power in Liquid Democracy
We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard Penrose-Banzhaf index in simple voting games. We show that computing the criticality of a voter is #P-hard even in weighted games with weights polynomially-bounded in the size of the instance. However, for specific settings, such as when the underlying network is a bipartite or complete graph, recursive formulas can compute these indices for weighted voting games in pseudo-polynomial time. We highlight their theoretical properties and provide numerical results to illustrate how restricting the possible delegations can alter voters' voting power
Independence of Irrelevant Alternatives under the Lens of Pairwise Distortion
We give a quantitative analysis of the independence of irrelevant alternatives (IIA) axiom. IIA says that the society's preference between x and y should depend only on individual preferences between x and y: we show that, in several contexts, if the individuals express their preferences about additional (``irrelevant'') alternatives, this information helps to estimate better which of x and y has higher social welfare.
Our contribution is threefold: (1) we provide a new tool to measure the impact of IIA on social welfare (pairwise distortion), based on the well-established notion of voting distortion, (2) we study the average impact of IIA in both general and metric settings, with experiments on synthetic and real data and (3) we study the worst-case impact of IIA in the 1D-Euclidean metric space
Approval with Runoff
We define a family of runoff rules that work as follows: voters cast approval
ballots over candidates; two finalists are selected; and the winner is decided
by majority. With approval-type ballots, there are various ways to select the
finalists. We leverage known approval-based committee rules and study the
obtained runoff rules from an axiomatic point of view. Then we analyze the
outcome of these rules on single-peaked profiles, and on real data
Approval with Runoff
International audienceWe define a family of runoff rules that work as follows: voters cast approval ballots over candidates; two finalists are selected; and the winner is decided by majority. With approval-type ballots, there are various ways to select the finalists. We leverage known approval-based committee rules and study the obtained runoff rules from an axiomatic point of view. Then we analyze the outcome of these rules on single-peaked profiles, and on real data