5,745 research outputs found
Crowdsourcing for Participatory Democracies: Efficient Elicitation of Social Choice Functions
We present theoretical and empirical results demonstrating the usefulness of
voting rules for participatory democracies. We first give algorithms which
efficiently elicit \epsilon-approximations to two prominent voting rules: the
Borda rule and the Condorcet winner. This result circumvents previous
prohibitive lower bounds and is surprisingly strong: even if the number of
ideas is as large as the number of participants, each participant will only
have to make a logarithmic number of comparisons, an exponential improvement
over the linear number of comparisons previously needed. We demonstrate the
approach in an experiment in Finland's recent off-road traffic law reform,
observing that the total number of comparisons needed to achieve a fixed
\epsilon approximation is linear in the number of ideas and that the constant
is not large.
Finally, we note a few other experimental observations which support the use
of voting rules for aggregation. First, we observe that rating, one of the
common alternatives to ranking, manifested effects of bias in our data. Second,
we show that very few of the topics lacked a Condorcet winner, one of the
prominent negative results in voting. Finally, we show data hinting at a
potential future direction: the use of partial rankings as opposed to pairwise
comparisons to further decrease the elicitation time
Comparing Election Methods Where Each Voter Ranks Only Few Candidates
Election rules are formal processes that aggregate voters preferences,
typically to select a single candidate, called the winner. Most of the election
rules studied in the literature require the voters to rank the candidates from
the most to the least preferred one. This method of eliciting preferences is
impractical when the number of candidates to be ranked is large. We ask how
well certain election rules (focusing on positional scoring rules and the
Minimax rule) can be approximated from partial preferences collected through
one of the following procedures: (i) randomized-we ask each voter to rank a
random subset of candidates, and (ii) deterministic-we ask each voter to
provide a ranking of her most preferred candidates (the -truncated
ballot). We establish theoretical bounds on the approximation ratios and we
complement our theoretical analysis with computer simulations. We find that
mostly (apart from the cases when the preferences have no or very little
structure) it is better to use the randomized approach. While we obtain fairly
good approximation guarantees for the Borda rule already for , for
approximating the Minimax rule one needs to ask each voter to compare a larger
set of candidates in order to obtain good guarantees
Efficient computation of the Shapley value for game-theoretic network centrality
The Shapley valueāprobably the most important normative payoff division scheme in coalitional gamesāhas recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo
Focused Power: Experimental Manifestation of the Shapley-Shubik Power Index
Experiments evaluate the fit of the Shapley-Shubik Power Index to a controlled human environment. Subjects with differing votes divide a fixed purse by majority rule in online chat rooms under supervision. Earnings serve as a measure of power. Chat rooms and processes for selecting subjects reduce or eliminate extraneous political forces, leaving logrolling as the primary political force. Initial proposals by subjects for division of the purse allow measurement of effects from focal points and transaction costs. Net results closely fit the Shapley-Shubik Power Index.Voting, Power Index, Focal Point, Shapley-Shubik, Experiment
- ā¦