47,734 research outputs found
Condorcet-Consistent and Approximately Strategyproof Tournament Rules
We consider the manipulability of tournament rules for round-robin
tournaments of competitors. Specifically, competitors are competing for
a prize, and a tournament rule maps the result of all
pairwise matches (called a tournament, ) to a distribution over winners.
Rule is Condorcet-consistent if whenever wins all of her matches,
selects with probability .
We consider strategic manipulation of tournaments where player might
throw their match to player in order to increase the likelihood that one of
them wins the tournament. Regardless of the reason why chooses to do this,
the potential for manipulation exists as long as increases by
more than decreases. Unfortunately, it is known that every
Condorcet-consistent rule is manipulable (Altman and Kleinberg). In this work,
we address the question of how manipulable Condorcet-consistent rules must
necessarily be - by trying to minimize the difference between the increase in
and decrease in for any potential manipulating
pair.
We show that every Condorcet-consistent rule is in fact -manipulable,
and that selecting a winner according to a random single elimination bracket is
not -manipulable for any . We also show that many
previously studied tournament formats are all -manipulable, and the
popular class of Copeland rules (any rule that selects a player with the most
wins) are all in fact -manipulable, the worst possible. Finally, we consider
extensions to match-fixing among sets of more than two players.Comment: 20 page
Learning to Place New Objects
The ability to place objects in the environment is an important skill for a
personal robot. An object should not only be placed stably, but should also be
placed in its preferred location/orientation. For instance, a plate is
preferred to be inserted vertically into the slot of a dish-rack as compared to
be placed horizontally in it. Unstructured environments such as homes have a
large variety of object types as well as of placing areas. Therefore our
algorithms should be able to handle placing new object types and new placing
areas. These reasons make placing a challenging manipulation task. In this
work, we propose a supervised learning algorithm for finding good placements
given the point-clouds of the object and the placing area. It learns to combine
the features that capture support, stability and preferred placements using a
shared sparsity structure in the parameters. Even when neither the object nor
the placing area is seen previously in the training set, our algorithm predicts
good placements. In extensive experiments, our method enables the robot to
stably place several new objects in several new placing areas with 98%
success-rate; and it placed the objects in their preferred placements in 92% of
the cases
- …