Vishal Chakraborty | University of Cambridge (original) (raw)

Papers by Vishal Chakraborty

We investigate the practical aspects of computing the necessary and possible winners in elections... more We investigate the practical aspects of computing the necessary and possible winners in elections over incomplete voter preferences. In the case of the necessary winners, we show how to implement and accelerate the polynomial-time algorithm of Xia and Conitzer. In the case of the possible winners, where the problem is NP-hard, we give a natural reduction to Integer Linear Programming (ILP) for all positional scoring rules and implement it in a leading commercial optimization solver. Further, we devise optimization techniques to minimize the number of ILP executions and, oftentimes, avoid them altogether. We conduct a thorough experimental study that includes the construction of a rich benchmark of election data based on real and synthetic data. Our findings suggest that, the worst-case intractability of the possible winners notwithstanding, the algorithmic techniques presented here scale well and can be used to compute the possible winners in realistic scenarios.

The POSSIBLE WINNER (PW) problem, a fundamental algorithmic problem in computational social choic... more The POSSIBLE WINNER (PW) problem, a fundamental algorithmic problem in computational social choice, concerns elections where voters express only partial preferences between candidates. Via a sequence of investigations, a complete classification of the complexity of the PW problem was established for all pure positional scoring rules: the PW problem is in P for the plurality and veto rules, and NP-complete for all other such rules. More recently, the PW problem was studied on classes of restricted partial orders that arise in natural settings, such as partitioned partial orders and truncated partial orders; in particular, it was shown that there are rules for which the PW problem drops from NP-complete to P on such restricted partial orders. Here, we investigate the PW problem on partial chains, i.e., partial orders that are a total order on a subset of their domains. Such orders arise naturally in a variety of settings, including rankings of movies or restaurants. We classify the complexity of the PW problem on partial chains by establishing that, perhaps surprisingly, this restriction does not change the complexity of the problem, namely, the PW problem is NP-complete for all pure positional scoring rules other than the plurality and veto rules. As a byproduct, we obtain a new and more principled proof of the complexity of the PW problem on arbitrary partial orders.

GreenFLY (greenfly.ucdavis.edu) is an airline flight search website which prominently displays gr... more GreenFLY (greenfly.ucdavis.edu) is an airline flight search website which prominently displays greenhouse gas emissions estimates along with the other important flight information, such as price and times, for each possible flight itinerary. We describe its software components and graphic design principles. Then we present a discrete choice experiment in which we asked participants to choose between itineraries presented in the GreenFLY format. Results suggest that consumers are willing to pay a significant amount for lower-emissions flights in the context of online flight search, especially when lower emissions are combined with fewer layovers.

We investigate the practical aspects of computing the necessary and possible winners in elections... more We investigate the practical aspects of computing the necessary and possible winners in elections over incomplete voter preferences. In the case of the necessary winners, we show how to implement and accelerate the polynomial-time algorithm of Xia and Conitzer. In the case of the possible winners, where the problem is NP-hard, we give a natural reduction to Integer Linear Programming (ILP) for all positional scoring rules and implement it in a leading commercial optimization solver. Further, we devise optimization techniques to minimize the number of ILP executions and, oftentimes, avoid them altogether. We conduct a thorough experimental study that includes the construction of a rich benchmark of election data based on real and synthetic data. Our findings suggest that, the worst-case intractability of the possible winners notwithstanding, the algorithmic techniques presented here scale well and can be used to compute the possible winners in realistic scenarios.

The POSSIBLE WINNER (PW) problem, a fundamental algorithmic problem in computational social choic... more The POSSIBLE WINNER (PW) problem, a fundamental algorithmic problem in computational social choice, concerns elections where voters express only partial preferences between candidates. Via a sequence of investigations, a complete classification of the complexity of the PW problem was established for all pure positional scoring rules: the PW problem is in P for the plurality and veto rules, and NP-complete for all other such rules. More recently, the PW problem was studied on classes of restricted partial orders that arise in natural settings, such as partitioned partial orders and truncated partial orders; in particular, it was shown that there are rules for which the PW problem drops from NP-complete to P on such restricted partial orders. Here, we investigate the PW problem on partial chains, i.e., partial orders that are a total order on a subset of their domains. Such orders arise naturally in a variety of settings, including rankings of movies or restaurants. We classify the complexity of the PW problem on partial chains by establishing that, perhaps surprisingly, this restriction does not change the complexity of the problem, namely, the PW problem is NP-complete for all pure positional scoring rules other than the plurality and veto rules. As a byproduct, we obtain a new and more principled proof of the complexity of the PW problem on arbitrary partial orders.

GreenFLY (greenfly.ucdavis.edu) is an airline flight search website which prominently displays gr... more GreenFLY (greenfly.ucdavis.edu) is an airline flight search website which prominently displays greenhouse gas emissions estimates along with the other important flight information, such as price and times, for each possible flight itinerary. We describe its software components and graphic design principles. Then we present a discrete choice experiment in which we asked participants to choose between itineraries presented in the GreenFLY format. Results suggest that consumers are willing to pay a significant amount for lower-emissions flights in the context of online flight search, especially when lower emissions are combined with fewer layovers.