Possible and necessary winners in voting trees: majority graphs vs. profiles

Authors:
Maria Silvia Pini;Francesca Rossi;Kristen Brent Venable;Toby Walsh
Affiliations:
University of Padova Padova, Italy;University of Padova Padova, Italy;Universita' di Padova Padova, Italy;NICTA and UNSW Sydney, Australia
Venue:
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Year:
2011

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Abstract

Given the preferences of several agents over a common set of candidates, voting trees can be used to select a candidate (the winner) by a sequence of pairwise competitions modelled by a binary tree (the agenda). The majority graph compactly represents the preferences of the agents and provides enough information to compute the winner. When some preferences are missing, there are various notions of winners, such as the possible winners (that is, winners in at least one completion) or the necessary winners (that is, winners in all completions). In this generalized scenario, we show that using the majority graph to compute winners is not correct, since it may declare as winners candidates that are not so. Nonetheless, the majority graph can be used to compute efficiently an upper or lower approximation of the correct set of winners.