TY - GEN
T1 - On voting and facility location
AU - Feldman, Michal
AU - Fiat, Amos
AU - Golomb, Iddan
N1 - Publisher Copyright:
© Copyright 2016 ACM.
PY - 2016/7/21
Y1 - 2016/7/21
N2 - We study mechanisms for candidate selection that seek to minimize the social cost, where voters and candidates are associated with points in some underlying metric space. The social cost of a candidate is the sum of its distances to each voter. Some of our work assumes that these points can be modeled on the real line, but other results of ours are more general. A question closely related to candidate selection is that of minimizing the sum of distances for facility location. The difference is that in our setting there is a fixed set of candidates, whereas the large body of work on facility location considers every point in the metric space to be a possible candidate. This setting gives rise to three types of candidate selection mechanisms which differ in the granularity of their input space (single candidate, ranking and location mechanisms). We study the relationships between these three classes of mechanisms. While it may seem that Black's 1948 median algorithm is optimal for candidate selection on the line, this is not the case. We give matching upper and lower bounds for a variety of settings. In particular, when candidates and voters are on the line, our universally truthful spike mechanism gives a [tight] approximation of two. When assessing candidate selection mechanisms, we seek several desirable properties: (a) efficiency (minimizing the social cost) (b) truthfulness (dominant strategy incentive compatibility) and (c) simplicity (a smaller input space). We quantify the effect that truthfulness and simplicity impose on the efficiency.
AB - We study mechanisms for candidate selection that seek to minimize the social cost, where voters and candidates are associated with points in some underlying metric space. The social cost of a candidate is the sum of its distances to each voter. Some of our work assumes that these points can be modeled on the real line, but other results of ours are more general. A question closely related to candidate selection is that of minimizing the sum of distances for facility location. The difference is that in our setting there is a fixed set of candidates, whereas the large body of work on facility location considers every point in the metric space to be a possible candidate. This setting gives rise to three types of candidate selection mechanisms which differ in the granularity of their input space (single candidate, ranking and location mechanisms). We study the relationships between these three classes of mechanisms. While it may seem that Black's 1948 median algorithm is optimal for candidate selection on the line, this is not the case. We give matching upper and lower bounds for a variety of settings. In particular, when candidates and voters are on the line, our universally truthful spike mechanism gives a [tight] approximation of two. When assessing candidate selection mechanisms, we seek several desirable properties: (a) efficiency (minimizing the social cost) (b) truthfulness (dominant strategy incentive compatibility) and (c) simplicity (a smaller input space). We quantify the effect that truthfulness and simplicity impose on the efficiency.
KW - Algorithmic mechanism design
KW - Approximate mechanism design without money
KW - Facility location
KW - Social choice
KW - Voting
UR - http://www.scopus.com/inward/record.url?scp=84983483105&partnerID=8YFLogxK
U2 - 10.1145/2940716.2940725
DO - 10.1145/2940716.2940725
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AN - SCOPUS:84983483105
T3 - EC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation
SP - 269
EP - 286
BT - EC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation
PB - Association for Computing Machinery, Inc
T2 - 17th ACM Conference on Economics and Computation, EC 2016
Y2 - 24 July 2016 through 28 July 2016
ER -