In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using protocols where determining a beneficial manipulation is hard. Especially among computational agents, it is reasonable to measure this hardness by computational complexity. Some earlier work has been done in this area, but it was assumed that the number of voters and candidates is unbounded. We derive hardness results for the more common setting where the number of candidates is small but the number of voters can be large. We show that with complete information about the others' votes, individual manipulation is easy, and coalitional manipulation is easy with unweighted voters. However, constructive coalitional manipulation with weighted voters is intractable for all of the voting protocols under study, except in the <i>Cup</i> protocol. Destructive manipulation tends to be easier, except in the <i>Single Transferable Vote</i> protocol. Randomizing over instantiations of the protocols (such as schedules of a Cup) can be used to make manipulation hard. Finally, we show that under weak assumptions, if weighted coalitional manipulation with complete information about the others' votes is hard in some voting protocol, then individual and unweighted manipulation is hard when there is uncertainty about the others' votes.
[1]
John J. Bartholdi,et al.
Single transferable vote resists strategic voting
,
2015
.
[2]
Eithan Ephrati,et al.
Multi-Agent Planning as a Dynamic Search for Social Consensus
,
1993,
IJCAI.
[3]
M. Trick,et al.
The computational difficulty of manipulating an election
,
1989
.
[4]
Ronald L. Rivest,et al.
Introduction to Algorithms
,
1990
.
[5]
Yuri Gurevich,et al.
Average Case Completeness
,
1991,
J. Comput. Syst. Sci..
[6]
Eithan Ephrati,et al.
The Clarke Tax as a Consensus Mechanism Among Automated Agents
,
1991,
AAAI.
[7]
G. G. Stokes.
"J."
,
1890,
The New Yale Book of Quotations.
[8]
Osamu Watanabe,et al.
Instance complexity
,
1994,
JACM.
[9]
M. Satterthwaite.
Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions
,
1975
.
[10]
M. Trick,et al.
Voting schemes for which it can be difficult to tell who won the election
,
1989
.