## Optimal false-name-proof voting rules with costly voting (2008)

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Citations: | 13 - 8 self |

### BibTeX

@MISC{Wagman08optimalfalse-name-proof,

author = {Liad Wagman},

title = {Optimal false-name-proof voting rules with costly voting},

year = {2008}

}

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### Abstract

One way for agents to reach a joint decision is to vote over the alternatives. In open, anonymous settings such as the Internet, an agent can vote more than once without being detected. A voting rule is false-name-proof if no agent ever benefits from casting additional votes. Previous work has shown that all false-name-proof voting rules are unresponsive to agents’ preferences. However, that work implicitly assumes that casting additional votes is costless. In this paper, we consider what happens if there is a cost to casting additional votes. We characterize the optimal (most responsive) false-name-proofwith-costs voting rule for 2 alternatives. In sharp contrast to the costless setting, we prove that as the voting population grows larger, the probability that this rule selects the majority winner converges to 1. We also characterize the optimal group false-name-proof rule for 2 alternatives, which is robust to coalitions of agents sharing the costs of additional votes. Unfortunately, the probability that this rule chooses the majority winner as the voting population grows larger is relatively low. We derive an analogous rule in a setting with 3 alternatives, and provide bounding results and computational approaches for settings with 4 or more alternatives.

### Citations

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Citation Context ...roof. If we assume additional structure—namely, each agent can make or receive payments and its preferences are quasilinear—then there are many strategy-proof mechanisms, for example, VCG mechanisms (=-=Vickrey 1961-=-; Clarke 1971; Groves 1973). But we will not consider mechanisms that use payments in this paper. Unfortunately, in open, anonymous environments such as the Internet, new manipulations are possible: n... |

954 | Optimal Auction Design - Myerson - 1981 |

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Citation Context ...sume additional structure—namely, each agent can make or receive payments and its preferences are quasilinear—then there are many strategy-proof mechanisms, for example, VCG mechanisms (Vickrey 1961; =-=Clarke 1971-=-; Groves 1973). But we will not consider mechanisms that use payments in this paper. Unfortunately, in open, anonymous environments such as the Internet, new manipulations are possible: namely, an age... |

583 |
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Citation Context ...l structure—namely, each agent can make or receive payments and its preferences are quasilinear—then there are many strategyproof mechanisms, for example, VCG mechanisms (Vickrey, 1961; Clarke, 1971; =-=Groves, 1973-=-). But we will not consider mechanisms that use payments in this paper. Unfortunately, in open, anonymous environments such as the Internet, new manipulations are possible: namely, an agent can vote m... |

354 |
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Citation Context ...ernatives, and each agent reports ordinal preferences over these alternatives. For this very general setting, negative results are known: for example, the Gibbard-Satterthwaite theorem (Gibbard 1973; =-=Satterthwaite 1975-=-) states that if there are at least three alternatives and preferences are unrestricted, then there exists no deterministic voting rule (mechanism) that is nondictatorial (more than one agent’s prefer... |

248 |
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Citation Context ...references. Mechanism design is the study of how to design the mechanism so that good outcomes will be chosen in spite of such self-interested behavior. By a result known as the revelation principle (=-=Gibbard, 1973-=-; Green and Laffont, 1977; Myerson, 1979, 1981), we can, in a sense, without loss of generality focus our attention on mechanisms that choose outcomes in such a way that no agent has an incentive to l... |

236 |
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Citation Context ...chanism design is the study of how to design the mechanism so that good outcomes will be chosen in spite of such self-interested behavior. By a result known as the revelation principle (Gibbard 1973; =-=Green & Laffont 1977-=-; Myerson 1979; 1981), we can, in a sense, without loss of generality focus our attention on mechanisms that choose outcomes in such a way that no agent has an incentive to lie. There are multiple way... |

222 | CAPTCHA: Using Hard AI Problems for Security - Ahn, Blum, et al. |

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Citation Context ...study of how to design the mechanism so that good outcomes will be chosen in spite of such self-interested behavior. By a result known as the revelation principle (Gibbard 1973; Green & Laffont 1977; =-=Myerson 1979-=-; 1981), we can, in a sense, without loss of generality focus our attention on mechanisms that choose outcomes in such a way that no agent has an incentive to lie. There are multiple ways of making th... |

123 | Complexity of mechanism design - Conitzer, Sandholm - 2002 |

112 |
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(Show Context)
Citation Context ...positive results. For example, if there are only two alternatives, then the majority rule (choose whichever alternative receives more votes) is strategy-proof. Also, if preferences are single-peaked (=-=Black 1948-=-) (roughly, alternatives are ordered on a line and agents always prefer alternatives closer to their most-preferred alternative), then choosing the most-preferred alternative of the median voter is st... |

89 |
Manipulation of Voting Schemes: A General Result. Econometrica 41(4): 587–601
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(Show Context)
Citation Context ...references. Mechanism design is the study of how to design the mechanism so that good outcomes will be chosen in spite of such self-interested behavior. By a result known as the revelation principle (=-=Gibbard 1973-=-; Green & Laffont 1977; Myerson 1979; 1981), we can, in a sense, without loss of generality focus our attention on mechanisms that choose outcomes in such a way that no agent has an incentive to lie. ... |

66 | Robust combinatorial auction protocol against false-name bids - Yokoo, Sakurai, et al. |

55 | Manipulation of schemes that mix voting with chance - Gibbard - 1977 |

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35 | The characterization of strategy/false-name proof combinatorial auction protocols: Price-oriented, rationing-free protocol
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Citation Context ...ld seem reasonable to give up on false-name-proofness in general social choice settings. (For combinatorial auction settings, some reasonable false-name-proof mechanisms do exist (Yokoo et al., 2001; =-=Yokoo, 2003-=-; Yokoo et al., 2006), but here, too, impossibility results are known (Yokoo et al., 2004; Rastegari et al., 2007).) Indeed, it has been proposed to perform some limited verification of agents’ identi... |

24 | Telling Humans and Computers Apart Automatically: How Lazy Cryptographers do AI - Ahn, Blum, et al. |

20 | Anonymity-proof voting rules
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(Show Context)
Citation Context ...ategy-proofness (that is, a dominant-strategies criterion), so we focus on false-nameproofness in the dominant-strategies sense in this paper. This also makes our positive results stronger.ssettings (=-=Conitzer 2007-=-a): this result implies that, unless the agents unanimously agree that one alternative is preferred to another, then the winning alternative must be chosen uniformly at random. Given this result, it w... |

20 | Revenue Monotonicity in Combinatorial Auctions. AAAI, 122–127 - Rastegari, Condon, et al. - 2007 |

15 | Limitied Verification of Identities to Induce False-Name-Proofness - Conitzer - 2007 |

12 | False-name-proof combinatorial auction protocol: Groves mechanism with submodular approximation - Yokoo, Matsutani, et al. - 2006 |

10 |
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Citation Context ...ons. For instance, one could derive the optimal false-name-proof rule that does not necessarily satisfy voluntary participation or strategy-proofness. One could also consider dichotomous preferences (=-=Inada 1964-=-), for which responsive strategy-proof rules exist. (Under such preferences, each voter (equally) approves of a set of alternatives and (equally) disapproves of the remaining alternatives.) Another di... |

7 | 2002 Complexity of mechanism design - Conitzer, T |

5 |
Incentives in Teams,” Econometrica, 41: 617-631. 18 T
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(Show Context)
Citation Context ...al structure—namely, each agent can make or receive payments and its preferences are quasilinear—then there are many strategy-proof mechanisms, for example, VCG mechanisms (Vickrey 1961; Clarke 1971; =-=Groves 1973-=-). But we will not consider mechanisms that use payments in this paper. Unfortunately, in open, anonymous environments such as the Internet, new manipulations are possible: namely, an agent can vote m... |

1 | False-name-proof auction protocol: Groves mechanism with submodular approximation - Yokoo, Matsutani, et al. - 2006 |