TY - JOUR
T1 - Convergence of iterative scoring rules
AU - Lev, Omer
AU - Rosenschein, Jeffrey S.
N1 - Publisher Copyright:
© 2016 AI Access Foundation.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - In multiagent systems, social choice functions can help aggregate the distinct prefer- ences that agents have over alternatives, enabling them to settle on a single choice. Despite the basic manipulability of all reasonable voting systems, it would still be desirable to find ways to reach plausible outcomes, which are stable states, i.e., a situation where no agent would wish to change its vote. One possibility is an iterative process in which, after everyone initially votes, participants may change their votes, one voter at a time. This technique, explored in previous work, converges to a Nash equilibrium when Plurality vot- ing is used, along with a tie-breaking rule that chooses a winner according to a linear order of preferences over candidates. In this paper, we both consider limitations of the iterative voting method, as well as expanding upon it. We demonstrate the significance of tie-breaking rules, showing that no iterative scoring rule converges for all tie-breaking. However, using a restricted tie- breaking rule (such as the linear order rule used in previous work) does not by itself ensure convergence. We prove that in addition to plurality, the veto voting rule converges as well using a linear order tie-breaking rule. However, we show that these two voting rules are the only scoring rules that converge, regardless of tie-breaking mechanism.
AB - In multiagent systems, social choice functions can help aggregate the distinct prefer- ences that agents have over alternatives, enabling them to settle on a single choice. Despite the basic manipulability of all reasonable voting systems, it would still be desirable to find ways to reach plausible outcomes, which are stable states, i.e., a situation where no agent would wish to change its vote. One possibility is an iterative process in which, after everyone initially votes, participants may change their votes, one voter at a time. This technique, explored in previous work, converges to a Nash equilibrium when Plurality vot- ing is used, along with a tie-breaking rule that chooses a winner according to a linear order of preferences over candidates. In this paper, we both consider limitations of the iterative voting method, as well as expanding upon it. We demonstrate the significance of tie-breaking rules, showing that no iterative scoring rule converges for all tie-breaking. However, using a restricted tie- breaking rule (such as the linear order rule used in previous work) does not by itself ensure convergence. We prove that in addition to plurality, the veto voting rule converges as well using a linear order tie-breaking rule. However, we show that these two voting rules are the only scoring rules that converge, regardless of tie-breaking mechanism.
UR - http://www.scopus.com/inward/record.url?scp=85016150320&partnerID=8YFLogxK
U2 - 10.1613/jair.5187
DO - 10.1613/jair.5187
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AN - SCOPUS:85016150320
SN - 1076-9757
VL - 57
SP - 573
EP - 591
JO - Journal of Artificial Intelligence Research
JF - Journal of Artificial Intelligence Research
ER -