Sequential Voting with Externalities: Herding in Social Networks Noga Alon, Moshe Babaioff, Ron Karidi, Ron Lavi, Moshe Tennenholtz Presented by Erez Shabat

Sequential Voting - Model Users vote either “like” or “dislike” (only 2 alternatives) Voting is sequential Each voter has a preferred alternative (type) Voters type are drawn independently from some prior distribution Votes are not anonymous

Sequential Voting - Model Utility externalities: voters value voting for the chosen winner Voters have utility function depending on 3 things only: the voter’s preference, the vote, and the chosen alternative Voters aim to maximize their utility

Examples Social network voting Committee voting Presidential primaries

Utility variables Assuming a voter prefers A over B, denote the utilities as: - voter votes A and A is chosen - voter votes A and B is chosen - voter votes B and B is chosen - voter votes B and A is chosen Assume the following holds

Utility variables For example, if the voters only care about conforming with the winner then = > =

2 Variants Infinite and countable number of voters, winner is announced when the gap in votes is at least some large number M. Finite population of size n (at least 3), the chosen alternative is the one with the most votes.

Result 1 When the winner is declared when the gap in votes is at least M: Increasing M does not result in aggregation of preferences of more voters in the decision The threshold start for herding is independent of M, and only depends on

Result 2 There are cases in which sequential voting is strictly better than simultaneous voting in the sense that it chooses the most preferred alternative with higher probability.

Result 2 More formally: For any number of voters n, there exists utility parameters, and a non-symmetric prior probability with a slight advantage for B Sincere voting is not a Nash equilibrium of simultaneous voting The strategies generating a “herd that follows the first voter” is the unique subgame-perfect equilibrium in sequential voting

Result 2 With these strategies the probability that the “correct” outcome is chosen is strictly higher than the probability it will be chosen in any Nash equilibrium of simultaneous voting

Further Work The paper considers only pure strategies Only 2 alternatives, either A or B Symmetric utility function All voters get equals weight