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

2. 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

3. 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

4. Examples
Social network voting
Committee voting
Presidential primaries

5. 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

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

7. 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.

8. 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

9. 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.

10. 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

11. 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

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