Costly Advice, Protests, and Nonbinding Elections

We study a scenario in which a receiver is collecting non-binding advice for a binary decision from partially informed senders who can send binary messages. This reflects situations such as non-binding voting of shareholders on a management proposal, protests by citizens, and polls. Under complete information, the preferences of the receiver and the senders are aligned but there is a conflict of interest over the trade-off of Type I and Type II errors. Existing work shows that for many such situations, the bias prohibits the transmission of any information. Here, in contrast to this work, we consider a setting in which one of the messages is costly. For example, there are positive costs of voting but no costs of abstention. We show that informative advice is given in any equilibrium. When there are many senders, with costly advice, the outcome is equivalent to the one under complete information. In our general model, we also allow for noise induced by other motives. With noise, participation in an election becomes a strategic complement, with citizens joining voices to overcome the noise and make their opinion heard.