I was at a series of presentations last week and every session included some time for questions at the end. Usually, in political science at least, a lot of interesting ground can be covered in the Q&A because so much of the research is left out of the presentation and few people have read the paper the presentation is based on. However, sitting through a Q&A when you have no questions can be frustrating. In fact, sometimes you feel like stabbing your hand with your pen just so that you can receive some cerebral stimulation. In some sessions, every time there is a small pause after the speaker says, "Any questions?", your heart leaps with expectant joy, only to be crushed when another audience member tentatively raises their hand. During one such session, while doodling abstract symbols, I started thinking that this regularized practice is not merely habitual but is governed by a set of social rules. This led me to wonder whether there might be a better system. Then I conceived of a better system. The new system is simple, easy, and better than the current system. Here is my argument in favor of the new system.
The current system is that when the speaker has finished speaking, they ask for any questions and everyone has a choice between staying silent and asking a question. Once everybody who had a question has asked their question, everyone leaves/goes for a break.
Assume that there are two types of agents, P agents and Q agents. The Q agents have a question that they want to ask. The P agents have no questions. Each agent gets utility from leisure time. The Q agents get utility from asking their question and having it answered. However, every question asked involves a penalty that everyone pays - the leisure time lost from having to stay and listen to the question and answer.This system potentially involves the imposition of negative externalities on some audience members, in that if there are any P agents they have to pay the waiting costs and do not get any say in whether the questions are asked. Q agents do pay waiting costs but would rather ask their question. The total utility from the current system is everyone's leisure or breaktime utility minus a utility cost from each question:
Here b stands for breaktime utility indexed across all agents and q stands for question time costs indexed across all agents and a stands for the utility gained from having a question answered indexed across all Q agents.
For Q agents, , so they would rather ask their question and wait, than stay silent and leave earlier. But the P agents pay that cost that they don't want to.
This problem could be solved with a simple institutional innovation. How about, after the speaker has finished speaking, they say, "If anyone has any questions, please stay, otherwise thank you and you can go." Then, each audience member can choose to stay or leave.
The situation is the same as the old system for the Q agents. They would choose to stay. However, as , P agents would choose to leave. Under this new system, the total utility is:
If , then . That is, if there are any people who do not have a question, the new institutional rule is preferable, otherwise it is equivalent. In fact, the new system is pareto-optimal. No one is left worse off under the new system and at least some people are better off.
I intend to suggest this new rule to the people running the seminars at my university. If they don't like it, I will refer them to this proof.