Problems with the Finger
(1.) People abuse the Finger, despite the admonition. It rewards the aggressive. This is especially important if there isn't enough time for everyone's questions, so that the patient Hands risk never having their questions addressed.(2.) The Finger rewards speed. If more than one person has a Finger, the first Finger gets to ask first.
Furthermore (2a.): If the person whose Hand it is is slow with their own follow-up, then the moderator is likely to go quickly to the fastest Finger, derailing the Hand's actual intended line of questioning.
(3.) Given the unclear border between following up and opening a new question, (a.) people who generously refrain from Fingering except in clear cases fall to the back of the queue, whereas people who indulge themselves in a capacious understanding of "following up" get to jump ahead; and (b.) because of issue (a), all participants who have a borderline follow-up face a non-obvious moral question about the right thing to do.
(4.) The Finger tends to aggravate unbalanced power dynamics. The highest-status and most comfortable people in the room will tend to be the ones readiest to Finger in, seeing ways to interpret the question they really want to ask as a "follow-up" to someone else's question.
Furthermore, the Finger serves no important purpose. Why does a follow-up need to be asked right on the tail of the question it is following up? Are people going to forget otherwise? Of course not! In fact, in my experience, follow-ups are often better after a gap. This requires the follower-up to reframe the question in a different way. This reframing is helpful, because the follower-up will see the issue a little differently than the original Hand. The audience and the speaker then hear multiple angles on whatever issue is interesting enough that multiple people want to ask about it, instead of one initial angle on it, then a few appended jabs.
Why It Matters
If all of this seems to take the issue of question order with excessive seriousness, well, yes, maybe! But bear in mind: Typically, philosophy talks are two hours long, and you get to ask one question. If you can't even ask that one question, it's a very different experience than if you do get to ask your question. Also, the question period, unfortunately but realistically, serves a social function of displaying to others that you are an engaged, interesting, "smart" philosopher -- and most of us care considerably how others think of us. Not being able to ask your question is like being on a basketball team and never getting to take your shot. Also, waiting atop a question you're eager to ask while others jump the queue in front of you on sketchy grounds is intrinsically unpleasant -- even if you do manage to squeeze in your question by the end.The Slow Sweep
So, no Fingers! Only Hands. But there are better and worse ways to take Hands.At the beginning of the discussion period, ask for Hands from anyone who wants to ask a question. Instead of taking the first Hand you see, wait a bit. Let the slower Hands rise up too. Maybe encourage a certain group of people especially to contribute Hands. At UC Riverside Philosophy, our custom is to collect the first set of Hands from students, forcing faculty to wait for the second round, but you could also do things like ask "Any more students want to get Hands in the queue?"
Once you've paused long enough that the slow-Handers are up, follow some clear, unbiased procedure for the order of the questions. What I tend to do is start at one end of the room, then slowly sweep to the other end, ordering the questions just by spatial position. I will also give everyone a number to remember. After everyone has their number, I ask if there are any people I missed who want to be added to the list.
Hand 1 then gets to ask their question. No other Hands get to enter the queue until we've finished with all the Hands in the original call. Thus, there's no jockeying to try to get one's hand up early, or to catch the moderator's eye. The Hand gets to ask their question, the speaker to reply, and then there's an opportunity for the Hand -- and them only -- to ask one follow up. After the speaker's initial response is complete, the moderator catches the Hand's eye, giving them a moment to gather their thoughts for a follow-up or to indicate verbally or non-verbally that they are satisfied. No hurry and no jockeying for the first Finger. I like to encourage an implicit default custom of only one follow-up, though sometimes it seems desirable to allow a second follow-up. Normally after the speaker answers the follow-up I look for a signal from the Hand before moving to the next Hand -- though if the Hand is pushing it on follow-ups I might jump in quickly with "okay, next we have Hand 2" (or whatever the next number is).
After all the initial Hands are complete, do another slow sweep in a different direction (maybe left to right if you started right to left). Again, patiently wait for several Hands rather than going in the order in which you see hands. Bump anyone who had a Hand in the first sweep to the end of the queue. Maybe there will be time for a third sweep, or a fourth.
The result, I find, is a more peaceful, orderly, and egalitarian discussion period, without the rush, jockeying, anxiety, and Finger abuse.
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[1] The best online source on the Finger-Hand tradition that I can easily find is Muhammad Ali Khalidi's critique here, a couple of years ago, which raises some similar concerns.
[2] All names chosen randomly from lists of my former lower-division students, excluding "Jesus", "Mohammed", and very uncommon names. (In this case, I randomly chose an "A" name, then a "B" name, etc.) See my reflections here.