Since I was at least one of the ones who sparked this:
Responsibilities and powers begin and end with the running of actual sessions.
I voted no. My responsibilities certainly don't end at the end of the session, since I'm planning the next session. And since I'm the one planning the next session, I'm the one making a lot of other decisions as well.
Primary (but not absolute) power to establish houserules and genre choices.
Absolute power over houserules, genre choices etc but only in advance.
Absolute power to establish and change any aspect of the game before or during play.
I voted no to the first two, and yes to the last one, but I don't think I mean what I think you mean. By that line, I suspect you think that I'm going to throw out the fantasy setting and start playing CoC or cyberpunk in the middle of a game, and I think that would be lousy DMing. However, if a DM realizes halfway through a session that a specific rule or feat is messing the adventure up in a big bad way, he has the responsibility to make the change on the fly.
The key here is to do it when it's appropriate -- when the game needs it, not when you the DM need it. Every rule change requires your players to remember one additional thing (and trust you a little more for going outside the core rules), and every rule change in mid-play draws on your credibility as a DM -- once or twice is probably fine, but if you're doing it every session, you're either a horrible planner or a DM who wants to force the players through your special story.
I also think that there's a difference between "absolute" and "unilateral". Yeah, if something is messing up the game and I need to make a rule-change on the fly, I have the final word -- but part of coming to a decision on that final word is bringing the matter up with the players to find out if it's bugging everyone. If it's bothering nobody save me, then it's likely not worth changing a rule to correct it.
I voted yes, since whenever I've DM'd, I was the one who made sure that we
had a next session -- I had to organize the calendar-checking to make sure we figured out a new time.
The other reason I voted "yes" is that if one player out of eight has to cancel at the last minute, the game can continue. If the DM has to cancel at the last minute, the group can still get together to play something else, but the game as such can't happen.
But if "final say" means cackling evilly and declaring that the players will come when I say so, dangit, and if they have a problem, tough luck, then no. My "final say" meant finding out when everyone could make it and choosing the time that worked for everyone.
Final say on group membership.
I voted yes, but only in that the DM is the one who can say, "I think we've got enough players. Any more, and the game becomes too unwieldy." Any decision regarding adding a player should otherwise be a group decision. I'd give the DM veto power, but not automatic-yes power. (And as the DM, I've never used veto power, although there have been times when I wished I had in retrospect -- for example, the guy who wanted me to give his character a hot girlfriend.)
Final say on social aspects (table rules, eating, smoking, etc)
I voted yes, but again, I only see this in terms of veto power in particular cases. Every time I've had a talk about something like this with the group (both as a player and as the DM), it's come down to the DM, but the DM has always gone with the majority opinion. That might just be because I game with friends, so it's not like the rest of us want a lighthearted but engaged session in a clean atmosphere and one guy is smoking like a chimney and spilling pizza on our books.
(And I'd also give veto power to the person whose house it is. Either of those people have the power to say "We need to not do that." They don't have the power to decide what the group does do, but they have the power to say "Please stop doing ___.")
Generally equal say on scheduling, membership and social aspects with the rest of the Group.
I voted no, since I voted yes on everything else. I think that from a practicaly standpoint, the DM should end up having about an equal say, but the DM should always have the veto power, and in cases where things are deadlocked, the DM should make the final call based on what's best for the group as a whole.