Despite much talk Monday about electing a mayor, the City Council took no vote — there was tacit agreement not to hold one while councillor Tim Toomey was away — and wound up only incrementally further along on addressing the issue: awaiting a report from the city solicitor and prepared to hold additional meetings, and votes, if the situation isn’t soon resolved.

A mayor is elected among the councillors on a five-vote majority, and there has been none since voting began at their inauguration Jan. 4. David Maher had a three-vote majority that day, expanded it to four but has been unable to pin down that last needed supporter.

Seeking to spur the panel into action, newcomer Leland Cheung had three proposals dated Feb. 1 ready to go Monday: change to a runoff (elimination) or instant runoff (ranked) style of vote within the council; hold extra meetings and therefore more balloting; and have the acting chairman — in this case, Ken Reeves — reappoint members and leaders of committees, with Cheung serving in place of Larry Ward, whom he replaced in the November elections.

The final suggestion was not discussed, but the first two won lengthy debate and approval of sorts. The additional-meetings idea presented by Maher was ultimately approved 7-1-1, with Craig Kelley in opposition and Toomey absent, despite some feeling, as Decker said, “I don’t think there’s anyone, after all the conversations I’ve had, who’s going to say, ‘I just don’t want to go to one more council meeting and vote on this, so I’m going to change my vote to so and so.’ I’m not aware of that as a motivating factor. Clearly, some of you think it is, and if that works I’m happy to try it. But I’m a little skeptical.”

She wondered at how the plan would be put into practice and suggested it would be at least as good to hold a single meeting councillors couldn’t leave until a mayor had been decided.

Kelley also said the proposal for more meetings was unlikely to work. “We could meet 20 times a week, and I’m not sure how that would change my opinion,” he said.

Debate about the runoff suggestion was longer and more muddled, with councillors seeming to repeatedly wander outside its text:

WHEREAS: Instant runoff voting provides a method of ranking choices that makes it possible to break through the gridlock of an undecided election by proceeding to a conclusion that reflects the choice of the majority in a more nuanced calculation; now therefore be it

ORDERED: That the City Council utilize a runoff election procedure in its election of the mayor for the 2010 mayoral election. [emphasis added]

Denise Simmons said she couldn’t support the motion, going so far as to reiterate her support for the city manager and citing the system seven decades ago when “we did have a popularly elected mayor, and the citizens rose up and said, ‘We want it to be different.’ It may be that time we really want to look at the type of charter we have or ways we could directly elect a mayor or have instant runoff voting.” Davis talked about a change in Portland, Maine, in which a popular vote for mayor could be put in place to use a ranking method similar to Cambridge’s proportional representation. And Sam Seidel said he was “eager that we pick a mayor and move on with the work of the council for this term, but I do feel we were elected by the people to exercise our judgment in many matters, including the choosing of a mayor … it is one of the prerogatives we get as councillors, once elected. So I am happy to hear what the city solicitor has to tell us, but ultimately it is our responsibility as councillors who we’re going to choose to lead us in the term.”

Cheung confirmed after the meeting that, as the text of his proposal said, a runoff election would  take place within the council, not among the entire electorate of the city.

Despite the misunderstandings, the council decided unanimously to send the matter to the city’s lawyers to see if the Cambridge charter allows it to hold a runoff election of mayor for the current term.

“I feel there are many people who don’t understand our form of government,” Reeves said, leading criticism by several members of a Boston Globe story that ran Monday and said, without attribution:

Some say Reeves, who is serving as acting mayor and has been getting the least support so far, is holding up the process by not dropping out of the running.

“I assure you I don’t have so much power that I am holding up — that the reason you don’t have a mayor is me,” Reeves said. “It breaks my heart it can be written about like Cambridge is some silly little city with a silly little council that can’t get this silly little thing done because, after all, the mayor has no gravitas …

“My bad analogy for this form of government — I don’t want to offend anyone who’s Catholic — it’s kind of like the election of the Pope. Nobody knows how that happens. They go into this little room and the smoke comes,” he said. “We have a municipal version of that. And nobody ever argues that doesn’t come out okay. It just takes as long as it takes.”

Earlier in the meeting Decker had her own analogy for Cambridge’s mayoral elections: That they were like a combination of chess and the TV show “Survivor.”

There will be further council coverage published Tuesday.