Thanks for the replies and input. Much appreciated. Here are some thoughts back:
Re Drake Savory's 8/30 response that my one candidate - one seat conclusion was incorrect -- thanks. I should clarify - I should have more precisely stated that in the case of one nominated candidate for one seat and no write-in names returned, the candidate would be elected with just one vote, as in that case the candidate has received all the votes, so is above 50%. I should also acknowledge, in the general situation of no more nominated candidates than open seats, that whether an election is uncontested under Robert's isn't something that is actually known until after ballots are returned, because of the possibility of write-in candidates. And in my second scenario with two candidates and two seats for clarity I should have shown places on the returned ballots for write-in candidates and shown them as empty on all three ballots.
Re Dan H (8/31) and Puzzling's (8/30) comments, thanks for the citations.Then as for weird consequences (my opinion) , I'll give two examples here. I'll continue to assume in the particular examples given that there are no write-in names returned.
1) In the two-person two-seat scenario in my original email, let's extend that scenario to the second round of voting. Suppose Smith is now the only candidate (no additional candidates nominated) in the second round. Suppose the voters have the same voting response with respect to Smith as they did in the first round, i.e. Ballot 1 X Smith, Ballot 2 __ Smith, Ballot 3 __ Smith. Voila, Smith is elected. So the net consequence is both candidates are elected, it just took two rounds according to (b) in my original email, rather than just one round if one assumed (a). So the situation of multiple seats seems artificially distinguished from the situation of one open seat. The presence of another candidate (Jones) seems to have some kind of voodoo effect on the fate of Smith, even though they are not running against each other or competing against each other.
2) Starting from scratch, consider three alternative scenarios; Each with the same two open seats. And continue to assume no write-in names are returned.
1. Adams is the only nominated candidate. Adams gets one vote, the rest of the returned ballots are unmarked. So Adams is elected with just the one vote.
2. Brown is the only nominated candidate. Brown gets no votes. So Brown is not elected.
3. Adams and Brown are the only two candidates. Adams gets one vote and Brown gets one vote. Then
In each of scenarios 1. and 2., Adams and Brown, respectively, would be elected with receiving just one vote. However, in scenario 3 neither Adams nor Brown are elected and so voting would go to a second round. (Lather, rinse, repeat?!) So in scenario 3 we see again that the mere presence of another candidate can affect the voting outcome, even though the 'strength' of the vote for Adams can be the same in both scenarios 1 & 3, likewise for Brown in 2 & 3. Even though there is no competition for the seats.
The nutshell summary is that while just one vote can suffice to elect a candidate who is ultimately unopposed, that doesn't generalize to multiple candidates for multiple seats who are ultimately unopposed. I do now understand that's the case with the 'majority of votes cast' meaning as explained. I just don't see why that makes sense - what value added or benefit it brings to the election process, versus treating a returned ballot not marked for a particular candidate as an abstension ballot for that candidate in an uncontested election.
Thanks again very much for the replies! My question of what Robert's says has been clearly answered.
Best,
Gary