Current New York law provides that if no one receives at least 40% of the vote for a New York city mayoral primary, a run-off primary is held. According to this story, the entrance of former Congressman Anthony Weiner into the Democratic race makes it somewhat likely that no one will get as much as 40% of the vote.
The run-off primary would be held on October 1, using the old-fashioned mechanical voting machines that have been outlawed for federal elections, if the legislature passes S.4088. The Senate passed it on May 6 but it has not yet had a hearing in the Assembly Elections Committee. Revival of the mechanical voting machines is opposed by Common Cause, the League of Women Voters, and other groups, according to this press release. However, one advantage of the lever voting machines is that they save time, because they avoid having to print hundreds of thousands of paper ballots.
Mayor Michael Bloomberg supports the lever machines; see this story. Anthony Weiner favors ranked-choice voting, at least for primaries. See his point #44, page 15, in his program.
I think Quinn wins the whole thing in the end.
State Senator Marty Golden has sponsored a bill, and the Senate passed it, that would require the New York City Board of Elections to bring back the old-fashioned lever machines.
State Assembly Speaker Sheldon Silver said there were no plans to take up the Assembly bill and passed a Senate bill allowing for three weeks between the primary and a runoff, which the SEnate feels should be sufficient to reprogram the new machines.
But using lever machines brings many legal problems like: No required paper trail, not ADA compliant, not HAVA or state approved, and not able to display all the new approved languages. There is also the need to get the run-off ballots to overseas and military voters. And finally, many of the lever machines in storage need mechanical repair that will require the expense of cannibalizing machines for parts and finding technicians who know how to fix them and a printer for the lever ballots.