Ballot query: To bullet, or not to bullet?
When he steps into the dim privacy of a voting booth on Nov. 6, Larry Davidson - Dorchester resident, Democrat, math teacher - will circle ovals next to the candidates he has chosen based not only on politics, but on the power of math.
Like all voters in Boston, Davidson will be allowed to choose four at-large candidates for the City Council from nine contenders. And like many other voters, he will contemplate using just one of those votes as a "bullet vote:" a single vote for one candidate, not only advancing that candidacy but denying other hopefuls his remaining votes.
But deciding whether you should cast a single ballot for your first-choice candidate, mathematicians say, you have to make strategic judgments about the race and how others will vote. And that requires a sophisticated view of the election.
"It all depends, truly, on your ability to understand who are the competitors for that last one or two seats," said Arlene Ash, a professor of medicine at Boston University School of Medicine and a statistician who testified in court about voting irregularities in the 2000 presidential election in Florida.
Although bullet voting is legal and has long been practiced in Boston's City Council elections, it carries a whiff of conspiracy.
No candidates publicly admit to asking their supporters to cast just one vote. But in Boston, bullet voting has often been deployed by voters, usually to boost the campaigns of those outside the Boston political establishment, especially minorities. In 2003, bullet votes for Felix D. Arroyo, a teacher born in Puerto Rico, are believed to have propelled him onto the council. That same year, the Boston Ward 3 Republican Committee urged a bullet vote for Ed Puglielli, a rare Republican candidate in the City Council race. Puglielli did not win.
"Anybody who suggests to you that there is no bullet voting doesn't understand city elections," says Larry DiCara, a lawyer and former Boston city councilor.
This is what mathematicians say about bullet voting: If you have one candidate who you care passionately about electing, and that candidate will likely win or lose the election by a small number of votes, it makes sense to cast a single bullet vote for him or her. A single vote will not only add to the candidate's total, it will deny votes to other candidates who may be competing for the same seat.
But if the outcome - win or lose - for your favored candidate isn't likely to be close, a single ballot cast for that candidate will probably not alter the results of the election. Meanwhile, your second or third choices in tighter races may lose to candidates you find less desirable. So in this scenario, it doesn't make sense to cast a bullet vote.
"The mathematics means that if there's one candidate you really like, it's worth doing that," Davidson said. "If there's a bunch of candidates you like, it can be counterproductive."
In the last election for Boston City Council, each ballot contained an average of 2.9 votes for at-large seats. However, not everyone who fails to vote for four candidates is necessarily making a tactical decision about voting - some may not have four candidates they wish to support, or may misunderstand voting instructions. Some voters cast a bullet vote to propel a favored candidate to a first-place finish, perhaps as a boost to future mayoral aspirations.
The danger is when voters don't use one of their votes for a popular candidate they support, gambling that that candidate will win anyway. If enough voters make that same calculation, the candidate could lose.
(In Cambridge's more complex electoral system, however, mathematicians say there is no value to bullet voting. Voters rank the order of their votes, so their first-choice candidate automatically receives a boost over others they may choose but give lower ranks.)
Davidson, a math teacher at Weston High School, also teaches a summer course at The Crimson Summer Academy at Harvard University on mathematics and voting.
Two years ago, Davidson voted for just two candidates, one of whom, Candidate A (he declines to name names), he really wanted to win. He figured Candidate A was likely to win a seat, but he wanted to make sure of it. Davidson cast his second vote for Candidate B, a longshot whose candidacy he also wanted to boost.
"I wanted those two to maximize their chances," he said.
In the end, Candidate A won, but Candidate B did not.
"I think maybe the most important thing to understand about voting is that the way in which you allow people to vote, especially in a situation where there are multiple candidates and multiple winners, will have an enormous impact on who wins," Ash said. Voting, she said, is "not so much the will of the people as the way of measuring the will of the people."
Still, Ash is a proponent of allowing bullet voting. "It lets people express a more subtle nuance of what they would like their vote to accomplish," she said.
This year in Boston, political insiders are debating whether John R. Connolly, a lawyer from West Roxbury, can oust one of the four incumbents. In the last election, Connolly placed fifth, fewer than 4,000 votes behind Stephen Murphy. Connolly would be a prime contender for bullet votes among supporters who feel very strongly about him.
"It's pointless to do it if your candidate is extremely popular or unpopular," Davidson said. "The case to do it is if your candidate is on the edge of being in the top four or not."
In the Nov. 6 general election, there will also be races for the councilors to represent each of the city's nine districts.
So far, this campaign season has been quiet. Since only nine candidates - the four incumbents and five challengers - decided to run this year for the at-large seats, the city canceled the traditional preliminary election in September to weed down the candidates to a pool of eight.
"When there is not a lot of activity, most anything can happen," DiCara said.
Kathleen Burge can be reached at kburge@globe.com
