Another thing Weicker and Blumenthal had in common was they didn't use their own money to try and buy their way into politics. Both did it the old-fashioned way, by sucking up to campaign contributors to get the money to run.
Arterton says one of McMahon's "big mistakes was relying so exclusively on her own sources of money."
He says extremely wealthy candidates often find it "easier to just write a check" than it is to set up a fundraising machine and make endless calls asking people to give money for a campaign.
"But raising money and raising political support go hand in hand," Arterton says.
Healy agrees: "If you make the mistake of being identified as a self-funder… you don't go through the regime of trying to get support from donors." And that "lets people off the hook," he adds.
Getting somebody to send in a campaign check for as little as $100 says "You're invested in this... It's sort of a marker you put down" to demonstrate real support for a candidate, Healy explains.
Arterton doesn't believe the era of millionaires running for office in Connecticut is over, in part because there is so damned much money that has to be spent these days to run political campaigns. The Citizen's United Supreme Court ruling allows super PACs to spend as much as they want, which puts greater pressure on candidates to be able to find big money of their own.
"I think what we'll see is well-funded candidates, partially self-funded and partially funded by putting in place fundraising operations," Arterton says.
And then there's always the attraction for a political party of choosing wealthy candidates willing to spend their own cash on their campaigns. That way, explains Arterton, a party doesn't have to worry about running often difficult and time-consuming efforts to find and stroke campaign contributors, or fear that one of its candidates might be taking contributions away from everybody else on its lineup.
"It's a lot easier," Arterton points out, "to go with somebody who comes to a campaign with their own fortune."
The problem with that philosophy is that, for some millionaires, money is all they can bring to a campaign.