CounterPAC is something like the first version of Mayday, but with a blunter approach. Funded mostly by Jim Greer, a Silicon Valley entrepreneur, the super PAC has no interest in legislation and cares mainly about eliminating the presence of undisclosed money in elections. In 2014, it picked a House race in West Virginia, where Nick Rahall, the Democratic incumbent, was ousted by Evan Jenkins, a Republican state senator. CounterPAC contacted both candidates, asking if they would sign a pledge calling for groups spending undisclosed money to avoid the race (the catch being that if a candidate signed and, say, a 501c4 group spent money on his behalf, the candidate would also agree to donate a similar amount to charity). To encourage participation, CounterPAC promised to spend money against whichever candidate did not sign, regardless of party.

Neither candidate ever signed the pledge, but they agreed to a public meeting with CounterPAC. When Mr. Rahall did not attend, CounterPAC spent $212,000 against him in the final weeks before the election and counted his defeat as a success. It’s unclear, though, what role CounterPAC played in the election. Multiple people involved in West Virginia politics gave it little or no credit in a race that attracted national attention and $10 million in outside spending.

Mr. Greer gave an additional $300,000 to the super PAC in January, suggesting another try in 2016. But few candidates seem eager to unilaterally disarm or penalize themselves when their political futures are on the line, and it’s debatable whether a pledge is really enforceable by the candidates, or by CounterPAC.

Rather than seeking pledges, another group of challengers is trying to harness small donations from many people to upend the campaign finance system. It, too, will face the question of whether it can have enough of an impact, but it tries to leverage citizen interest in issues before Congress rather than make campaign finance the main issue.

If.then.fund, created by Jonathan Zucker, a campaign finance lawyer, and Joshua Tauberer, (who also created GovTrack.us, a site tracking congressional activity) acts as a conduit, collecting money that will then be given to a candidate based on how current legislators vote. For example, if a donor is interested in a bill about privacy, she can pledge money to a particular lawmaker or race. If she agrees with the incumbent’s vote, the incumbent gets the money. If not, the money goes to a challenger.