I agree that the likes of Cenk Uygur and Lawrence Lessig are not doing what they could. But are they familiar with alternatives to FPTP? I have no idea one way or the other.
Lessig straight out dismisses the voting system as being a problem. He has said in a video and in an email to an approval voting advocate that money in politics is the only thing that matters and everything else is a side issue. I think Cenk partly believes this as well as he constantly says the same thing, but doesn't specifically address voting reform. Another issue is that he appears to be really bad at math. When he hosted a debate for Henry Maxman's seat he constantly said that CA's top two primary allows you to vote your conscience even though it doesn't stop vote splitting and allows the two worst candidates to move on to the general if you actually do vote your conscience.
First past the post is well-known for being vulnerable to spoiling. But what about the others?
You can see a comparison of different simulations of voting systems
here.
IRV is better than plurality, but it still doesn't negate the effects of vote splitting. It is good for when a third party or fringe candidate gets knocked off in the early rounds, but it also possible for vote splitting to cause the fringe candidates knock off generally popular candidates in the early rounds and cause bad candidates to advance in the later rounds. This can be seen in the Burlington Vermont mayoral election in 2009. Progressive candidate Bob Kiss won in spite of losing a pairwise battle with the Democratic candidate Andy Montroll. Since the Democratic candidate lost in the early round, the final round paired up a weak candidate (Republican) to face off against the Progressive in final round. This combined with general confusion over IRV allowed it to be repealed by referendum in 2010.
It is like how party primaries can help candidates to advance in the primary who are popular in the party, but are not viable in the general election.
The usual two-round runoff is also vulnerable to spoiling, but less vulnerable than FPTP. This proposed system has the opposite vulnerability. It's a two-round runoff scheme with the first round being approval voting. It's instead vulnerable to teaming. Two or more similar candidates can become the top two, thus moving on to the second round. So that's why I can't support it.
I don't think the regular top two helps much at all. It gives independent voters a little more of a voice as it allows them to participate in the primary, but that is about it. Vote splitting would be much less of an issue if it were a runoff in the general, but an open primary is going to have much more candidates which means more opportunity for vote splitting and getting two bad candidates in the general.
I also don't see the problem with having two similar candidates. Approval voting ensures that the probability is very high that you are going to get two very good candidates for the general. This will make the primary and the general much more competitive whereas most of the districts are currently non-competitive in the general and don't matter at all. If you don't have competitive elections, you don't have accountability. The primary would be the real election in which voters can vote on issues and the general would be a fine tuning of which candidate is best at addressing those issues.
This also gives much more power to third parties even if their token candidate doesn't make it to the general. Since the primary is going to be extremely competitive as you have many candidates and no vote splitting, all candidates are going to need as many endorsements from as many parties and advocacy groups as possible. All candidates will have to pay attention to all issues important to the voters to eke out a victory.
As an example of this, getting money out of politics is a very important issue that the American people really care about. Lawrence Lessig's PAC would be able to endorse all candidates and only the candidates that support this reform and create a powerful voter block. The candidates couldn't ignore this voter block if they want to make it to the general election. Right now, the Democrats can just ignore the PAC and be content knowing that the only other choice voters have is the Republican who is even worse. If we had this voting system in every state, the problem with money in politics would have already been solved.
In addition to making it easier to elect candidates who will vote in support of legislation to get money out of politics, the voting system itself will dampen the effects of money in politics. Political parties and advocacy groups will be able to build a reputation over time with fewer resources. Voters can rely on multiple trusted advocacy groups to compile a list of candidates that support the issues they care about. There will be less need for candidates to raise enough money to gain enough name recognition to become one of the two default candidates that you have to vote for. The focus of elections will be able to become more issue oriented than candidate oriented.
Even in the general election the advocacy groups will play an important role. Since there is no clear left or right candidate and it will be a lot hard to use wedge issues as a strategy, the two candidates would have to fight harder to win the endorsement of the important advocacy groups and political parties. It would strengthen the candidates commitments to the issues and provide accountability.
Please reconsider. We need to have the ability to hold politicians accountable.