What I mean to say is that, roughly speaking, one should compare the world where people like them vote to the world where people like them don't vote, and choose the better world. That can yield a different decision than when one decides without considering the fact that they're not deciding just for themselves.

When one assumes that the number of people that are similar to them (roughly speaking) is sufficiently small, I agree.

What I wrote is indeed aligned with evidential decision theory (EDT). The objections to EDT that you mentioned don't seem to apply here. When you decide whether to vote you don't decide just for yourself, but rather you decide (roughly speaking) for everyone who is similar to you. The world will become better or worse depending on whether it's good or bad that everyone-who-is-similar-to-you decides to vote/not-vote.

tl;dr

• In a close election in the US, you have a 1 in a 10 million chance to swing the election if you live in a competitive district.
• A 1 in 10 million (10,000,000) chance might sound small, but since the US government spends $17,500,000,000,000, it's worth nearly $2 million.
• Other countries spend less money, but their districts are often smaller. In competitive districts, your vote can still be worth a lot.
• Government spending is easy to quantify, but there is also foreign policy, social and political freedoms. How valuable is a 1 in 10 million chance to halve the chance of nuclear war?
• If you aren't informed here are two tips:
  • Find someone informed who shares your values. Ask them how they will vote and match them.
  • Read and follow international opinion polling - your country might be 50/50 but the world might not.
• If you think it's worth voting, it's probably worth telling your friends to as well. 
• In conclusion
  • If you already follow politics, often it will be effective to vote.
  • If you would have to spend time researching, that time might be better spent working on one of the world's pressing problems or earning to give to an effective charity.

Sure.

Though that's not what I meant. I more mean an op-ed style version of the same content that is lighter and more chatty. But maybe I'm misunderstanding the process? I guess if a journalist wants to summarise it, they'll do that themselves?

Eg in this style https://unherd.com/2020/10/why-do-people-believe-such-complete-rubbish/