I do not mean this to come off as blunt as it sounds, but I’m trying to be both clear and concise.

What you’re talking about is not how game theory works. What you’re doing is taking the most basic, highly abstracted representation of a generic idea and expecting it to correlate with reality. It’s the same thing people do when they ascribe some kind of wish fulfillment to the free market or to evolutionary dynamics. It’s not even a platonic ideal - it’s drawing a supply/demand curve and thinking you understand how prices work in a market economy. Here’s the main issues you’re running into when you try to play Ultimatum with something the size of the Democratic Party:

1. Noise. There is a permanent base of 3-5% of the electorate that’s going to vote Green, or whatever. The protest voters almost never rise above that noise floor. Focus on a single (potentially complex) issue would help. Green rallies (and others) often have everything from antivax to prison reform to the environment to voting rights to BDS and BLM. All of those things (except the antivax) might be important, but there needs to be a central focus. IMO it’s voting rights - I’d love DSA to drop everything to just start suing states and protesting for voting rights, because everything else is lost without that. We can even both/and, as long as there’s a vision and a focus on a main first objective. Right now we’re coming off like a bunch of verses from We Didn’t Start the Fire. Ultimatum with multiplayer and a noise function is a completely different game.
2. Feedback loop. The consequences for actions needs to be tightened up, and they need a wide base. There needs to be visible and constant representation out in front of both cameras and politicians. This can be people like the Squad or figures like Robert Reich, but there needs to be a uniform voice that doesn’t wait for the election cycle. Groups like Moms for Liberty have this kind of thing on lock. They have a brand and spokespersons and will host and endorse, or else attack on Fox News within hours of a political decision. They’re shit in every way, but they can work the machine. Ultimatum with a delayed feedback loop is a completely different game because the failure of the deal is less attributable.
3. Solidarity and messaging. The majority of Americans want universal health care. The majority of Americans want green energy. The majority of Americans want a cease fire in Gaza. By spreading opinions across multiple realizations of this top level policy objectives, we dilute the message. Ultimatum requires identifiable players with identifiable agendas.

We as voters aren’t playing Ultimatum. Instead, we are playing minimax as an emergent strategy to defend the rights of marginalized populations.