Here is another possible solution (which might be bad in other respects):
Maybe a formal declaration of membership only serves to increase the visibility of the group (by boosting numbers on their website). The actual position on issues cannot be "influenced". Instead, the New Center platform preforms imperial surveys of the general population to find issues on which there is broad agreement.
Or: official bloc membership might get you a voice in determining which issues get put on the surveys. But ultimately the surveys determine the New Center position.
This would make it difficult to take over the New Center and make it a mouthpiece for non-moderates (albeit not impossible).
That's an empirical question!
See my refined proposal.
Some of the other comments have reminded me of your linkpost about digital democracy. Specifically, the idea of seeking surprising agreement which was mentioned.
In the OP, I posited that "the new center" should have a strong, simple set of issues, pre-selected to cater to people who are sick of both sides. But I think Stuart Anderson is right: it shouldn't focus so much on the battle between the two sides; it should focus on the surprising commonality between people.
As Steven Byrnes mentioned, swing voters aren't exactly moderate; rather, they tend to have extreme views which don't fit within existing party lines. The article Byrnes linked to also points out that the consensus within party elites of both parties is very different from the consensus within the party base.
I find myself forming the hypothesis that politicians have a tendency to over-focus on divisive issues, and miss some issues on which there is broad agreement. (This would be an interesting question to investigate, if someone really did a feasibility study on the whole idea.)
My new suggestion for the new-center platform would be, rather than distilling complaints about both sides, seek surprising agreement in the way mentioned in that podcast you linked.
The proposal would be something like this:
Hmm, on further reflection, I had an effect in mind which doesn't necessarily break your argument, but which increases the degree to which other counterarguments such as AlexMennen's break your argument. This effect isn't necessarily solved by multiplying the contract payoff (since decisions aren't necessarily continuous as a function of utilities), but it may under many circumstances be approximately solved by it. So maybe it doesn't matter so much, at least until AlexMennen's points are addressed so I can see where it fits in with that.
OK, here's my position.
As I said in the post, the real answer is that this argument simply does not apply if the agent knows its action. More generally: the argument applies precisely to those actions to which the agent ascribes positive probability (directly before deciding). So, it is possible for agents to maintain a difference between counterfactual and evidential expectations. However, I think it's rarely normatively correct for an agent to be in such a position.
Even though the decision procedure of CDT is deterministic, this does not mean that agents described by CDT know what they will do in the future. We can think of this in terms of logical induction: the market is not 100% certain of its own beliefs, and in particular, doesn't typically know precisely what the maximum-expectation-action is.
One way of seeing the importance of this is to point out that CDT is a normative theory, not a descriptive one. CDT is supposed to tell you what arbitrary agents should do. The recommendations are supposed to apply even to, say, epsilon-exploring agents (who are not described by CDT, strictly speaking). But here we see that CDT recommends being dutch-booked! Therefore, CDT is not a very good normative theory, at least for epsilon-explorers. (So I'm addressing your epsilon-exploration example by differentiating between the agent's algorithm and the CDT decision theory. The agent isn't dutch-booked, but CDT recommends a dutch book.)
Granted, we could argue via dutch book that agents should know their own actions, if those actions are deterministic consequences of a know agent-architecture. However, theories of logical uncertainty tell us that this is not (always) realistic. In particular, we can adapt the bounded-resource-dutch-book idea from logical induction. According to this idea, some dutch-book-ability is OK, but agents should not be boundlessly exploitable by resource-bounded bookies.
This idea leads me to think that efficiently computable sequences of actions, which continue to have probability bounded away from zero (just before the decision), should have CDT expectations which converge to EDT expectations.
(Probably there's a stronger version, based on density-zero exploration type intuitions, where we can reach this conclusion even if the probability is not bounded away from zero, because the total probability is still unbounded.)
One conjecture which was supposed to be communicated by my more recent post was: in learnable environments, this will amount to: all counterfactual expectations converge to evidential expectations (provided the agent is sufficiently farsighted). For example, if the agent knows the environment is trap-free, then when counterfactual and evidential hypotheses continue to severely differ for some (efficiently enumerable) sequence of actions, then there will be a hypothesis which says "the evidential expectations are actually correct". The agent will want to check that hypothesis, because the VOI of significantly updating its counterfactual expectations is high. Therefore, these actions will not become sufficiently rare (unless the evidential and counterfactual expectations do indeed converge).
In other words, the divergence between evidential and counterfactual expectations is itself a reason why the action probability should be high, provided that the agent is not shortsighted and doesn't expect the action to be a trap.
If the agent is shortsighted and/or expects traps, then it normatively should not learn anyway (at least, not by deliberate exploration steps). In that case, counterfactual and evidential expectations may forever differ. OTOH, in that case, there's no reason to expect evidential expectations to be well-informed, so it kind of makes sense that the agent has little motive to adjust its counterfactual expectations towards them.
(But I'll still give the agent a skeptical look when it asserts that the two differ, since I know that highly informed positions never look like this. The belief that the two differ seems "potentially rational but never defensible", if that makes sense. I'm tempted to bake the counterfactual/evidential equivalence into the prior, on the general principle that priors should not contain possibilities which we know will be eliminated if sufficient evidence comes in. Yet, doing so might make us vulnerable to Troll Bridge.)
I disagree, I don't think it's a simple binary thing. I don't think Dutch book arguments in general never apply to recursive things, but it's more just that the recursion needs to be modelled in some way, and since your OP didn't do that, I ended up finding the argument confusing.
But what does that look like? How should it make a difference? (This isn't a rhetorical question; I would be interested in a positive position. My lack of interest is, significantly, due to a lack of positive positions in this direction.)
I don't think your argument goes through for the imp, since it never needs to decide its action, and therefore the second part of selling the contract back never comes up?
Ah, true, but the imp will necessarily just make EDT-type predictions anyway. So the imp argument reaches a similar conclusion.
But I'm not claiming the imp argument is very strong in any case, it's just an intuition pump.
Select whoever defected least.
An important mechanism for avoiding this failure mode would be to encourage new-centrists to be involved in political primaries.
This comment makes me want to reiterate that I am not proposing a new party. A new party needs more than 1/3rd of voters, at least regionally, in order to be viable (that is, in order to avoid shooting itself in the foot by causing its base to waste votes). I agree that splitting an existing party is mostly the only way a new centrist party could happen.
Instead, the proposal is to organize a legible voting bloc. More like "environmentalists" than "the green party".
The fact that new parties empirically can pop up in the middle is, however, encouraging.
I think voting reform is highly implausible, because "voting reform" has come to mean instant runoff voting, which is barely better (and probably much worse for political polarization in particular, due to the center-squeeze problem).
Not to say that "a new center" is really plausible, though ;p