There is some overlap. Among other things, I never stop caring for the people I love, although I'm a lot less selfish about it when Neutral. This is really quite important, since the fact that they care for me means that I always need to extend some modicum of care to myself on their behalf, even if I'm truly loathing myself at the time. Being forced to that contradiction sometimes makes me hate them, or my care for them, but it doesn't diminish my care for them, and is still powerful.
if you have a serious mental illness that might temporarily make you do something you don't value on average then sometimes only other people can force you not to do what that transitory you wants to do
I think I agree with the rest of your argument that agents need to have some common ground, but this seems to indicate that all their ground must be common (utilities with the same sign, if not the same weight). I don't think this is the case, and I think I've done many things that I don't value on average. Self-mutilation is something that even Depressed almost never assigns a positive value to, but I have done that.
I did personally experience this a few times.
Would you mind elaborating?
Related to: Akrasia as a collective action problem and Self-empathy as a source of "willpower".
The Less Wrong community has discussed negotiating with one's conflicting sub-agents as a method to defeat akrasia and other forms of dynamic inconsistency, with some mix of reactions about how possible or effective that strategy can be. This article presents a successful example in my life, though it is probably an extreme outlier for a number of reasons.
I have been diagnosed with bipolar II disorder. It is one of the most significant challenges in my life, and certainly the one with the most dire implications. I can be fairly well modeled as three major sub-agents1:
Neutral feels it necessary to let Hypomanic take control more often to ensure that the compromise has weight to Depressed, but has started using Hypomanic to accomplish goals that are otherwise too exhausting to attain (a several-day code crunch or a need to meet and make a good impression on dozens of people). Meanwhile, Hypomanic has been more responsible lately in relinquishing control within days rather than weeks, partially because of these negotiations, but mostly because of other people in my life who have been conscripted to help monitor and rein me in.
I do not have a great deal of proven success with this strategy. I started doing this less than a year ago, and have not dealt with a full-blown major depressive episode since then. During that time I have also been more successful than ever at preventing myself from slipping into depression in the first place and treating early depression aggressively. In the end, that makes a much more significant difference, but on the two occasions when I became depressed enough to start feeling suicidal I was positively influenced by this agreement.
It seems unlikely that this approach will help many people with anything, but I feel like it is interesting in the debate about dynamic inconsistency, and I encourage others to find mutually-beneficial agreements they can make with themselves if they also feel like they deal with mutually incompatible agents from time to time. Also, this is my first post that is more than a link, so please be constructive.
Notes
1 I've never used names to refer to myself in different states, and don't think of my major sub-agents as individuals, but I felt that it was useful for didactic purposes to refer to myself in different states as different proper nouns.
2 I don't race cars, do drugs, or get in fights (except at the dojo). I do push my physical limits farther than I should (do parkour that I'm not be ready for, run 20km when I usually run 5, etc.), and I have injured myself this way, but just pulled muscles, sprains and once a broken finger.
3 I haven't heard this argument before, but this is the reason I haven't signed up for cryonics.
If it's not obvious, I was in a neutral state when I wrote this. It would have been impossible for me to do while depressed, and unlikely for me to try while hypomanic. I tried to de-bias myself, but no matter what state I'm in, I prefer my own viewpoint, and speak less highly of the others that diverge.