Is it completely alien to you, or just extreme? Do you never feel like you are being run by agents with different goal systems?
If not normally, have you ever been in an altered state (such as from drugs or alcohol) where you behaved in a way that doesn't make sense to you at other times?
Looking at myself as separate individuals could be a bad idea because of a propensity to reinforce those divisions and cause internal dissonance, but it feels useful and productive to me. Moreover, I'm under the impression that most people feel this way some of the time, I just do so more often and more strongly. If you can't even imagine what that would feel like, that's useful information to me in how I should approach talking about it with other people.
EDIT: this is something that I haven't actually talked to my psychiatrist or my close circle of friends and relatives about, partially because it's minor among my other maintenance operations, but really because I'm afraid it would upset them. If this is too alien, I'm not sure I should try talking about it, and in some way, this post is testing the waters.
I think most people have very strong defense mechanisms against noticing their conflicting subsystems, because it goes against the sense of having a central continuous identity. So it's difficult to acknowledge the conflict unless you've experienced relatively extreme states of mind that are suicidal or homicidal or the like, that are so clearly not part of the 'central' agent that they can't be written off as just a brief lapse of judgement.
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.