LDRs can be challenging, and I think it just makes sense not to be bogged down with rules in a long-distance arrangement, since it would only make it more difficult. Dealing with the distance is usually enough of a trial.
A lot of people engage in poly relationships without rules. However, that does not necessarily mean that they don't have agreements (say, to always use condoms, or to call at certain times, for instance). In general, I think that the people who eschew rules feel that having rules is fear-based, that they will only get involved with people they trust, and that no amount of rules will make a dishonorable person act honorably -- so it's all about being with people whom you know well enough to trust that they will behave decently. Of course, there are the less than honorable people who don't want to be tied down by rules just so they can go and do whatever the hell they want with no consideration for their partners, but it seems obvious that is not the case here.
Also, I think that when you don't have a long list of rules, it requires even more communication than if you do. It seems to me, the issues with people who have long lists of rules seem usually to center around breaking those rules. And most of their communications revolve around the rules, re-negotiations, damage control, suspicions, indignation, and that sort of thing. Whereas if you're not always dealing with rules, your communications can be more about the meat and potatoes: your needs, wants, feelings, goals, deeply felt emotions, and so on.
I love what sagency said about this is in another thread:
Originally Posted by sagency
The alternative to making rules is being clear about what you want, what you need, and how you feel to the point where your partner can accurately predict how you would respond to a situation. Then, if the partner is respectful, you likely have minimal problems. If your partner is not respectful, then the issue is either what you need versus what [he or she] can provide or the lack of respect. In order to be clear you must be proactive and speak in concrete terms. No hazy, wishy-washy bullshit. If you can't put into words what you need, then don't get your panties in a knot over not getting whatever mysterious thing it was you didn't articulate.
That all being said, having a set of negotiated rules can give people a sense of security. So, rules work well for some people, and they keep them in place for years and years. But I think it will be an exciting challenge for you not to have rules.
As far as not having any primary designation and feeling jealous... well, you asked how one can tell whether or not the jealousy you feel could be "a sign that there's something wrong with your situation." Hmm, I'm not sure jealousy is ever really an indicator of something wrong "out there." I think it is always sitting on top of other emotions and a sign of something not right "in here." In other words, it tells you there is stuff you need to work on inside of you, things like fear and insecurity. In fact, I would caution anyone to never let their jealousy guide them in any decision. For me, it always helps to step back and drill down through each level of my feelings to understand what is at the base of the jealousy. "Why do I feel this way?" "So what if such-and-such happened?" "What would it mean if blablabla?" Eventually, I reach a place where I can see things with more objectivity, and there is relief from the jealousy. But I tend not to be a very jealous person anyway, so I know it can be harder to do all that for some people for whom jealousy is a more constant habitual reaction.
I think having an additional lover will help a lot! As Mae West said, "the best way to get over a man is to get under another one." Well, you don't want to get over your man, but another lover could help you get over the jealousy. See how nice it is that you don't have rules?? You have the freedom to look for and be with another without "getting permission" first!
Lots of poly people feel no need for hierarchy. It is possible! Many people who are "solo poly" choose not to use primary/secondary labels, or prefer to have co-primaries. If you feel like reading other threads, there is one about the different ways you can live poly as a solo person, a large part of which addresses not having a primary, here:
Solo poly people - what's your ideal?
and this master thread on the topic:
Primary/Secondary: Merged Threads, General Discussion / Debate
You can also do a search for the word "primary" and see what comes up.