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You're right, it is not unlike a romantic relationship, and just as in such a relationship, the contribution goes both ways. If a writer is rude, uncooperative, apathetic, and punishes their audience for things that they cannot help, the voters will leave, as you have said. However, if the audience is rude, uncooperative, apathetic, and punishes the writer for things that they cannot help, the writer will lose motivation to write. Of course, I do not have to deal with a rude or otherwise assholeish audience, and I'm sure most of THP writers don't. However, apathy can be just as damaging. If an audience is continuously apathetic, the writer will lose the drive to work together with them. To take this relationship analogy even further -- if you put your all into pleasing your partner during sexual relations, it is not unreasonable to expect them to do the same. Just like people quit relationships when their partner stops caring, if voters are constantly apathetic about reading, voting, and discussing, there's not gonna be much writing.
This isn't my job, it is a hobby. I write CYOAs because I enjoy doing it. Yes, I am responsible for my work, but I do not have an obligation to put in 150% just because my audience is putting in 50%. Again, if I wanted to write linear stories, I would. I write CYOAs because I want to craft a work with my audience. I enjoy writing and I enjoy working with my audience. I enjoy the CYOA process. There is no point in railroading. It doesn't accomplish what I came here to do, and it doesn't give my audience what they came for (an interactive story).
In your analogy, I am not the driver. I am the car. I take my audience where they want to go. I show them the world outside. I take them down roads that have been laid out for them. My audience is the driver; they choose where to go and what to do next. If the driver refuses to decide where to go, the car does not decide for them.
I would like to make it clear that I do not see a tie and immediately throw hands and walk away. I do wait. I do poke. And, sometimes, I do flip that coin. One must consider how often I should be flipping that coin, and the threshold on the amount of influence a given vote should lead to before I leave it to chance. Certainly, if my audience has gone back and forth over a vote for a bit and nobody seems to be budging on their decision, it would be prudent for me to step in. In my experiences, however, this has hardly been the case. The amount of discussion that goes into these important ties are not exhaustive. They come down to a few people voting with minimal, if any, back and forth. If you read some of the older stories on this site, you may find that many of the decisions are debated at length by their audiences. This is simply not the case in my experiences. I realize that the amount of traffic on THP has dwindled, but evidence suggests that voters still do exist. A little bit of discussion goes a long way. If I see that my audience is at least putting in the effort to think about these important decisions, I have something to work with. If I understand what my audience thinks of the situation at hand and how they weigh the risks, I can create compromises. However, I can't do any of that if my audience doesn't at least discuss the decision at hand.