I think this is a very important distinction. I prefer to use “maximizer” for “timelessly” finding the highest value of an objective function, and reserve “optimizer” for the kind of stepwise improvement discussed in this post. As I use the terms, to maximize something is to find the state with the highest value, but to optimize it is to take an initial state and find a new state with a higher value. I recognize that “optimize” and “optimizer” are sometimes used the way you’re saying, as basically synonymous with “maximize” / “maximizer”, and I could retreat to calling the inherently temporal thing I’m talking about an “improver” (or an “improvement process” if I don’t want to reify it), but this actually seems less likely to be quickly understood, and I don’t think it’s all that useful for “optimize” and “maximize” to mean exactly the same thing.
(There is a subset of optimizers as I (and this post, although I think the value should be graded rather than binary) use the term that in the limit reach the maximum, and a subset of those that even reach the maximum in a finite number of steps, but optimizers that e.g. get stuck in local maxima aren’t IMO thereby not actually optimizers, even though they aren’t maximizers in any useful sense.)
I’m very surprised that in that particular form that worked, because the extremely obvious way to postpone (or, in the end, avoid) the penalty is to not go next time either (or, in the end, ever again). I guess if there’s agreement that pretty close to 100% attendance is the norm, as in if you can only show up 60% of the time don’t bother showing up at all, then it could work. That would make sense for something like a D&D or other tabletop RPG session, or certain forms of competition like, I dunno, a table tennis league, where someone being absent even one time really does cause quite significant harm to the event. But it eliminates a chunk of the possible attendees entirely right from the start, and I imagine would make the members feel quite constrained by the club, particularly if it doesn’t appear to be really required by the event itself. And those don’t seem good for getting people to show up, either.
That’s not to say the analogy overall doesn’t work. I’d imagine requiring people to buy a ticket to go to poker night, with that ticket also covering the night’s first ante / blind, does work to increase attendance, and for the reasons you state (and not just people being foolish about “sunk costs”). It’s just payment of the penalty after the fact, and presumably with no real enforcement, that I don’t get. And if you say it works for your book club, I guess probably it does and I’m wrong somehow. But in any case, I notice that I am confused.