At decision time
Since this is the core of the question I'm putting my advice to it first. I have very little patience for this sort of behavior, so when it's time to go out/start the game/initiate whatever activity you'll be doing, the time for consideration is just about up. I'll usually say something along the lines of
We're about to [head out/start the game/etc.], so unless you come join us now you're deciding "no".
Depending on the people you're with this phrasing might be too impolite or not impolite enough. Its most important features, to my mind, are:
- It reiterates that events are not waiting on this person's
decision: events are moving forward no matter what, and this person
can join or not. The activity is for everyone, and it does not center around the least decisive person present.
- It emphasizes that indecision can't last forever. When the last
possible moment to decide arrives, the person can actively choose to
join in or else their decision is equivalent to deciding not to join.
I've found the "you're making a decision either way" framing useful
because it jars people out of the idea that they can be passive here.
The decision is theirs to make, and events will proceed from that
With this strategy it's important not to equivocate or allow extra decision time. If the person decides to join after all, then I'll tolerate any necessary delays (finding a coat, getting shoes on, etc.). But they get zero additional time to consider the decision of whether or not to join-- again, anything that isn't a clear "yes" should be treated as a clear "no".
Before decision time
Some people are really indecisive, and actually dither a lot about this kind of choice. The above strategy has worked well for me in dealing with such. But some people seem to have other considerations at play which lead them to pretend that they simply can't make up their minds:
1. Were they told they could join, or asked to join?
For some, the passive invitation ("we've got an extra seat...") isn't enough. A more assertive invitation ("Come join us!") can make it clearer that their presence and participation is desired by the rest of the group. Even when that isn't exactly the case (like when you don't really care if they join or not), it can be helpful to make the situation clearer: you're part of the group, the group is doing a thing, you can/should/might enjoy doing that thing with the group.
2. How much discussion of the indecision has there been?
Some people have legitimate reasons to consider joining an activity more carefully, but they won't necessarily share those reasons. When I don't care if the person joins it's less likely that I will try to get that information, and when I don't have the information the reasoning seems opaque and needlessly indecisive. If you're all going to a bar to dance, but person A's foot is hurting a bit and they aren't sure they'll have fun dancing, a very brief discussion can reveal that and allow for new information to come into play and (maybe) resolve the indecision:
Me: Hey, we're going out dancing. Would you like to come with us?
A: I don't know, I haven't decided yet. // This is where conversations might end, if I don't care about the person coming along or not
Me: Why don't you want to come?
A: Oh, my foot's been bothering me, I don't think I'd have much fun dancing all night.
Me: Well, if you don't want to come that's fine. But there is plenty of other stuff to do there besides dance. They have [bar games/sports on TV/whatever], and we won't all be dancing all the time. For the most part we'll probably just be sitting at a table talking over drinks!
It's a contrived example, I know. But now instead of silently thinking about whether or not their foot is in good enough condition for dancing, A has reasons to come along besides the dancing, and the reasoning behind the original reluctance is visible. That last point is important-- when you don't know the reasons, it all seems like useless dithering.
3. Be prepared for "no", and don't require that the person explicitly reject joining
Not every person enjoys every activity equally, all the time. And not every person likes direct communication. It's totally possible that an activity doesn't really appeal to someone, but for whatever reason they don't want to just say "no"-- they'd rather sort of seem interested, but then find that everyone has moved on without them. They don't have to join in, and they don't have to opt out. Treating these situations as potential yes-es can cause friction, as this type of person may not want to say yes or no.
So this one ties in with my suggestion at the top: the closer it gets to decision time, the more an indecisive stance should be treated as a standing "no". Totally changeable, and without any sort of penalty, but until they say "yes, I'd like to join" plans should primarily be organized around the idea that the person will not be joining. The closer it gets to decision time the more strongly I would weight a "maybe" towards "no".