Maireadplastic Re "Just ask. And ask if they need you to stay." Great answer, so sensible.
Fluffy re "If I allow one sibling to join the party simply because s/he is a sibling then I would be setting a precedent for all 20 children's siblings to join in. Therefore a party for 20 becomes 40 - or more!" I doubt if all 20 kids would each have a sibling, let alone want them to attend!
Waltermittythesequel Re "Better to decline the invitation with an explanation why. That way, they can decide whether to extend the invitation or not." This sounds like a terrible idea, it has all the 'emotional blackmail' element along with a 'party decline' to an invitation. It seems really unfair to the child who was invited. Children do know quite early on who is invited, who is coming to their party etc. I've known a friend fall out over a party invite or rather a child saying 'You are not coming to my party.' The mum might say so-and-so can't come and that could put a dampener on the friendship. WHICH is so much more vital than a bloody party invite.
The birthday child may not be able to understand the finer points of 'so-and-so's mum felt worried my mum would be put out' and the invited child would most likely think my "Mum is a meddling in my friendships, grrrrr!"
Floey re "My god are babysitters extinct?" Not everyone has people who will look after their kids for free. How much could it cost to have someone look after your child or children so one can attend a party? Some babysitters might charge £5 an hour. My dd went to quite a lot of parties when she was younger, if we had had younger children I would not have been able to afford babysitters for these. As I said before I've got a husband who doesn't work weekends but not everyone does, some parent alone and they cannot just find someone to look after their child.
Waltermittythesequel Re "But why not just drop her? There's no reason to stay." My dd did not stay at parties until she was at least 7 or 8, she was quite shy, has autistic tendencies and would have found it very hard for me to drop and run! Our son is adopted and and quite emotional - and at 6, now, we would not leave him at a party. In fact when he had his party for age 6, and many of the other kids are older then him, still a number of mums stayed with younger sibs.
I said I was off but I had to come back when I read someone call children's parties a 'minefield'. It is not a minefield (unless you let it be). It is a chance to celebrate your child's birthday with their friends. This may mean you end up feeding a child who has had no choice but to come because their sibling has been invited and their mum or dad wisely, in my mind, chose to bring the invited child along even if sib had to come too.
Of course telling the party host, or asking, is best but please stop over thinking this, demonizing the person who brings a sibling (some borderline bullying comments for run who was just being open about what they do). And some generally most uncharitable comments about a child's party!
Having known many kids who struggle to make friends I am literally gobsmacked so many parents are willing to over-think such a simple thing as a child's party. Please just be glad you can afford to give you child a party and most of all that they have friends to invite.
I think a large dollop of generosity is needed with the birthday cake. 