You know the people you are inviting, and that makes you the best judge of what to say when inviting them, by phone or email, in person or however you do it.
Here is the sort of thing you could say, but put it in your own words:
“I’d like to invite you to be part of a kitchen table conversation that I’m arranging on [day and date, starting and finishing time, and location.”
Alternatively, you might give them some dates and times to choose from.
“Like many of us, you may be feeling frustrated with Australian politics. It does sometimes produce good results, but overall it could do a great deal better. A new organisation, OurDemocracy, aims to contribute to the process of improving Australian democracy, and as part of this it is seeking to generate 1000 Conversations for a Better Democracy. These are conversations of up to nine people invited by a host – that’s me in this case.”
“In this conversation we’ll discuss some questions supplied by OurDemocracy about our thoughts on the state of Australian politics and how we’d like to see it work better, including particular issues we’re concerned about and how we want our Federal MP to represent us.”
“Our comments will then (anonymously) contribute to a Citizens’ Report on Building a Better Democracy, which will be distributed to politicians and the broader community.”
“If, after this conversation, you are interested in forming or joining a group in your electorate to help make this happen, you’ll have the opportunity to do this.”
“The conversation will go for two hours, you don’t have to know anything in particular, and there are no right answers. Please bring a plate of refreshments [or refreshments are provided].”
“I hope you can make it. It’s a conversation I’m really looking forward to having!”
If you’re writing this as opposed to telling them, give them an opportunity to discuss it with you, and maybe, about three days before the conversation, send them a reminder email, along the lines of:
“Looking forward to seeing you on [day, date and time] for our kitchen table conversation on building a better democracy…”