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Sometimes, picking the right people for the workshop is harder than running it. An external facilitator isn't the best person to decide who should be invited and who shouldn't; job titles don't say much about the possible contribution.
But picking the right people can become as annoying as choosing tables for friends and relatives at your wedding: "Why wasn't I invited?" and "Why was I invited?" are two equally nasty problems to handle. There is no perfect way to make the selection work.. Maybe the best solution is not having the invitation responsibility at all and letting human beings be responsible for their own choices.
Therefore
Make people aware that you're running the workshop, let the information spread, and self-organisation do some magic for you.
Keep a pattern of open invitation: you need to keep the head count under control for booking an appropriate room (but be ready for some last minute joins).
Secure the few key people you really need and let their presence be the main driver, but let commitment be the main driver for other participants; you may discover that you have some unexpected sponsors inside your organization. In some cases, you may need to keep some aces up your sleeve: depending on the company culture, some people may be afraid to be in the same room with their bosses.
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Selling the workshop format is not your goal. Don't use the invitation to explain what EventStorming is. Your workshop has a purpose ; EventStorming is just one of the possible tools to achieve it.
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You'll probably have a few people that are going to be needed, but that don't consider the event worth of their time (see also [Dungeon Master](#dungeon-master),) in this case you may want to ask their participatiion as an explicit request for help. If you fail, you will have gained valuable insight into where your key problem might lie.
Expect quite a few questions about the event: keeping some of the answers public in a FAQ can be a good way to be consistent with your answers.
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Please remind that 'open' doesn't mean half-hearted: the ones joining the workshop are supposed to give full attention. Getting in and out, and asking for summaries and recaps, negatively impact everybody's experience.
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Size Matters
The organisation's size clearly influences the strategy: Open Invitation plays well in mid-sized organisations where the number of people involved is still relatively manageable. Twenty to thirty people is a common number for a Big Picture workshop, and it maps relatively well with a single line of business, but every organization is different.
Sometimes, there is no way to make the first workshop perfect. Maybe the only goal of the first workshop is to make the right one possible. See also [Iterative invitations](#iterative-invitation) and [Leave stuff around](#leave-stuff-around).
Manage selection biases
Volunteering for the workshop may provide you with an unbalanced audience. It's probably still the best possible outcome, but it could impact specific stages like [Arrow Voting](#arrow-voting). Make sure that you don't give too much political significance to the collective opinion of only one side of the organization.