Pick a name at random, in front of everyone

In a workshop, who goes next is a real decision disguised as a trivial one. Left to the facilitator, the order carries meaning whether or not any was intended: the confident people go first, the quiet ones are asked last, and a group learns very quickly whose contribution is treated as optional. Handing the choice to something visibly arbitrary removes that, and removes it in front of everybody, which is the part that counts.

The visibility is the whole mechanism. A facilitator saying they picked at random is asking to be believed. A wheel spinning on the screen is not asking anything. It is the same reason a raffle is drawn in public rather than announced afterwards, and it costs nothing to do it the honest way.

Weighting exists for the cases where fairness is not the same as equal. Somebody who has already presented twice should not be as likely as somebody who has not spoken, and pretending otherwise in the name of randomness produces a session where the same three people do all the work. Remove the winner does the blunter version of the same job, and is usually what a running order actually needs.

Randomness itself is worth a sentence, because it is easy to do badly. Taking a random number and dividing by the list length introduces a small bias towards the early entries, which for eight names does not matter and for a prize draw might. This uses the browser's cryptographic source and avoids that bias, which is the sort of detail that only matters when it is wrong.

The draw history is the practical part. If the picking is meant to be fair across a whole day, somebody has to be able to see what happened, and memory is not that. Exporting the sequence also settles the occasional good natured argument about whether the wheel has it in for somebody.

It runs entirely in your browser and keeps nothing after you close the tab, which is what you want from something displayed on a screen in a room full of other people's colleagues.