What is a good set-up for the board of directors/executive committee of research institutes? I have been elected as employee representative for the board (edit: not really a board of directors, the competences seem partially advisory and partly decision making) of a new interdisciplinary research institute at my university. The board in its current setup consists of ~ 10 professors (all stakeholder in the institute as department heads) + dean + 1 employee representative, all with the right to vote, only the employee representative is elected, there is no student representative. 

Is this a common setup? Are there any good examples of other boards with better parity/more egalitarian representation of relevant groups?
There are many examples of University research boards and their makeup (as I'm unsure what your research institute focuses on, it's difficult for me to pick a similar one, but it's easy to find examples on the net) however I'd definitely recommend a few things from my experience on non-profit boards.

Firstly, all those influenced by your decisions should have a representative. This means students in your case - it's vital to stop problems down the line.

Secondly, wherever possible, all members should be elected as impartially as possible. This isn't always easy, but it's an important step in proving the high standards of the board.

Lastly, realise that a board of any kind tends to get into cliques. Anything you can do to stop that is important. Examples to stop that would include a rotation of positions, or setting tenure lengths.