If you provide a tenth 'alternate' slot, you can handle the case of a tie. In the case of a tie of 2 or more, use the alternate slot to count which of the tiees get the most votes. In this case you have several places where ties make a difference.
Btw, why are you not using cumulative voting? Why can't someone vote more than once for the same person? This is the most democratic method of voting, no? It supports minority viewpoints best as a small group could insure a voice on the committee.
