It all depends on the committee's terms of reference. It would be normal for a terms of reference to entitle a committee to be responsible to elect their chair for whatever term decided. The ex-officio position is just that a position given because of the person's position in the organisation and carries no specific entitlement to any position in the committee.If the committee decided to elect the Mayor as Chair etc. then it would be their democratic decision not the Mayor's "entitlement"