Respect comes mostly with age, so that old - and hopefully wise - Patricians have a definite advantage, but Prestige also helps a great deal. These factors are known and predictable, but there is also a hidden variable called the "Campaign Fund", which is how much money a Family has reserved for the next election campaign; including things like bribes, strong-arming and good old fashioned blackmail.
However, unlike Feudal Elective realms where your "default" heir is chosen by Agnatic-Cognatic Primogeniture, in Merchant Republics it is done by Agnatic Seniority. So you can never play as a woman in Merchant Republics; instead you will tend to play a lot of grumpy old men... but there is a neat loophole. Since you are in many ways the leader of a "family firm", you can designate your heir and pick any male family member by giving him a special honorary title. Be careful with your choice though; it cannot be undone. Also, a child cannot be elected Doge, and a young man will have a much harder time winning an election.