Both VISA and Mastercard were started by big banks. Banks like Citibank(member in both Allainces), Bank of America(member in Visa only Purchased MBNA got voting rights in Mastercard),Chase(member in both banks as they purchased Bank one original member in Visa),HSBC(Mastercard Member only), Deutsche bank (member in VISA) amoung other large international banks are the original members. They allowed smaller banks to join the allainces back in the mid 80's on the condition these other banks stop issueing American Express cards as many smaller banks used to issue co-branded American Express cards in the early to mid 80's. That is whole bais for American Express current lawsuit against both Visa and Mastercard and larger controlling members of the 2 credit card allainces.
Only orginal member banks have ownership interest in the Visa and Mastercard networks and voting rights. All other member allanice banks more or less agree to terms of the allanice set up.