Yeah if you want enough votes to actually make a difference you need to buy them with loyalty or whatever. Always try make a habit of looking at both paths before moving when doing class cat quests. Don't know how many times I've joined and went down a path without looking and there's a core on the other path. It will be gone when you rejoin.
You need a lot of mystic cores (the 5th for maximum MD level is 80 mystic core), you can exchange in loyalty for 8k loyalty (per one mystic core) when it’s available, or use units to purchase mystic cores.. if you use plenty of mystic champions, you have to set 4 to 5 points for Mystic Dispersion.. some say 3:5 is enough, my suggestion is 4:5.. but if you want to go all in.. 5:5.. there is no right or wrong, as long as your mastery setup maximize your champion skill and abilities.
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They are also sometimes available as a pick-up prize on the map in those Mystic Class Catalyst quests.