And what happens after that vote? Still equality? Again you have narrowed the definition of equality down to the single act of voting.
Let's play it out, majority wins. Puts whoever in power, that person pushes a bunch of stuff the majority likes and none of what the minority does. Where is the equality? Where is the minorities representation? They may have a vote, but that vote doesnt mean anything, therefore no equality. You have removed their value from the equation. Without representation they have no avenue to express themselves in the system. That's not equality in any way, shape, or form.