Game theory - three voters for two candidates nash equilibrium

Question

There are 3 voters (x, y, and z) and two candidates (Alice and Bob). For either Alice or Bob to win they need 2 votes. If Alice wins x gets 1, y and z get 0. If Bob wins, x gets 0 and y and z get 1 each. Pure nash equilibria are 3 votes for alice, one alice two bob, three bob. I don't understand why those would be nash equilibria, because in each of those outcomes (alice wins or bob wins) either x will want to change strategy or y and z will want to change strategy. How come those are nash equilibria?

Answer 1

"1 vote for Alice-2 votes for Bob" and "3 votes for Bob" are Na$$h equilibrium because Bob wins and changing the strategy can be a worse impact on $x$.

"3 votes for Alice" is Nash equilbrium because $y$ and $z$ don't know what they are doing.

Answer 2

A Nash equilibrium does not mean that every player is satisfied with the result, only that no player can change their strategy to improve the result.

In the case that Y and Z vote for Bob, Bob wins, and X is dissatisfied but has no power to change the outcome. Y and Z might be able to change the outcome, but they are already happy and thus cannot improve.

When all three players vote for Alice, both Y and Z are dissatisfied, but neither can unilaterally change the outcome. Of course, if both would vote for Bob they'd be happier, but that does not change the fact that neither can change the outcome on their own, which is sufficient for it to be a Nash equilibrium.