How do we know that the word “acts” in “acts twice” refers specifically to Mafia “Actions” and not to actions in the more general sense of the word?
This isn't philosophy class. We're not debating the meaning of words. You're the one that needs to prove that those words mean what you say they mean because you'd be providing evidence if they did, which you've ceased to do. No evidence means your words mean nothing. And if your words are meaningless, they can be ignored as if you said nothing.
Actually, worse. They can be used against you.
This is Mafia. Where's the evidence? Here's mine.
Acting (or action) is defined as using a role ability. Since
Day is a modifier, the following could be construed as the definition for action, since Day Actions and Night Actions can be assumed to differ only by their Phase:
Night Actions, or Night Choices, are the role-related actions that players must send in and mods must accept. These range from Cops deciding who to investigate, to the Mafia deciding who they will send to kill whom, to X-Shot Commuters deciding whether they wish to use their action at all.
A Passive Role is one which has no ability to choose when or how to use their role abilities. Examples include Bulletproof, Bomb, and Lovers. Note that role modifiers such as X-Shot can sometimes change a passive role to an Active Role; this is known as an Activated role.
A Doublevoter is a Passive role. Your vote merely counts as two votes. If you were an
activated Doublevoter, it is possible your vote could count as more, and thus a 1-Shot Doubler Doublevoter might get two or three or four votes, but we're not talking about that. We're talking about a Doubler Doublevoter, which could use two actions, but the act of voting is not in itself an action, on account of it not being an active role-related ability, as explained.
As furtherance of this, we can look at a Townie:
Its members post and vote like anyone else during the Day, and cannot act at Night without the help of power roles.
...
"Townie" is a role designation for a pro-Town role that has no active ability.
A Townie can vote, or
do you believe that a Townie is incapable of even the act of voting, posting, living, etc.?
Thus, we can assume that voting does not fall into the category of acting in regards to your definition of Doubler, and thus, that acting/action refers to the set of role abilities that are actively used.
A_Curious_Cat