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## detailed solution

Since the vote turns out to be six votes for Jacob and four votes for Allison, we know that everyone votes for one of these two people. All of the clues in which people state that they vote for anyone other than these two are clearly lies. Statements where people claim to vote for either Jacob or Allison could be true or false, as we’ll see below.

Jacob tells Peter: "I'm voting for Allison."

This must be a true statement. Jacob can only vote for Allison or Jacob, and no one votes off themselves. This means that Jacob and Peter are in the same alliance, and Allison is in a different alliance.

Allison tells Chris: "I'm voting for Jacob."

Similarly, this must also be a true statement, since Allison cannot vote off herself. This means that Allison and Chris are in the same alliance.

Jacob tells Chris: "I'm voting for Teresa."

This is clearly a lie, since no one ended up voting for Teresa. If Teresa were in Jacob's alliance, Jacob would be claiming to vote off someone from his own alliance, which can't happen. If Teresa were in Chris's alliance, Jacob would be threatening to vote off someone from Chris's own alliance, which also doesn't happen. This means that Teresa must be in an alliance separate from Jacob and Chris.

Jacob to Teresa: "I'm voting for Michael."

Again, this is clearly a lie, since no one ended up voting for Michael. If Michael were in Jacob's alliance, Jacob would be claiming to vote off someone from his own alliance, which can't happen. If Michael were in Teresa's alliance, Jacob would be threatening to vote off someone from Teresa's own alliance, which doesn't happen. Finally, if Michael were in Allison's alliance, Jacob would be indicating to Teresa the alliance from which he is actually going to vote a person off, which also doesn't happen. Thus, Michael must be in the fourth alliance.

Allison tells Genevieve: "I'm voting for Sara."
Allison tells Sara: "I'm voting for Michael."

Genevieve and Sara must be in different alliances. Otherwise, when Allison tells Genevieve she's voting for Sara, Allison would be threatening to vote off someone in Genevieve's own alliance. Since we know that Allison is voting for Jacob, she's lying to both Genevieve and Sara, so neither of them are in Allison's alliance.

If Sara were in Michael's alliance, Allison would be threatening to vote off someone from Sarah's own alliance, which doesn't happen. If Sara were in Jacob's alliance, then Allison couldn't tell Genevieve that she was voting off Sara – this would violate the rule about not implicating the alliance from which you are really voting off someone. Thus Sara must be in Teresa's alliance.

We have already established that Genevieve cannot be in Allison's alliance, nor can she be in Sara's alliance. We know that there must be an alliance of only one person, and now, all but one of the alliances has more than one person. This means that Michael must be in his own alliance, which means that Genevieve cannot be in an alliance with him. This leaves Genevieve to be in Jacob's alliance.

Samantha to Donte: "I'm voting for Teresa."

This means that Samantha and Donte are in different alliances, since this is clearly a lie. It also means that neither Samantha nor Donte are in Teresa's alliance. If Samantha were in Teresa's alliance, she would be telling Donte that she was voting off a person in her own alliance, which wouldn't happen. If Donte were in Teresa's alliance, Samantha would be threatening to vote off someone in Donte's alliance, which doesn't happen. Samantha and Donte cannot be in Michael's alliance of one person. This leaves one of them to be in Jacob's alliance, and the other to be in Allison's alliance. This also means that Teresa and Sara make up the alliance of two people, while Allison's alliance must have three people and Jacob's alliance must have four people.

Michael to Donte: "I'm voting for Allison."

Since Michael is in an alliance by himself, this is actually a lie. This means that Michael is voting for Jacob. More importantly, it also means that Donte cannot be in Allison's alliance, since if he were, Michael would be threatening to vote off someone in Donte's own alliance. This means that Donte is in Jacob's alliance, and Samantha is in Allison's alliance.