The local restaurants include a Chinese, French, Italian, Tex-Mex, Indian and Pub-Grub.
Choosing with FPTP:
FPTP: "Where do you want to eat"
You: "I like Indian most"
You: "But if people don't like Indian food, then I'd go for Tex-Mex"
FPTP: "You only get one choice."
You: "Oh... I like Indian and TexMex but others might think its too spicy, I don't want Chinese... OK I'll say 'Italian', thats safe not my favourite but should beat the Chinese".
Chosing with AV:
AV: "Where do you want to eat"
You: "I like Indian most, but if we cant do that Tex-Mex, but if we cant do that French..."
See how FPTP makes you 'self-censor' yourself? If you aren't absolutely sure your favourite will win, there is a strong reason to chose something you don't really want just to avoid something even worse!
With AV you just say exactly what you want - simple.