Well, those negative ones are quite often given in the meaning ”I agree, that’s awful” or… how my forum used quite alot after one election.
Here in Finland we use quite often two examples when discussed this context:
- ”My dog/cat died” — is the ”right” reaction
or 
- ”It is snowing, again” — again,
or 
So, it depends how and to what an user reacts.
But in this context, I can understand down votes when there is a poll, but deducting amount of likes 
Absolutely no.
And yet it could be an option. Like ads are, and pop-ups.