Reddit has an appropriate solution: you can unclick the arrow.
People can stand by their point or concede that they were wrong somehow.
If your opinion does a 180, it's probably for the better that your - new - opinion doesn't count.
As a side though, if somebody keeps changing opinions on a given topic, it would be somewhat sensible to lower the effect of such votes.
The ability to change opinions is an important difference between rational and overly stubborn people.
Sometimes I can be convinced during a discussion. Then people are often very surprised that I change my opinion at all. Then I wonder why the bother to discuss, if they don't expect me to actually change my opinion.