How important is it to you that an opposing party knows how wrong their viewpoint is?

When I was younger it was very important. Now I'm content to understand that every human being has the right to shoot him/herself in the foot if they must.

And it seems they must.

It's not. .. comes a time in any discussion when you realise they either wish to learn or listen. .. or not

Not that much, unless they really are open and ready to a exchange of ideas. When I join posts where I don't agree, it will mostly be to debunk a distorted presentation of a topic. As an example, like when Sweden was presented as the rape capital of Europe without looking further into the statistics and the way data is collected. Another example, like when BBC is shown to present a news story about the killing of a priest in France by a manipulated picture telling the priest stapled and fell on a knife, just to mock liberals. It's not satire, it's plain evil and showing no respect to the victims and their loved ones. I could go on with examples, but these will be some of the latest where I have chosen not to stick to my mantra of staying out of these attention hungering posts. Not to convince the poster and their friends. That will be a case lost. It has been to show others what's upside down on the story behind the post.

I guess that depends on the viewpoint being expressed. 

I have a low tolerance for the distortion of truth, hypocrisy, and/or  bigotted remarks.   I may over-compensate in my responses given that I'm a strongly-opinionated person. 

The bottom line is that if I do get into a discussion or debate... in the end, I make sure that my positon is very clear.

Well, it is not about the opposition knowing.  That never works.  Point the finger and  you KNOW what happens . They retort and do not listen.  

What is being done, hopefully, is connecting with the undecided.  If they see both sides, they can still choose which is the most sensible, sane and worthy of consideration. 

Of course, THAT never works either. 

All that is left is to PRAY.  I am kneeling and praying right now.  This is the worst situation we have ever been in with Trump even MAYBE having a chance to run this country.

Not very.  But that all depends on how much I respect their opinion in the first place.  I like to hear opposing views .. and people are entitled to them.  If I'm sure about my stance on something ... I will just let them believe what they like.

It depends on how determined the other party is to tell me how wrong I am.  And how they go about doing it. I can usually talk with people civilly if they can as well. 

With respect to the Internet, it's not necessarily about convincing the "other party", it's about not conceding the rhetorical space. As propagandists throughout history have intuitively inferred, and as linguists and cognitive scientists have verified through empirical investigation, the truth of a proposition is not necessarily relevant to its acceptance. True or not, any proposition which gets sufficiently repeated tends to stay in the minds of those exposed to it.

Hence, you have a large plurality of Americans who believe President Obama is a Muslim, despite the near-complete lack of evidence to support that proposition.

Pleas note the large plurality believes the proposition despite copious amounts of published information refuting it. Imagine how many more would believe it if there WASN'T any refutation.

Cognitive linguist George Lakoff explains the process (and why our conventional notions of rational discourse are often misguided) in this analysis of how supporters of health care reform failed to make a persuasive case for their proposals in the video below. While it's focused on one particular subject, the principles apply broadly to rhetoric and persuasion.

While this is certainly a great discourse  by Mr. Lakoff, he is missing a key ingredient.  Most people do not want to listen to anything that requires more than one paragraph to explain.    Their eyes glaze over and they are thinking of ways to change the channel. 

We are a nation of parrots.  If we can parrot something back, that is sufficient.  If it takes an explanation, even as short as Mr. Lakofff's, above, most people are turning the channel  to see what Trump is doing. 

Why should I have to strain my brain and think and accept, when there is an easy solution.  Let Trump do it, he knows how to deal. 

People are lazy, there are too few that even comprehend what the man is explaining, even though it is clear, concise and to the point.

So, how can Democratic leaders  explain any process, and the how and why of it,  when half of America is too stupid to even absorb something as complex as health care?    Does it take more than five minutes to explain?  Love Boat is on and so is Duck Dynasty.  That is more their speed.

There is much truth to what you say. The propaganda effect interacts with other aspects of our cognition, including existing narrative frames (e.g. Repeat "Hillary has never been charged with anything" and it won't matter one whit to the "Jail Hillary" crowd) and, as you mentioned, the desire for cognitive simplicity. It's much easier to form and maintain the concept "Hillary is a crook" then to delve into the actual charges against her, compare them to misdeeds by other politicians, and come up with a "Where does Hillary lie on the Crooked Politician scale relative to [other politician]?"

Honestly?  I don't care what their viewpoint is.  It may well be repulsive or depressing but I'm unlikely to change it.  I'm much more interested in how people arrive at their opinions and the 'facts' they use to justify or confirm them to themselves.  So I'll rarely try to tell someone, 'you're wrong!' but will happily point out selected bits of information used incorrectly as justification for an opinion.

I like that guy though.  He's got it down. 

I have generally adopted the attitude that I don't have to educate the world.