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It strikes me that there was something contrary to the stated aims of Stack Overflow about the accepted answer button. SO set out not to provide an answer to one individual but to create a permanent collection of questions and answers that would be valuable to many people. Given this, what is the point of giving the original asker a super vote? If the answers are supposed to serve multiple people with the same problem, what special status does the first asker have to bless a particular answer?

The point of a social proof system is that the best answer is proved by accumulating the most votes. Not a perfect system, but it has its merits. But it is compromised if the person who asks the question is given a super vote. And we see this all the time, low vote questions accepted by the original asker, either because they accepted too soon before a better answer was posted, or they did not like the best answer for some reason. 

It seems to me that there are three reason to upvote an answer:

1. I tried the solution provided and it worked. 

2. I am an expert (or think I am) and I agree with this answer.

3. I have heard this answer before and assume it is correct. 

Now it seems to me that there are two kinds of validation here, experience and agreement, and that they have distinct value as social proof. The accepted answer button is (tacitly and inexactly) a tried it and it worked vote. A regular upvote could be either. 

If you wanted to distinguish two kinds of up votes:

1. It worked!
2. I agree!

You could, but they should apply equally for all voters. The asker should not have a privileged It worked! button. If the answer is for everyone, anyone for whom that answer worked should be able to cast an It worked! vote. 

I'm not sure if having two distinct kinds of up vote would work, or if people would respect the difference. But this strikes me as capturing the difference between an accepted answer button and a regular upvote, and if you want to preserve the distinction between It worked! and I agree! then both vote types should be available to everyone.