"Should we judge others by our own values?"

Yes. We hold our values because we believe they are true, relevant, and useful. We sure shouldn't judge others by any values that don't meet that standard =) However, while we cannot help but judge matters of every kind and at every scale, it is utterly necessary to consider our own attainment of our values in assessing the validity of our judgment.

In other words, I know I am not a rocket scientist, so do not expect my judgment regarding the design of rockets to be particularly useful to folks building rockets. I am just as much not someone else, and thus my judgments about their lives, decisions, and social interactions are just as inconsequential as my judgments about rockets and brain surgery.

In all judgments, our humility is a critical component, and the hubris with which people judge others is a direct result of their lack of honest self reflection and excess of conceit, which brings violence and woe to humanity. Were we suitably humble, and I definitely speak for myself here, we would instead associate haply and bring joy and good company to our fellows.

Essentially, this is what is encouraged by the aphorism 'Judge not lest ye be judged.' It's not that we are even capable of not judging, but that when we do we must not criticize others for what we do not criticize with equal censure in ourselves. Because of this, I prefer the saying 'Love your neighbor as you love yourself.' In the context of this QOTW, I would restate these proverbs as 'Judge others as you judge yourself.'

That's how we should judge others: with love.

Thanks!

Edit: I didn't even undertake to enter the contest, so please do not consider this an entry, because it doesn't meet the standard for entries. I was just intrigued by the question, and led to comment. Others have much greater interest in tokens, and rewards should go to them. I just want to be proved wrong when I am, so I can change my mind and become right. It's also useful to me to know when I am not wrong, so I can base further understanding on my current grasp with confidence.

To me, that is the greatest reward: the good opinion and pleasant discourse of my peers. Nothing else has such value.