To debate or not to debate? and When to debate? and How to debate?

When we have several people with different understanding of Buddhism, how should we decide who is right? Debate is very tempting in Buddhism, but on the other hand, we must respect other people's views and not create conflicts in the Sangha, so what should we do? Sometimes Buddhists cannot agree with each other, especially if these Buddhists come from different schools or traditions. An idea that is considered correct in one linage may be considered wrong in another. Did the Buddha teach how to handle these situations? How were these disagreements handled in the past? (See also: [famous debates in canonical Buddhist texts](https://buddhism.stackexchange.com/questions/8182/what-are-the-famous-debates-in-canonical-buddhist-texts)) ADDITIONAL QUESTIONS by @Yeshe Tenley: Under what conditions is it proper? Under what conditions is it improper? Is it a bad thing? Can it be a good thing? What is the proper motivation to do so? What are improper motivations? What is skillful? What is unskillful? Assuming it is desirable to show respect while debating, how should this respect be manifested? What are examples of disrespectful debate and how can the line be drawn? What's the difference between debate and proselytizing? ... and references to dharma teachings, historical events, or opinions/literature of noted teachers also welcome and encouraged!