It's not just about saying "yes" or "no"

80% Consensus + 20% Compromise = 100% Progress

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Resolution has nothing to do with winning

The strength of this matrix is in its simplicity. No one can argue with it's obvious message: if you want to proceed as a team, you need to make decisions in the top right-hand box.
A farmer will never forget to harvest his crops, but how many managers do you know who can argue for hours without coming to a decision.
Agreeing in principle is relatively easy. Agreeing on the last 20% is nearly impossible, simply because nobody really knows what will happen in detail before it has happened.

Avoid the traps

From an early age, we are brought up to succeed, to strive to win and to try to achieve our goals. I also reccomend teams set clear targets and focus on their attainment.
These are generally great attitudes, but thinking outside the box for a minute, do they really help in a dispute situation?

The first simple thing I do when mediating a dispute is ask each party to prepare their thoughts about what they agree on and to talk about where they are prepared to back down. You would be amazed how productive these talks can turn because the opposite party sees their challenge shrinking with every sentance. If both parties are truely interested in progress, a fragile foundation of trust can be built by simply discussing these points first before we move on to the difficult topics.

In order to then move on and make progress with the dispute at hand, we need to avoid falling into two types of traps: purely for the sake of simplicity, let's imagine two groups of people: those who never agree and those who never discuss...

The perpetual discussion groups

We are all human and sometimes get stuck in the lower half of this coordinate system. We have to win, regardless what our opinion is or how much we know about the subject. We may feel they need to have an opinion to be worthwhile and may need to prove others wrong in order to confirm our own self-esteem.
We must learn that compromising is not giving in, that leadership is about delegating and that we can only grow through tapping into others' resources.

The group of no arguments

Confrontation is never the easy way and our second group may put too much emphasis on harmony. The instant agree crowd need to embrace discussions, simply as a process of coming closer. With a little practice, they will soon benefit by conciously spending more time in the lower left quadrant.
Sure we need consensus to proceeed, but where is the value in agreeing on something we do not believe in or do not want to support. This second group must be managed and can be more dangerous than the first because you often find them in the coffee corner, just 5 minutes after the meeting, discussing how useless it was and making sure the decisions do not get implemented.

True consensus is a process

The challenge of course is that these two groups do not really exist. We all belong to both groups at times and often switch groups during a discussion. So how do we avoid these traps?
Team leaders must make clear to our instant agree crowd that a decision can only be made after the subject is understood. Meanwhile, they must chose the right moment to tell our perpetual discussers that we will never 100% agree on everything. There is a time to discuss, but progress is not built on opinions, it is built on action.

IN SUMMARY: Everything is clear in hindsight

If your team is stuck in a perpetual argument, get them to clearly state what points they agree on before discussing further.

80% consensus should be sought in the bottom left quandrant of this coordinate system by way of respectful discussion. As soon as we agree in principle, the team should immediately move to the top right, take a 20% hit on compromise and then get on with 100% progress.

IF YOU CANNOT AGREE IN PRINCIPLE: Simply break your question down into finite elements and discuss each topic, one at a time.

See these articles for tips on accelerating progress.