Famously a quote by former President Theodore Roosevelt, although can be traced back to a 15th century priest, he said this to describe how he dealt with other countries with conflicting interests. However, it is an idea that we can all learn from, and one that can help us achieve anything while protecting our own interests. This matters whether you are negotiating car payments as much as it does a trade agreement.
The heart of the idea of speaking softly and carrying a big stick is that calmness is the best approach to find a resolution for any negotiation or disagreement. Stay measured in your words, never lose your temper, keep control and never give in to anger. Act on logic and facts, avoid emotions and remain reasonable in your communications until all avenues of compromise have been exhausted.
However, once those avenues are gone, and all that is left is action, then you don’t hold back. Never threaten something you cannot back up, for a President, that meant having the military power to defend a position where necessary, for us, it could be anything.
It reminds us that diplomacy and a calm, non-aggressive approach are always the best option, but you must always be ready to back that up with forceful action when needed. One aspect of this phrase that many suggest is that if other parties know you will back up your position with forceful action, they are more likely to find a compromise that works for you all during calm discussions too. If ignoring your words is viewed as having no consequence, then a compromise is much less likely.
So, in this phrase, we find an understanding that it is better to stay rational and calm, but taking action where needed, and having a reputation for taking action where needed, are a big part of finding solutions without force.