An idiom describing the end of argument?

Solution 1:

You might say that the concerned party gave the last word:

2 a : the power of final decision
b : a definitive statement or treatment • this study will surely be the last word on the subject for many years
_{definition from m-w.com}

Solution 2:

You could use the expression

have the final say

1. To say the final words in an argument or discussion, especially ones that decisively or conclusively end it. The whole meeting just descended into chaos as everyone tried to have the final say. David is so smug and always has to have the final say in every debate.

2. To have the authority to decide how something ultimately happens or is done. As the editor in chief, I have the final say on the layout design for every issue.

So,

• the committee had the final say on the argument.