This time by prior agreement, the mathematicians all know:
Ariana represents 0 if she receives a blue ticket and 5 if she receives red;
Bob represents 1 for blue and 6 for red;
Caroline represents 2 for blue and 7 for red;
David represents 3 for blue and 8 for red; and
Ellen represents 4 for blue and 9 for red.

Jordan adds up the numbers on all the hats. He divides them by 10 and takes the remainder. For example, suppose the numbers are 3 2 7 9 5 by alphabetical order of participant. He adds them up and gets 26. The remainder after dividing by 10 is 6.

He sends a ticket reflecting the remainder value to the appropriate person. In this example he would send a red ticket to Bob to represent 6.