The one hundred U.S. Senators are standing in a line in alphabetical order. Each senator either always tells the truth or always lies. The $i$th person in line says:

"Of the $101-i$ people who are not ahead of me in line (including myself), more than half of them are truth-tellers.''

How many possibilities are there for the set of truth-tellers on the U.S. Senate?

[i]Proposed by James Lin[/i]
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   - We need to determine the possible sets of truth-tellers that satisfy the conditions for all \(i\).

6. **Simplifying the Problem:**
   - Consider the last person in line (the 100th person). They say that more than half of the 1 person (themselves) is a truth-teller. This is trivially true if they are a truth-teller.
   - Moving to the 99th person, they say that more than half of the 2 people (themselves and the 100th person) are truth-tellers. This means at least 2 out of 2 must be truth-tellers if the 99th person is a truth-teller.
   - Continuing this logic, the \(i\)-th person’s statement imposes a condition on the number of truth-tellers among the last \(101-i\) people.

7. **Generalizing the Pattern:**
   - For the \(i\)-th person to be a truth-teller, the number of truth-tellers among the last \(101-i\) people must be at least \(\lceil \frac{101-i}{2} \rceil + 1\).
   - This recursive condition must hold for all \(i\).

8. **Counting the Possibilities:**
   - The problem can be reduced to counting the number of ways to distribute truth-tellers such that the conditions are satisfied for all \(i\).

9. **Conclusion:**
   - By analyzing the conditions and the recursive nature of the problem, we find that there is only one way to distribute the truth-tellers such that all conditions are satisfied.

The final answer is \( \boxed{1} \)