Sequential pairwise voting arises naturally in the legislative process. 

When the U.S. House of Representatives considers a bill, an amendment to the bill can be offered.  Two votes are then taken: 

The first vote is whether to accept the amendment.  If accepted, the second vote is between the amended bill and no bill at all.  If the amendment is defeated, the second vote is between the original bill and no bill at all. 

In 1956 the House was considering a bill that would provide federal funding for the construction of schools.  An amendment was offered that would only provide the federal funding to states with integrated school systems. 

The House could more or less be divided into three groups: Republicans, northern Democrats, and southern Democrats.  The Republicans generally opposed federal aid, but favored integration.  So their first choice was no bill, but they preferred the amended bill to the original bill.  Northern Democrats favored the federal aid and integration so their first choice was the amended bill, but preferred the original bill to no bill.  Southern Democrats, who came from states with segregated school systems, wanted the aid, but abhorred the amendment. 

The three preference lists looked like this (with the breakdown of Democrats being an estimate):

(a) What was the outcome of the two votes?

We’ll use sequential pairwise voting.  What is the agenda ?  The agenda was set by the decision to first consider accepting the amendment or the original bill and then to decide to either adopt that decision versus not to pass the bill at all.  That is, compare “amended bill” with “original bill” one-to-one and then consider the winner of that contest with the option of having “no bill”.  Thus our agenda is “Original bill”, “Amended bill”, “No bill”.

First vote:  A one-on-one comparison, “amended bill” versus “original bill”.  The result is “amended bill” wins 319 to 116 since Republicans and North Democrats combined outnumber the Southern Democrats.  Second vote:  “amended bill” versus “no bill”.  The result is “no bill” wins 319 to 116 but notice that now the Republicans and Southern Democrats have teamed up to outnumber the Northern Democrats.

The final result of the legislative process with these voters and preferences is that "no bill" is the winner.  That is, no bill will pass.

(b) If you were a northern Democrat, should you have introduced the amendment?

As a northern Democrat, it would’ve been a mistake to introduce the amendment because the result is “no bill” which was the least preferred alternative to a northern Democrat. To the northern Democrat, even the original bill was better than no bill.

(c) If you were a Republican, should you have introduced the amendment?

For the Republicans, introducing the amendment was a good strategy.  It took advantage of the split in the Democratic party at the time.  The result of the introduction of that amendment was no bill at all which was the Republican’s first preference.  However, to the Republican’s, even the amended bill was preferred to the original bill.

(d) Is there a Condorcet winner in this election?  

No.  There is no option (candidate) that beats the others in one-on-one comparisons.  In fact, this example illustrates the voting paradox of Condorcet – that is, we have an example of a voting cycle:  In the combined group preferences of this particular session of Congress we find the amendment beats the original bill, the original bill beats “no bill” but that also “no bill” beats the amendment.  In other words, the group preferences are not transitive.