Usually, the goal of a second (or third) ballot is to get a step closer to the
Condorcet winner -- the candidate that would win the election if every candidate faced every other candidate in isolated head-to-head elections. In other words, you have subsequent ballots in order to ensure that the eventual winner is as close to the community's overall preference as possible.
You can do this like the U.S. political parties did before 1968, without artificially removing
any candidates from the second ballot, and you just keep on voting and voting until somebody gets a majority of the vote. The benefit is that you know that the winner really is something quite close to the Condorcet winner. The cost is that you might go to four or five ballots... or you might deadlock and end up voting 103 times, as at the infamous
Klanbake (or at a few hotly contested medieval papal conclaves).
Assuming simple majority rule (which was not in place at the Klanbake), you can force the voting to end after a certain number of rounds by eliminating candidates after each round. If you drop the bottom candidate after each round, you are guaranteed to have a result within n rounds, where n=the total number of candidates.
The problem is, if you drop too many candidates at a time (to reduce the number of rounds of voting), you may distort the result. For example, if the top two finishers are popular but polarizing, while the third-place finisher is not especially popular but is generally considered an acceptable compromise, dropping every option but the top-two finishers ensures that the extreme camps will battle it out for 50%+1 instead of settling on a broad compromise. But keeping the top three might have allowed the community to reach a solution satisfactory to the 80% not firmly committed to one of the two extremes. This is especially true in multi-candidate races without clear leaders or coalitions, like the election we just had -- sure, there's two leaders at the end, but no single candidate had more than 14% of the vote. Making those two (which, combined, had barely a quarter of the vote) the sole options in the runoff is highly likely to distort the outcome and produce a winner who would not have won under a more painstaking voting process.
But, of course, many communities don't have the time or resources to vote again and again until reaching a clear consensus winner. Voters themselves lose patience with endless balloting and reballoting, meaning less turnout in subsequent elections, which itself distorts the outcome. That's life. Even if you
do vote again and again, the truth is that some elections
don't have Condorcet winners, and
Arrow's Impossibility Theorem proves it's literally impossible to divine the "true" community preference from any number of ballots in any form anyway. You've got to cut it off at some point.
You decided to cut it off at two ballots, with the second ballot a simple-majority runoff between the top two finishers of the first ballot. It's a perfectly reasonable decision. But it does mean the vote is less likely to reflect the truest version of the collective will.
![[Fed]](https://www.trekcc.org/forum/images/smilies/icon_federation.gif "Federation")
![[Kli]](https://www.trekcc.org/forum/images/smilies/icon_klingon.png "Klingon")
![[NA]](https://www.trekcc.org/forum/images/smilies/icon_nonaligned.png "Non-Aligned")
![[Vul]](https://www.trekcc.org/forum/images/smilies/icon_vulcan.png "Vulcan"){kind=icon}
![[OS]](https://www.trekcc.org/forum/images/smilies/icon_1e_os.png "Original Series"){kind=icon}
![[Holo]](https://www.trekcc.org/forum/images/smilies/icon_hologram.jpg "Hologram"){kind=icon}
or not and I dread it.