[EM] Condorcet corresponding to some variant of IRV?

[Bjarke Dahl Ebert]

Here's an idea:

If you modify IRV to not cancel first votes when progressing to secondary
votes, would that method find the Condorcet Winner?

Further explanation of the counting algorithm:
Everyone votes for their first candidate on the ballot.
Then, in each turn, each voter enters a vote for their next candidate on
their list, unless the "current election winner" is more preferred by them.

Example:
48% A>B>C
25% B
27% C>B>A

First round:
A: 47%
B: 25%
C: 27%

Now, the 27% will place a vote for B also:
A: 48%
B: 52%
C: 27%

So B is the winner.

This can be seen as a "simulated series of Approval Voting elections". In
each turn, voters lower their "threshold for approval", until they are
satisfied with the current winner.

This method will always find a unique winner (unless there is vote count
equality, of course).
Questions:
  A: Will this winner always be in the Smith set?
  B: If there is a Condorcet Winner, will it be the same as the one found by
this method?
(A implies B).
In case of B, it could serve as an alternative justification of Condorcet
Voting: "Just like IRV, but don't forget candidates just because they were
temporarily discarded (until we knew better)".


Kind regards,
Bjarke