[EM] Equal-ranking in Condorcet, SCRIRVE (was" Condorcet-Approval hybrid method")

[Chris Benham]

Kevin,
You wrote:

"Suppose we're using a WV method:

40 A>B>C
35 B>C>A
25 C>A>B

There's an A>B>C>A cycle. B>C is the strongest win (75 votes), followed
by A>B (65 votes) and C>A (60 votes). So C>A is discarded and A wins.

But suppose the B>C voters see this coming and perhaps don't feel
as strongly between B and C. They might instead vote B=C>A. When
that happens, there is still a cycle, but now B>C is the weakest win
with only 40 votes. Now C wins.

(Incidentally, this also works in the CDTT method I suggest. The CDTT
is {a,b,c} at first; when the B>C voters rank B=C, the CDTT becomes
just {c}.)

I don't consider that the B>C voters get this advantage for free. In
order for it to work, they have to give up the opportunity to distinguish
between B and C."

Those last two sentences are just putting a bizarre spin on rewarding 
indecisiveness. Suppose those B=C voters
(in the modified example) really are too stupid and lazy to decide which 
they prefer out of B and C, they just hate A.
Then they *are* "getting an advantage for free"!

Based on the sincere rankings, what possible case is there that electing 
C is  "better" than electing A?  In this classic
3-candidate cycle scenario, if the method meets Majority then there are 
always voters with an incentive to Compromise.
Based on these particular sincere rankings, I can't see that we really 
have any guide as to which is the "best" winner other than the
Borda scores, and C is the big Borda loser (having the fewest 
first-preferences and the most last-preferences)!

Russ and others might be interested to know that there is a method that 
meets Woodall's  Symmetric Completion and Plurality criteria,
doesn't have any 0-info. strategy incentives (meets NZIS), meets all the 
Condorcet criteria,  (mutual)Majority, 3-small Mono-raise
(monotonicity with no more than three candidates) ,Clone Independence 
and "naturally" meets Minimal Defense.

SCRIRVE!
Ranked ballots, truncation allowed. Then the ballots are "symmetrically 
completed" and reversed. Based on the resulting profile, repeatedly
eliminated the IRV "winner" (until one candidate remains).
This is the definition that fits the acronym, but the "symmetrically 
complete" stage can be omitted, and then working on the reverse profile,
"fractional" equal-ranking IRV is used to repeatedly exclude candidates.

When  there are three candidates in a cycle, then SCRIRVE is equivalent 
to "elect the candidate with the fewest last-place rankings (fractional)".
It handles this example very well. Assuming that we are allowing 
non-last equal-rankings, it elects B both times.

Chris Benham