[EM] Re; Ranked-Pairs (wv) can lose a Cond. Winner

[MIKE OSSIPOFF]

Steph--

[a shift key isn't working, and so some letters may be incorrectly
uncapitalized. i'll use brackets for parentheses.]

here's your example:

A family of examples with (11+2x) (x>=0) voters and 3 candidates is:
2+x: A
2: A > B > C
2: B > A > C
1+x: B > C > A
4: C
Ranked pairs with winning votes produces:
A (6+x) > C (5+x) , B (5+x) > C (4) and A (4+x) > B (3+x).
A is the Condorcet winner and wins.
Margins and relative margins produce of course the same result.
If I am one of the two B > A > C voter, my 2nd (A)
choice harms my favorite 1st choice (B).
The proof is, if I and my co-thinker vote B only:
2+x: A
2: A > B > C
2: B   (truncated !)
1+x: B > C > A
4: C
Ranked pairs with winning votes produces:
B (5+x) > C (4), C (5+x) > A (4+x) and A (4+x) > B (3+x) can't lock.
B wins now.

i reply:

i assume that you're saying that in your example x can have any
nonzero value without changing the result. For simplicity i let X = 1.

maybe i made an error, but by my count, B is the BeatsAll winner,
regardless of whether the BAC voters truncate.

Would you re-post the example that you intended, preferably with
exactly-determined numbers of voters?

if you say that truncation can take victory from a CW in wv, you're
probably intending the old example in which a poorly-supported CW loses
to truncation. i've many times said that truncation can work against
a cw when there's lots of indifference toward that cw. When there's
no majority voting the cw over the candidate who steals the election.
A candidate can be CW even if he beats the other candidates with
sub-majority defeats. And if he beats y with a submajority defeat,
i make no claim that y can't steal the election by truncation.

if that's your point, then you're right. it's something that i've
often said.

please note that SFC is about a CW who is preferred to
candidate y by a majority who vote sincerely. Re-read SFC & GSFC.
Those criteria, though they don't mention truncation, tell what i
claim for wv when no one order-reverses.

mike ossipoff




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