[EM] Mono-switch-plump criterion
C.Benham
cbenham at adam.com.au
Wed May 7 12:13:48 PDT 2014
Mono-switch-plump:
*The probability of candidate X winning must not be reduced if one or
more ballots that
plump for any not-X are replaced by an equal number of ballots that
plump for X.*
Mono-raise is the traditional monotonicity criterion, but I don't see
why anyone would
see failure of Mono-switch-plump as less embarrassing than failing
Mono-raise.
25 A>B
26 B>C
23 C>A
22 C
04 A
B>C 51-45 C>A 71-29 A>B 52-26
Top Preferences: C45 > A29 > B26
When there are three candidates the MinMax , Beatpath (aka Schulze),
Ranked Pairs and River algorithms
are all equivalent. When they use Winning Votes as the measure of defeat
strength they all elect C.
IRV (aka the Alternative Vote) and Benham (and Woodall) also elect C.
But if we replace the 4A ballots
with 4C ballots the winner with all these methods changes from C to B.
25 A>B
26 B>C
23 C>A
26 C
B>C 51-49 C>A 71-29 A>B 48-26
Top Preferences: C45 > B26 > A25
Total Approval Chain Climbing also fails.
25 A>B
06 A>C
32 B>C
27 C>A
08 C
02 B
C>A>B>C, Approvals C73 > B59 > A58
TACC elects C, but if the 2B ballots are changed to 2C, then the
winner changes to A.
25 A>B
06 A>C
32 B>C
27 C>A
10 C
C>A>B>C, Approvals C75 > A58 > B57
In another post I'll discuss how some methods meet this criterion.
Chris Benham
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