# [EM] Mono-switch-plump criterion

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

```